MediaWiki API result
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{
"compare": {
"fromid": 1,
"fromrevid": 1,
"fromns": 0,
"fromtitle": "Il-Pa\u0121na prin\u010bipali",
"toid": 2,
"torevid": 2,
"tons": 0,
"totitle": "Matematika",
"*": "<tr><td colspan=\"2\" class=\"diff-lineno\" id=\"mw-diff-left-l1\">Linja 1:</td>\n<td colspan=\"2\" class=\"diff-lineno\">Linja 1:</td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>'''<del class=\"diffchange diffchange-inline\">MediaWiki \u0121ie installat b</del>'<del class=\"diffchange diffchange-inline\">su\u010b\u010bess.</del>'''</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-kelma </ins>'''<ins class=\"diffchange diffchange-inline\">Matematika''' \u0121ejja mill-[[lingwa Griega|Grieg]] \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1 (''m\u00e1thema''), li tfisser \"tg\u0127alim\", jew \"xjenza\"; \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2 (</ins>''<ins class=\"diffchange diffchange-inline\">mathematik\u00f3s</ins>''<ins class=\"diffchange diffchange-inline\">) tfisser \"wie\u0127ed li jrid jitg\u0127allem\".</ins></div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">Ikkonsulta l</del>-<del class=\"diffchange diffchange-inline\">[https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents Gwida g\u0127all</del>-<del class=\"diffchange diffchange-inline\">utenti] sabiex tikseb iktar informazzjoni </del>dwar <del class=\"diffchange diffchange-inline\">kif tu\u017ca' s</del>-<del class=\"diffchange diffchange-inline\">softwer </del>tal-<del class=\"diffchange diffchange-inline\">wiki</del>.</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Fid</ins>-<ins class=\"diffchange diffchange-inline\">dixxiplina tal</ins>-<ins class=\"diffchange diffchange-inline\">Matematika nistudjaw problemi </ins>dwar <ins class=\"diffchange diffchange-inline\">il</ins>-<ins class=\"diffchange diffchange-inline\">kwantit\u00e0, estensjoni u figuri spazjali, moviment </ins>tal-<ins class=\"diffchange diffchange-inline\">korpi, u l-istrutturi kollha fejn nistg\u0127u ne\u017caminaw dawn l-aspetti b'mod \u0121enerali</ins>.</div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>== <del class=\"diffchange diffchange-inline\">Biex tibda </del>==</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-'''Matematika''' g\u0127andha tradizzjoni qadima fil-\u0121nus kollha; kienet l-ewwel dixxiplina li adottat metodi rigoru\u017ci \u0127afna, u b'hekk la\u0127qet l-istatus ta\u2019 [[xjenza]]; progressivament il-metodi tag\u0127ha \u017cviluppaw u nfirxu ma \u0127afna oqsma fejn jistg\u0127u ikunu ta\u2019 g\u0127ajnuna fil-komputazzjoni u l-immudellar. </ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>* [<del class=\"diffchange diffchange-inline\">https</del>://<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Manual</del>:<del class=\"diffchange diffchange-inline\">Configuration_settings Lista </del>ta' <del class=\"diffchange diffchange-inline\">preferenzi </del>g\u0127all-<del class=\"diffchange diffchange-inline\">konfigurazzjoni</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>* [<del class=\"diffchange diffchange-inline\">https</del>://<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org/wiki/Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage/Manual</del>:<del class=\"diffchange diffchange-inline\">FAQ Mistoqsijiet rikorrenti </del>fuq il-<del class=\"diffchange diffchange-inline\">MediaWiki</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Storja ==</ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>* [<del class=\"diffchange diffchange-inline\">https</del>://<del class=\"diffchange diffchange-inline\">lists</del>.<del class=\"diffchange diffchange-inline\">wikimedia</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">postorius</del>/<del class=\"diffchange diffchange-inline\">lists</del>/<del class=\"diffchange diffchange-inline\">mediawiki</del>-<del class=\"diffchange diffchange-inline\">announce</del>.<del class=\"diffchange diffchange-inline\">lists</del>.<del class=\"diffchange diffchange-inline\">wikimedia</del>.<del class=\"diffchange diffchange-inline\">org/ </del>Il-<del class=\"diffchange diffchange-inline\">lista </del>tal-<del class=\"diffchange diffchange-inline\">posta t\u0127abbar </del>'l <del class=\"diffchange diffchange-inline\">MediaWiki</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{{artiklu prin\u010bipali|Kronolo\u0121ija tal-matematika}}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{{...|1}}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Analisi Matematika ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-<nowiki></nowiki>'''analisi matematika''' bdiet mill-formulazzjoni rigoru\u017ca tal-[[kalkulu infinite\u017cmali]]. Hija ferg\u0127a tal-[[matematika]] li tikkon\u010bentra fuq l-ideja tal-[[limitu (matematika)|limitu]]: il-[[limitu ta\u2019 su\u010b\u010bessjoni]] jew il-[[limitu ta\u2019 funzjoni]]. Tinkludi wkoll it-teoriji tad-[[Derivata|differenzazzjoni]], [[Integral|integrazzjoni]] u [[Me\u017cura (matematika)|me\u017cura]], [[Serje (matematika)|serji infiniti]], u [[funzjoni analitika|funzjonijiet analiti\u010bi]]. L-istudju ta\u2019 dawn it-teoriji \u0127afna drabi jsir fil-kuntest tan-[[numru reali|numri reali]], [[numru kompless|numri komplessi]], u\u00a0 [[funzjoni (matematika)|funzjonijiet]] reali u komplessi. Madankollu, nistg\u0127u niddefinixxu u nistudjaw dawn it-teoriji f\u2019kull [[spazju#Matematika u spazju|spazju]] ta\u2019 o\u0121\u0121etti matemati\u010bi li fih hu possibbli li nag\u0127tu definizzjoni ta\u2019 \"distanza\" ([[spazju metriku]]) jew\u00a0 i\u017cjed \u0121enerali ta\u2019 \"qrubija\" ([[spazju topolo\u0121iku]]).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== G\u0127aliex l-Analisi Astratta? ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Stampa:Hilbert.jpg|thumb|right|200px| David Hilbert t.1862 m.1943]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">G\u0127andna nistudjaw l-analisi matematika fil-kuntest i\u017cjed wiesa' ta\u2019 l-ispazji topologi\u010bi jew spazji metri\u010bi g\u0127al \u017cew\u0121 ra\u0121unijiet:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* l-ewwel, g\u0127ax l-istess metodi ba\u017ci\u010bi \u0127afna drabi japplikaw g\u0127al klassi ta\u2019 problemi li hi \u0127afna usa\u2019 (pere\u017cempju, l-istudju ta\u2019 [[Analisi Funzjonali|spazji ta\u2019 funzjonijiet]]).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* it-tieni, u mhux inqas importanti, g\u0127ax meta nifhmu l-analisi fi spazji aktar astratti\u00a0 sikwit nsibu li nistg\u0127u napplikawha direttament g\u0127al problemi klassi\u010bi. Pere\u017cempju, fl-[[Analisi armonika|analisi ta\u2019 Fourier]], nistg\u0127u nesprimu kull funzjoni b\u0127ala \u010berta serje infinita (ta\u2019 funzjonijiet trigonometri\u010bi\u00a0 jew esponenzjali komplessi). Fi\u017cikament, b\u2019din id-dekompo\u017cizzjoni nirridu\u010bu mew\u0121a (tal-\u0127oss) arbitrarja fil-frekwenzi li jikkomponuha. Il \"pi\u017cijiet\" jew koeffi\u010bjenti tat-termini fl-espansjoni ta\u2019 Fourier ta\u2019 funzjoni, jistg\u0127u jitqiesu b\u0127ala l-komponenti ta\u2019 vettur fi spazju ta\u2019 dimensjoni infinita li nsibuh b\u0127ala [[spazju ta\u2019 Hilbert]]. Mela l-istudju tal-funzjonijiet definiti f\u2019dil-qag\u0127da i\u017cjed \u0121enerali jipprovdi metodu konvenjenti g\u0127ad-derivazzjoni ta\u2019 ri\u017cultati fuq kif il-funzjonijiet ivarjaw fl-ispazju u mal-\u0127in, jew f\u2019termini aktar matemati\u010bi fuq l-[[ekwazzjoni differenzjali|ekwazzjonijiet differenzjali parzjali]], fejn din it-teknika nafuha b\u0127ala separazzjoni tal-[[varjabbli]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Storja tal-Analisi Matematika ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-[[matematikuGrieg|matemati\u010bi Griegi]] b\u0127al [[Ewdossu ta\u2019 Knidu|Ewdossu]] u [[Arkimede]] meta applikaw il-[[metodu ta\u2019 l-e\u017cawriment]] biex jikkalkulaw l-arja u l-volum ta\u2019 xi re\u0121juni u solidi u\u017caw il-kun\u010betti tal-limiti u l-konvergenza b\u2019mod informali. Fl-[[matematiku Indjan|Indja]], il-matematiku tas-[[seklu 12]], [[Bhaskara]] \u0121a kellu l-ideja tal-[[kalkulu differenzjali]] u ta e\u017cempji tad-[[derivata]], flimkien mal-propo\u017cizzjoni ta\u2019 dik li nsej\u0127ulu llum it-[[Teorema ta\u2019 Rolle]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Fis-[[seklu 14]], l-analisi matematika bdiha [[Madhava ta\u2019 Sangamagrama]],\u00a0 meqjus b\u0127ala\u00a0 l-\"[[fundatur ta\u2019l-analisi matematika]]\". Hu \u017cviluppa idejat fundamentali: l-i\u017cvilupp ta\u2019 funzjoni f\u2019[[serje infinita]], [[serje ta\u2019 potenzi]], is-[[serje ta\u2019 Taylor]], u l-approssimazzjoni razzjonali ta\u2019 serje infinita. \u017bviluppa wkoll is-serje ta\u2019 Taylor g\u0127all-[[funzjonijiet trigonometri\u010bi]] tas-[[senu]], [[kosenu]], [[tan\u0121enti]] u [[arktan\u0121enti]], u stima l-i\u017cbal li nag\u0127mlu meta naqtg\u0127u is-serje. \u017bviluppa l-[[frazzjonijiet kontinwati]] infiniti, l-[[Integral|integrazzjoni]] b\u2019termini wara termini, l-approssimazzjoni b\u2019serje ta\u2019 Taylor tas-senu u kosenu, u s-serje f\u2019potenzi tar-[[ra\u0121\u0121]], [[diametru]], [[\u010birkonferenza]], [[\u03c0]], \u03c0/4 u l-anglu [[\u03b8]]. Id-dixxipli tieg\u0127u fl-i[[Skola ta\u2019 Kerala]] baqg\u0127u ikkabru x-xog\u0127ol tieg\u0127u sas-[[seklu 16]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Stampa:Gottfried Wilhelm von Leibniz.jpg|thumb|right|200px|Gottfried Leibniz t.1646 m.1716]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Fl-Ewropa, fit-tieni nofs tas-[[seklu 17]], [[Isaac Newton|Newton]] u [[Gottfried Leibniz|Leibniz]] independement minn xulxien \u017cviluppaw il-kalkulu, li bl-istimulu ta\u2019 l-applikazzjonijiet matul is-[[seklu 18]] rabba \u0127afna frieg\u0127i b\u0127all-[[kalkulu tal-varjazzjonijiet]], l-[[ekwazzjonijiet differenzjali ordinarji]] u [[parzjali]] u l-[[analisi ta\u2019 Fourier]] . F\u2019dal-perijodu, il-metodi tal-kalkulu \u0121ew applikati biex japprossimaw [[problemi diskreti]] b\u2019o\u0127rajn kontinwi.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Fis-[[seklu18]], [[Leonard Euler|Euler]] introdu\u010ba il-kun\u010bett ta\u2019 [[Funzjonijiet (matematika)|funzjoni matematika]]. Fis-[[seklu19]], [[Augustin Louis Cauchy|Cauchy]] kien l-ewwel li stabbilixa l-kalkulu fuq pedament lo\u0121iku sod bl-introduzzjoni ta\u2019 l-ideja tas-[[su\u010b\u010bessjoni ta\u2019 Cauchy]]. Beda wkoll it-teorija formali ta\u2019 l-[[analisi komplessa]]. [[Simeon Poisson|Poisson]], [[Liouville]], [[Jean-Baptiste Joseph Fourier|Fourier]] u o\u0127rajn studjaw l-ekwazzjonijiet differenzjali parzjali u l-[[analisi armonika]]. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">F\u2019nofs is-seklu [[Bernhard Riemann|Riemann]] introdu\u010ba t-teorija tieg\u0127u tal-[[Integral|integrazzjoni]]. F\u2019l-a\u0127\u0127ar terz tas-seklu 19, [[Karl Weierstrass|Weierstrass]] li l-fehma tieg\u0127u kienet li l-argumenti \u0121ometri\u010bi jistg\u0127u iqarqu bina, da\u0127\u0127al l-aritmetizzazzjoni ta\u2019 l-analisi u introdu\u010ba id-definizzjoni \"epsilon-delta\" tal-[[limitu]]. Wara, il-matemati\u010bi bdew jinkwietaw li kienu qeg\u0127din jassumu l-e\u017cistenza tal-[[kontinwu]] tan-[[numri reali]] ming\u0127ajr prova. [[Dedekind]] imbag\u0127ad ta kostruzzjoni tan-numri reali bil-methodu tal-[[qtug\u0127 ta\u2019 Dedekind]], li bih il-matemati\u010bi jikkrejaw numri rrazzjonali li jimlew il-\"vojt\" bejn in-numri razzjonali, u hekk jo\u0127olqu sett [[komplet]]: il-kontinwu tan-numri reali. Madwar dak i\u017c-\u017cmien l-isforzi g\u0127ar-raffinar tat-[[teoremi]] ta\u2019 l-[[integrazzjoni ta\u2019 Riemann]] wasslu g\u0127all-istudju tal-\"qies\" tas-sett tad-[[diskontinwitajiet]] tal-funzjonijiet reali.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Fl-istess \u0127in, bdew jin\u0127olqu \"[[mostri]]\" (funzjonijiet [[mkien kontinwi]], funzjonijiet kontinwi imma mkien differenzjabbli, [[kurvi li jimlew l-ispazju]]). F\u2019dal-kuntest, [[Camille Jordan|Jordan]] \u017cviluppa t-teorija tieg\u0127u tal-[[me\u017cura]], [[Georg Cantor|Cantor]] \u017cviluppa dik li da\u017c-\u017cmien insej\u0127ulha it-[[teorija sempli\u010bi tas-settijiet]], u [[Baire]] ipprova it-[[teorema tal-kategoriji ta\u2019 Baire]]. Fil-bidu tas-[[seklu 20]], il-kalkulu \u0121ie formalizzat b\u2019l-u\u017cu tat-[[teorija assjomatika tas-settijiet]]. [[Henri Leon Lebesgue|Lebesgue]] irri\u017colva l-problema tal-mi\u017cura, u [[David Hilbert|Hilbert]] introdu\u010ba l-i[[spazji ta\u2019 Hilbert]] biex jirri\u017colvi l-[[ekwazzjonijiet integrali]]. L-ideja ta\u2019 l-i[[spazji vettorjali normati]] kienet infirxet, u f\u2019l-20ijiet tas-seklu [[Stefan Banach|Banach]] \u0127oloq l-[[analisi funzjonali]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>=== <ins class=\"diffchange diffchange-inline\">Oqsma ta' l-Analisi ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-Analsi Matematika\u00a0 tinkludi dawn l-oqsma: </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Analisi Reali]], l-istudju [[rigoru\u017c]] tad-[[Derivata|derivati]] u l-[[Integral|integrali]] ta\u2019 funzjonijiet b\u2019varjabbli reali. Dan jinkludi l-istudju tas-[[su\u010b\u010bessjonijiet]] u l-[[limiti]] tag\u0127hom, is-[[serji]], u l-[[me\u017curi]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Analisi komplessa|Analisi Komplessa]], l-istudju ta\u2019 funzjonijiet mill-[[pjan kompless]] g\u0127all-pjan kompless li huma komplessament differenzjabbli.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Analisi Funzjonali]], l-istudju ta\u2019 spazji ta\u2019 funzjonijiet b\u2019l-u\u017cu ta\u2019 kun\u010betti b\u0127al [[spazji ta\u2019 Banach]] u [[spazji ta\u2019 Hilbert]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Analisi armonika|Analisi Armonika]] l-istudju tas-[[Serje ta' Fourier|serji ta' Fourier]] u l-astrazzjonijiet tag\u0127hom..</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[\u0120ometrija Differenzjali u Topolo\u0121ija]], l-applicazzjoni tal-kalkulu g\u0127al spazji matemati\u010bi astratti li g\u0127andhom struttura interna komplikata.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Analisi Numerika]], l-istudju ta\u2019 l-algoritmi u\u017cati g\u0127all-approssimazzjoni ta\u2019 problemi tal-matematika kontinwa.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-kelma '''Analisi Klassika''' s-soltu tfisser analisi ming\u0127ajr l-u\u017cu tal-metodi tal-analisi funzjonali.\u00a0 L-istudju tal-[[Ekwazzjoni differenzjali|ekwazzjonijiet differenzjali]] issa\u00a0 huwa mferrex ma frieg\u0127i o\u0127ra b\u0127as-[[sistemi dinami\u010bi]], imma \u0121\u0127adu mportanti \u0127afna fl-analisi konvenzjonali.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">== Al\u0121ebra ==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-'''al\u0121ebra''' hi wa\u0127da mill-frieg\u0127i prin\u010bipali tal-[[matematika]] u titratta l-istudju ta\u2019 [[strutturi al\u0121ebrin]], [[relazzjonijiet]] u [[kwantit\u00e0]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-kelma al\u0121ebra (mill-G\u0127arbi \u0627\u0644\u062c\u0628\u0631, ''al-\u0121abr'' li tfisser \"\u0121abra\") \u0121ejja mill-isem tal-ktieb tal-matematiku [[Persjan]] [[G\u0127arbi]] [[Mu\u0127ammad ibn Musa al-Khwari\u017cmi]], intitolat ''Al-Kitab al-\u0120abr wa-l-Muqabala'' (\"Il-Ktieb tal-\u0120abra u t-Tqabbil\"), li jittratta ir-ri\u017coluzzjoni tal-[[ekwazzjonijiet linjari]] u [[kwadrati\u010bi]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-[[al\u0121ebra elementari]] li normalment tifforma parti mill-kurrikulu ta\u2019 l-iskejjel sekondarji, tintrodu\u010bi l-ideja ta\u2019 [[simboli]] jew [[varjabbli]] li jirrepre\u017centaw kwantitajiet mhux mag\u0127rufa. Nitg\u0127almu wkoll kif ng\u0127oddu u nimmoltiplikaw dawn il varjabbli, fuq il-polinomji mibnija minnhom u l-fattorizzazzjoni u l-kalkulazzjoni tar-[[radi\u010bi]]. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Per\u00f2, l-al\u0121ebra hi \u0127afn\u2019 usa\u2019 minn hekk. L-g\u0127add u l-moltiplikazzjoni nistg\u0127u nqisuhom b\u0127ala [[operazzjoniet]] \u0121enerali\u00a0 u d-definizzjoni e\u017catta tag\u0127hom twassalna g\u0127al strutturi \u0121odda b\u0127al [[gruppi]], [[\u010brieki]] u [[kampi]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Klassifikazzjoni ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{{...|7}}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== L-Al\u0121ebra Elementari ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-'''Al\u0121ebra elementari''' hija l-forma l-i\u017cjed ba\u017cika ta\u2019 l-al\u0121ebra. Jitg\u0127almuha l-istudenti li m\u2019g\u0127andhomx tg\u0127alim tal-mathematika i\u017cjed avvanzat mill-prin\u010bipji ba\u017ci\u010bi ta\u2019 l-aritmetika. Fl-aritmetika, nsibu biss in-numri u l-operazzjonijiet aritmeti\u010bi fuqhom (b\u0127al +, \u2212, \u00d7, \u00f7). Fl-al\u0121ebra, in-numri spiss nirripre\u017centawhom bis-simboli (b\u0127al ''a'', ''x'', ''y''). Din ir-repre\u017centazzjoni g\u0127andha dawn il-vanta\u0121\u0121i:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Biha nistg\u0127u nag\u0127tu formulazzjoni \u0121enerali tar-regoli aritmeti\u010bi (pere\u017cempju ''a'' + ''b'' = ''b'' + ''a'' g\u0127al kull ''a'' u ''b''), u hekk nistg\u0127u nag\u0127mlu l-ewwel pass fl-esplorazzjoni sistematika tal-propjetajiet tas-sistema tan-numri reali.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Biha nistg\u0127u nirreferu g\u0127an-numri \"mhux mag\u0127rufin\", nifformulaw ekwazzjonijiet u nistudjaw kif nirri\u017colvuhom (pere\u017cempju, \"Sib numru ''x'' sabiex 3''x'' + 1 = 10\").</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Biha nistg\u0127u nag\u0127mlu formulazzjoni ta\u2019 relazzjonijiet funzjonali\u00a0 (b\u0127al \"Jekk tbig\u0127 ''x'' biljetti, jkollok qlig\u0127\u00a0 ta\u2019 3''x'' - 10 ewri, jew ''f''(''x'') = 3''x'' - 10, fejn ''f'' hija l-funzjoni u ''x'' huwa n-numru li ta\u0121ixxi fuqu l-funzjoni .\").</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== X'inhi l-Al\u0121ebra Astratta ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-'''al\u0121ebra astratta\u2019'' testendi il-kun\u010betti li nsibu fl-al\u0121ebra elementari g\u0127al o\u0127rajn i\u017cjed \u0121enerali.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''[[Settijiet]]''': Minnflok\u00a0 nikkunsidraw biss it-tipi ta\u2019 [[numri]] differenti, fl-al\u0121ebra astratta nqisu il-kun\u010bett i\u017cjed \u0121enerali ta\u2019 ''sett'' li hu \u0121abra ta\u2019 o\u0121\u0121etti (li jg\u0127idulhom [[elementi]]) li g\u0127andhom \u010berta propjet\u00e0 spe\u010bifika g\u0127as-sett. Pere\u017cempju in-numri reali jiffurmaw sett u n-numri komplessi sett ie\u0127or. E\u017cempji o\u0127ra ta\u2019 settijiet jinkludu is-sett tal-[[matri\u010bi]] ta\u2019 tnejn-bi-tnejn, is-sett tal-[[polinomji]] tat-tieni ordni (''ax''<sup>2</sup> + ''bx'' + ''c''), is-sett tal-[[vetturi]] bi-dimensjonali, u [[gruppi finiti]] varji b\u0127all-[[gruppi \u010bikli\u010bi]], ji\u0121ifieri l-gruppi tan-numri interi [[modulo]] ''n''. It-[[Teorija tas-settijiet]] hija ferg\u0127a tal-[[lo\u0121ika]] u teknikament mhux ferg\u0127a ta\u2019 l-al\u0121ebra.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''[[Operazzjonijiet binarji]]''': L-ideja ta\u2019 l-[[g\u0127add]] (+) nistg\u0127u nag\u0127mluha i\u017cjed astratta biex ittina ''operazzjoni binarja'', * ng\u0127idu a\u0127na. Il-kun\u010bett ta\u2019 operazzjoni binarja ma jfisser xejn jekk ma nag\u0127tux is-sett li fuqu qed niddefinixxu l-operazzjoni. G\u0127al \u017cew\u0121 elementi ''a'' u ''b'' f\u2019sett ''S'' ''a''*''b'' ittina element ie\u0127or fis-sett, (dil-kundizzjoni ng\u0127idulha [[g\u0127eluq]] ta\u0127t l-operazzjoni). L-[[G\u0127ad]] (+), it-[[Tnaqqis]] (-), il-[[moltiplikazzjoni]] (\u00d7), u d-[[matematika divi\u017cjoni|divi\u017cjoni]] (\u00f7) huma operazzjonijiet binarji meta niddefinuhom fuq settijiet addattati, kif ukoll l-g\u0127add u l-moltiplikazzjoni tal-matri\u010bi, vetturi u polinomji.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''[[Elementi ta\u2019 l-identit\u00e0]]''': Il-kun\u010bett ta\u2019 l-\u201celement ta\u2019 l-identit\u00e0\u201d huwa l-astrazzjoni tan-numri \u017cero u wie\u0127ed. \u017bero huwa l-element ta\u2019 l-identit\u00e0 g\u0127all-g\u0127add and u wie\u0127ed l-element ta\u2019 l-identit\u00e0 g\u0127all-moltiplikazzjoni. G\u0127al operazzjoni binarja \u0121enerali * l-element ta\u2019 l-identit\u00e0 ''e'' irid jissodisfa ''a'' * ''e'' = ''a'' u ''e'' * ''a'' = ''a''. G\u0127all-g\u0127add din hi sodisfatta billi ''a'' + 0 = ''a'' u 0 + ''a'' = ''a'' u g\u0127all-moltiplikazzjini wkoll g\u0127ax ''a'' \u00d7 1 = ''a'' u 1 \u00d7 ''a'' = ''a''. Imma, jekk nie\u0127du in-numri naturali po\u017citivi u l-operazzjoni ta\u2019 l-g\u0127add, m\u2019hemmx element ta\u2019 l-identit\u00e0.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''[[Elementi inversi]]''': Minn-numri negattivi no\u0127olqu l-kun\u010bett ta\u2019 ''element invers'' jew sempli\u010biment l-''invers''. G\u0127all-g\u0127add, l-invers ta\u2019 ''a'' huwa ''-a'', u g\u0127all-moltiplikazzjoni l-invers hu 1/''a''. L-element invers \u0121enerali ''a''<sup>-1</sup> jrid jissodifa r-relazzjoni ''a'' * ''a''<sup>-1</sup> = ''e'' u ''a''<sup>-1</sup> * ''a'' = ''e''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''[[Asso\u010bjattivit\u00e0]]''': L-g\u0127add tan-numri interi g\u0127andu propjet\u00e0 li nsej\u0127ulha asso\u010bjattivit\u00e0. Ji\u0121ifieri, l-kumbinazzjoni tan-numri li nkunu qed nog\u0127du ma tbiddilx is-somma tag\u0127hom. Pere\u017cempju: (2+3)+4=2+(3+4). Fil-kuntest generali, din issir (''a'' * ''b'') * ''c'' </ins>= <ins class=\"diffchange diffchange-inline\">''a'' * (''b'' * ''c''). Il-bi\u010b\u010ba kbira ta\u2019 l-operazzjonijiet binarji g\u0127andhom din il-propjet\u00e0 imma t-tnaqqis u d-divi\u017cjoni le. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''[[Kommutattivit\u00e0]]''': L-g\u0127add tan-numri interi g\u0127andu wkoll propjet\u00e0 o\u0127ra li ng\u0127idulha kommutattivit\u00e0. Ji\u0121ifieri, l-ordni tan-numri li nkunu qed nog\u0127du ma tbiddilx is-somma tag\u0127hom. Pere\u017cempju: 2+3=3+2. Fil-kuntest generali, din issir ''a'' </ins>* <ins class=\"diffchange diffchange-inline\">''b'' = ''b'' * ''a''. Mhux l-operazzjonijiet binarji kollha g\u0127andhom din il-propjet\u00e0. L-g\u0127add u l-moltiplikazzjoni tan-numri interi g\u0127andhom din il-propjet\u00e0 imma l-</ins>[<ins class=\"diffchange diffchange-inline\">[moltiplikazzjoni tal-matri\u010bi]] le.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==== Gruppi\u2014strutturi ta\u2019 sett b\u2019operazzjoni binarja wa\u0127da ====</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Meta ni\u0121bru flimkien il-kun\u010betti li rajna qabel, ikollna wa\u0127da mill-i\u017cjed strutturi mportanti fil-matematika: il- '''[[Grupp (Matematika)|grupp]]'''. Grupp jikkonsisti f\u2019sett ''S'' u [[operazzjoni wa\u0127da]] li rridu, li niktbuha '*', imma li jrid ikolla dawn il-propjetajiet:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Irid ikun hemm element ta\u2019 l-identit\u00e0 ''e'', li g\u0127al kull membru ie\u0127or ''a'' ta\u2019 ''S'', ''e'' * ''a'' u ''a'' * ''e'' huma t-tnejn ugwali g\u0127al\u00a0 ''a''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Kull element irid ikollu invers</ins>: <ins class=\"diffchange diffchange-inline\">g\u0127al kull membru ie\u0127or ''a'' ta\u2019 ''S'', irid je\u017cisti\u00a0 membru ''a''<sup>-1<</ins>/<ins class=\"diffchange diffchange-inline\">sup> sabiex ''a'' * ''a''<sup>-1</sup> u ''a''<sup>-1</sup> * ''a'' huma t-tnejn ugwali g\u0127all-element ta\u2019 l-identit\u00e0.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* L-operazzjoni hi asso\u010bjattiva: g\u0127al ''a'', ''b'' u ''c'' membri ta\u2019 ''S'', (''a'' * ''b'') * ''c'' hija ugwali g\u0127al ''a'' * (''b'' * ''c'').</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Jekk grupp hu anki [[kommutattiv]] - ji\u0121ifieri, g\u0127al kull \u017cewg membri ''a'' u ''b'' ta\u2019 ''S'', ''a'' * ''b'' hija ugwali g\u0127al ''b'' * ''a'' \u2013 il-grupp ng\u0127idu li hu [[Abeljan]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Pere\u017cempju, is-sett tan-numri interi bl-operazzjoni ta\u2019 l-g\u0127add huwa grupp. F\u2019dal grupp, l-identit\u00e0 hija 0 u l-invers ta\u2019 kull element ''a'' huwa n-negativ tieg\u0127u, -''a''. Il-kundizzjoni ta\u2019 asso\u010bjattivit\u00e0 hi sodisfatta, g\u0127ax g\u0127al kull tliet numri interi\u00a0 ''a'', ''b'' u ''c'', (''a'' + ''b'') + ''c'' = ''a'' + (''b'' + ''c'').</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Imma l-interi bl-operazzjoni tal-moltiplikazzjoni ma jiffurmawx grupp. Dan ji\u0121ri g\u0127ax, in \u0121enerali, l-invers moltiplikattiv ta\u2019 numru interu mhuwiex interu. Pere\u017cempju, 4 huwa interu, imma\u00a0 l-invers moltiplikattiv tieg\u0127u hu 1</ins>/<ins class=\"diffchange diffchange-inline\">4, li mhux interu.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-istudju tal-gruppi jsir fit-[[teorija tal-gruppi]]</ins>. <ins class=\"diffchange diffchange-inline\">Wie\u0127ed mir-ri\u017cultati l-i\u017cjed importanti f\u2019din it-teorija kien il-[[klassifikazzjoni tal-gruppi finiti sempli\u010bi]] li l-ikbar parti tag\u0127ha \u0121iet ippublikata bejn xi l-1955 u l-1983</ins>. <ins class=\"diffchange diffchange-inline\">Din tqassam il-[[gruppi sempli\u010bi]] [[finiti]] f\u2019xi 30 tip ba\u017ciku.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{| class=\"toccolours\" border=\"1\" cellpadding=\"4\" cellspacing=\"0\" style=\"border-collapse: collapse; margin:0 ;\" </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| colspan=11|'''E\u017cempji'''\u00a0 (MA = Mhux Applikabbli, b\u017c = bla \u017cero)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">!Sett:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">! colspan=2|[[Numri naturali]] <math>\\mathbb{N}<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">! colspan=2|[[Numri interi]] <math>\\mathbb{Z}<</ins>/<ins class=\"diffchange diffchange-inline\">math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">! colspan=4|[[Numri razzjonali]] <math>\\mathbb{Q}</math>, [[Numri reali]] <math>\\mathbb{R}</math> u [[Numri komplessi]] <math>\\mathbb{C}</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">! colspan=2|Interi mod 3</ins>: <ins class=\"diffchange diffchange-inline\">{0,1,2}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">!Operazzjoni</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| + </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| \u00d7 (b\u017c)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| +</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| \u00d7 (b\u017c)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| +</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| \u2212</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| \u00d7 (b\u017c)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| \u00f7 (b\u017c)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| +</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| \u00d7 (b\u017c)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|Mag\u0127luq</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Identit\u00e0</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 0</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 1</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 0</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 1</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 0</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| MA</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 1</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| MA</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 0</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 1</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Invers</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| MA</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| MA</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| -a</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| MA</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| -a</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| a</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| <math>\\begin{matrix} \\frac{1}{a} \\end{matrix}</math></ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| a</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| 0,2,1, respettivament</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| MA, 1, 2, respettivament</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Asso\u010bjattiv</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Le</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Le</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Kommutativ</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Le</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Le</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Iva</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|-</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| Struttura</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| [[monoid]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| [[monoid]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| grupp Abeljan </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| [[monoid]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| grupp Abeljan</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| [[kwa\u017cigrupp]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| grupp Abeljan</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| [[kwa\u017cigrupp]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| grupp Abeljan</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">| grupp Abeljan (<math>\\mathbb{Z}_2</math>)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">|}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Semigruppi]], [[kwa\u017cigruppi]], u [[monoidi]] huma strutturi simili g\u0127all-gruppi, imma i\u017cjed \u0121enerali. Jikkonsistu f\u2019sett u operazzjoni binarja mag\u0127luqa, imma ma jissodisfawx il-kondizzjonijiet l-o\u0127ra ne\u010bessarjament. [[Semigrupp]] g\u0127andu operazzjoni binarja ''asso\u010bjattiva'', imma jista\u2019 jkun li m\u2019g\u0127andux element ta\u2019 l-identit\u00e0. [[Monoid]] huwa semigrupp li g\u0127andu identit\u00e0 imma jista\u2019 jkun li m\u2019g\u0127andux invers g\u0127al kull element. [[Kwa\u017cigrupp]] g\u0127andu l-propjet\u00e0 li kull element jista\u2019 jinbidel f\u2019kull ie\u0127or bi pre- jew post-operazzjoni unika; imma l-operazzjoni binarja jista\u2019 jkun li mhux asso\u010bjattiva.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-gruppi kollha huma monoidi, u l-monoidi kollha huma semigruppi.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==== \u010arieki u Kampi\u2014strutturi ta\u2019 sett b\u2019\u017cew\u0121 operazzjonijiet binarji, (+) u (\u00d7) ====</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-gruppi g\u0127andhom operazzjoni binarja wa\u0127da biss. Biex nispjegaw il-mekkani\u017cmu tat-tipi ta\u2019 numri differenti kompletament, hemm b\u017conn li nistudjaw strutturi b\u2019\u017cew\u0121 operazzjonijiet. L-i\u017cjed importanti fost dawn huma \u010b-[[\u010arieki]], u l-[[Kampi]]. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Id-'''[[Distributtivit\u00e0]]''' ti\u0121\u0121eneralizza l-''li\u0121i distributtiva'' tan-numri u tiffissa\u00a0 f\u2019liema ordni g\u0127andna napplikaw l-operazzjonijiet, (ng\u0127idulha l-[[pre\u010bedenza]]). G\u0127all-interi (''a'' + ''b'') \u00d7 c = ''a''\u00d7''c''+ ''b''\u00d7''c'' u ''c'' \u00d7 (''a'' + ''b'') = ''c''\u00d7''a'' + ''c''\u00d7''b'', u ng\u0127idu li \u00d7 hija '' distributtiva '' fuq +.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''[[\u010airku]]''' g\u0127andu \u017cew\u0121 operazzjonijiet\u00a0 (+) u (\u00d7), fejn \u00d7 hu distributtiv fuq +. Ta\u0127t l-ewwel operazzjoni (+) jifforma ''grupp Abeljan''. Ta\u0127t it-tieni operazzjoni (\u00d7) hu asso\u010bjattiv, imma m\u2019hemmx b\u017conn ta' identit\u00e0 jew ta' invers, u allura ma nistg\u0127ux niddividu. L-element ta\u2019 l-identit\u00e0 ta\u2019 l-g\u0127add (+) niktbuha b\u0127ala 0 u l-inverse ta\u2019 l-g\u0127add ta\u2019 ''a'' jinkiteb -''a''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">In-numri interi huma e\u017cempju ta\u2019 \u010birku. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">'''[[Kamp]]''' hu ''\u010birku'' b\u2019propjet\u00e0 o\u0127ra mi\u017cjuda li l-elementi kollha barra 0 jiffurmaw\u00a0 ''grupp Abeljan'' ta\u0127t \u00d7. L-identit\u00e0 moltiplikattiva (\u00d7) niktbuha b\u0127ala 1 u l-invers moltiplikattiv ta\u2019 ''a'' jinkiteb ''a''<sup>-1<</ins>/<ins class=\"diffchange diffchange-inline\">sup>.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">In-numri razzjonali, in-numri reali u n-numri komplessi huma kollha e\u017cempji ta\u2019 kampi.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Al\u0121ebriet ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-kelma '''''al\u0121ebra''''' nu\u017cawha wkoll g\u0127al xi [[strutturi al\u0121ebrin]]</ins>:</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Al\u0121ebra fuq kamp]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Al\u0121ebra fuq sett]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Al\u0121ebra Boolejana]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[F-al\u0121ebra]] u [[F-koal\u0121ebra]] fit-[[teorija tal-kategoriji]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [[Sigma-al\u0121ebra]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=== Storja </ins>ta' <ins class=\"diffchange diffchange-inline\">l-al\u0121ebra ===</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-al\u0121ebra nistg\u0127u nsibu l-ori\u0121ini tag\u0127ha fil-[[Babilonja]] antika. Il-Babilonjani \u017cviluppaw\u00a0 [[sistema aritmetiku]] avvanzat li bih setg\u0127u jag\u0127mlu kalkulazzjonijiet b\u2019metodu al\u0121ebri. Permezz ta\u2019 dan is-sistema, setg\u0127u japplikaw formoli u jikkalkulaw valuri mhux mag\u0127rufa g\u0127al klassi ta\u2019 problemi li da\u017c-\u017cmien nirri\u017colvuhom bl-u\u017cu ta\u2019 [[ekwazzjonijiet linjari]], [[ekwazzjonijiet kwadrati\u010bi]] u [[ekwazzjonijiet linjari indeterminati]]. G\u0127all-kontrarju, il-bi\u010b\u010ba kbira tal-matemati\u010bi [[E\u0121izzjani]] ta\u2019 dak i\u017c-\u017cmien, u l-bi\u010b\u010ba kbira tal-matemati\u010bi [[Indjani]], [[Griegi]] u [[\u010aini\u017ci]] f\u2019l-[[ewwel millennju QK]], is-soltu kienu jirri\u017colvu dawn il-problemi b\u2019metodi [[\u0121ometri\u010bi]], b\u0127al dawk imfissra\u00a0 fil-''[[Papiru Matematiku ta\u2019 Rhind]]'', ''[[Sulba Sutras]]'', ''[[L-Elementi ta\u2019 Ewklidi]]'', u ''[[Id-Disg\u0127a Kapitli fuq\u2019 l-Arti Matematika]]''.\u00a0 Ix-xog\u0127ol \u0121ometriku tal-Griegi, li l-Elementi huwa e\u017cempju tajjeb \u0127afna tieg\u0127u, ipprovda s-sisien </ins>g\u0127all-<ins class=\"diffchange diffchange-inline\">\u0121eneralizzazzjoni tal-formuli mis-soluzzjoni ta\u2019 problemi partikulari g\u0127al sistemi i\u017cjed \u0121enerali li jistg\u0127u jintu\u017caw g\u0127all-formulazzjoni u s-soluzzjoni tal-ekwazzjonijiet.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Stampa:Image-Al-Kit\u0101b al-mu\u1e2bta\u1e63ar f\u012b \u1e25is\u0101b al-\u011fabr wa-l-muq\u0101bala.jpg|thumb|right|200px|L-ewwel pa\u0121na tal-ktieb ta' al-Khwari\u017cmi]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Il-kelma \"''al\u0121ebra''\" \u0121ejja mill-G\u0127arbi \"''al-\u0121abr''\" fit-titlu tal-ktieb\u00a0 \"''al-Kitab al-muhtasar fi \u0127isab al-\u0121abr wa-l-muqabala''\", li jfisser ''Il-ktieb fil-qosor fi \u0127sib il-\u0121bir u tqassim''. Dan kitbu il-matematiku Persjan\u00a0 [[Mu\u0127ammad ibn Musa al-Khwari\u017cmi]] (G\u0127arbi: \u0645\u062d\u0645\u062f \u0628\u0646 \u0645\u0648\u0633\u0649 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0651 \u0627\u0644\u0645\u062c\u0648\u0633\u064a\u0651 \u0627\u0644\u0642\u0637\u0631\u0628\u0651\u0644\u064a\u0651) fit-820. Il-matematiku Grieg [[Diofantu]] (Grieg: \u0394\u03b9\u03cc\u03c6\u03b1\u03bd\u03c4\u03bf\u03c2 \u1f41 \u1f08\u03bb\u03b5\u03be\u03b1\u03bd\u03b4\u03c1\u03b5\u03cd\u03c2 t. bejn [[200]] u [[214]], m. bejn [[284]] u [[298]] AD) hu tradizzjonalment mag\u0127ruf b\u0127ala \u201cmissier l-al\u0121ebra\u201d imma hemm argument jekk Al-Khwari\u017cmi g\u0127andux jo\u0127odlu dan it-titlu. Dawk li j\u017commu ma Al-Khwari\u017cmi jsossnu li \u0127afna mix-xog\u0127ol tieg\u0127u fuq \u201cil-\u0121bir\u201d jew riduzzjoni g\u0127adu u\u017cat sa llum u li hu ta spjegazzjoni kompleta fuq is-soluzzjoni ta\u2019 l-ekwazzjonijiet kwadrati\u010bi. Dawk li j\u017commu ma [[Diofantu]] jg\u0127idu li l-al\u0121ebra li nsibu f\u2019''Al-\u0120abr'' hi i\u017cjed elementari mill-al\u0121ebra fl- ''Aritmetika'' ta\u2019 Diofantu u li l-''Aritmetika'' hi miktuba fi stil sinkopat waqt li ''Al-\u0120abr'' hi kollha fi stil retoriku. Matematiku Persjan ie\u0127or, [[Omar Khajjam]] (Persjan: \u063a\u06cc\u0627\u062b \u0627\u0644\u062f\u06cc\u0646 \u0627\u0628\u0648 \u0627\u0644\u0641\u062a\u062d \u0639\u0645\u0631 \u0628\u0646 \u0627\u0628\u0631\u0627\u0647\u06cc\u0645 \u062e\u06cc\u0627\u0645 \u0646\u06cc\u0634\u0627\u0628\u0648\u0631\u06cc t. 18 ta\u2019 Mejju, 1048, m. 4 ta\u2019 Di\u010bembru, 1131), \u017cviluppa l-[[\u0121ometrija al\u0121ebrija]] u sab soluzzjoni \u0121enerali \u0121ometrika ta\u2019 l-[[ekwazzjonijiet kubi\u010bi]]. Il-matemati\u010bi Indjani [[Ma\u0127avira]] u [[Baskara II]], u l-matematiku \u010aini\u017c [[\u017bu Xi\u0121je]], irri\u017colvew xi ka\u017ci ta\u2019 ekwazzjonijiet kubi\u010bi, [[kwarti\u010bi]], [[kwinti\u010bi]] u [[polinomjali]] ta\u2019 ordni og\u0127la.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">F\u2019nofs is-seklu 16 kien hemm \u017cvilupp importanti ie\u0127or ta' l-al\u0121ebra. Dan kien is-soluzzjoni al\u0121ebrija \u0121enerali tal-ekwazzjonijiet kubi\u010bi u kwarti\u010bi. L-ideja ta\u2019 [[determinant]] \u017cviluppha l-matematiku \u0120appuni\u017c [[Kowa Seki]] fis-seklu 17, u g\u0127axar snin wara [[Gottfried Leibniz]] u\u017ca d-determinanti biex jirri\u017colvi sistemi ta\u2019 ekwazzjonijiet linjari simultanji premezz tal-[[matri\u010bi]]. Fis-seklu 18, [[Gabriel Cramer]] ukoll \u0127adem fuq il-matri\u010bi u d-determinanti. L-i\u017cvilupp ta\u2019 l-[[Al\u0121ebra astratta]] sar fis-seklu 19. Fil-bidu dan ix-xog\u0127ol ikkon\u010bentra fuq li da\u017c-\u017cmien insej\u0127ulha it-[[teorija ta\u2019 Galois]] u fuq kwistjonijiet tal-[[kostruttibbilt\u00e0]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">L-istadji ta\u2019 l-i\u017cvilupp ta\u2019 l-al\u0121ebra simbolika kienu bejn wie\u0127ed u ie\u0127or dawn:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Al\u0121ebra retorika, li \u017cviluppawha l-Babilonjani u baqet dominanti sas-seklu 16;</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Al\u0121ebra \u0121ometrika kostruttiva, li tawha \u0127afna mportanza il-matemati\u010bi Indjani u l-matemati\u010bi klassi\u010bi Griegi;</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Al\u0121ebra sinkopata, li kienet \u017cviluppata minn [[Diofantu]</ins>] <ins class=\"diffchange diffchange-inline\">u fil-''[[Manuskritt Bakxali]]''; </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>* <ins class=\"diffchange diffchange-inline\">Al\u0121ebra simbolika, li la\u0127qet il-qu\u010b\u010bata fix-xog\u0127ol ta\u2019 </ins>[<ins class=\"diffchange diffchange-inline\">[Leibniz]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Kronolo\u0121ija ta\u2019 \u017cviluppi kriti\u010bi fl-al\u0121ebra:</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 1800 QK: Fit-[[tavletta ta\u2019 Strassburg]] il-Babilonjani jfittxu s-soluzzjoni ta\u2019 ekwazzjoni ellittika kwadratika.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 1600 QK</ins>: <ins class=\"diffchange diffchange-inline\">It-tavletta ta\u2019 ''[[Plimpton 322]]'' tag\u0127ti tavola ta\u2019 [[trippli Pitagori\u010bi]] fi skritt [[Kuneiformi]] Babilonjan</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 800 QK: Il-matematiku Indjan [[Bawdajana]], fix-xog\u0127ol tieg\u0127u ''[[Sulba Sutra]]'', jiskopri\u00a0 trippli Pitagori\u010bi b\u2019metodi al\u0121ebrin, jsib soluzzjonijiet \u0121ometri\u010bi ta\u2019 ekwazzjonijiet linjari u ekwazzjonijiet kwadrati\u010bi tal-forma ax<sup>2<</ins>/<ins class=\"diffchange diffchange-inline\">sup> = c u ax<sup>2<</ins>/<ins class=\"diffchange diffchange-inline\">sup> + bx = c, u jsib \u017cew\u0121 settijiet ta\u2019 soluzzjonijiet integrali po\u017cittivi g\u0127al sett ta\u2019 ekwazzjonijiet simultanji Diofantini</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 600 QK: Il-matematiku Indjan [[Apastamba]], fix-xog\u0127ol tieg\u0127u ''Apastamba Sulba Sutra'', jirri\u017colvi l-ekwazzjoni linjari \u0121enerali u ju\u017ca ekwazzjonijiet simultanji Diofantini b\u2019sa \u0127ames kwantitajiet mhux mag\u0127rufa</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 300 QK: Fit-tieni ktieb ta\u2019 l-Elementi, [[Ewklide|Ewklidi]] jag\u0127ti kostruzzjoni \u0121ometrika b\u2019metodi Ewklidej g\u0127as-soluzzjoni ta\u2019 l-ekwazzjoni kwadratika g\u0127al radi\u010bi posittivi reali.\u00a0 Il-kostruzzjoni hi dovuta g\u0127all-iSkola Pitagorika tal-\u0121ometrija.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 300 QK</ins>: <ins class=\"diffchange diffchange-inline\">Titfittex kostruzzjoni \u0121ometrika g\u0127as-soluzzjoni ta\u2019 l-ekwazzjoni kubika.\u00a0 Issa nafu li bil-metodi Ewklidej ma nistg\u0127ux insibu soluzzjoni g\u0127all-ekwazzjoni kubika \u0121enerali.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 100 QK</ins>: <ins class=\"diffchange diffchange-inline\">Il-ktieb tal-matematika \u010aini\u017c ''[[\u0120ju\u017cang Suwanxu]]'' (''Id-Disg\u0127a Kapitli </ins>fuq <ins class=\"diffchange diffchange-inline\">l-Arti Matematika''), jittratta Ekwazzjonijiet al\u0121ebrin. Dal-ktieb fih soluzzjonijiet ta\u2019 ekwazzjonijiet linjari bl-u\u017cu tar-[[regola tal-po\u017cizzjoni falza doppja]], soluzzjonijiet gometri\u010bi ta\u2019 ekwazzjonijiet kwadrati\u010bi, u soluzzjonijiet ta\u2019 matri\u010bi, ekwivalenti g\u0127all-metodi moderni, g\u0127as-soluzzjoni tas-sistemi ta\u2019 ekwazzjonijiet linjari simultanji.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 100 QK: Il-''[[Manuskritt ta\u2019 Bakxali]]'', miktub fl-Indja, ju\u017ca forma ta\u2019 notazzjoni al\u0121ebrija bl-ittri u sinjali o\u0127ra, u fih ekwazzjonijiet kubi\u010bi u kwarti\u010bi, soluzzjonijiet al\u0121ebrin ta\u2019 [[ekwazzjonijiet linjari]] b\u2019sa \u0127ames kwantitajiet mhux mag\u0127rufa, </ins>il-<ins class=\"diffchange diffchange-inline\">formula al\u0121ebrija \u0121enerali g\u0127all-ekwazzjoni kwadrati\u010bi, u soluzzjonijiet ta\u2019 ekwazzjonijiet kwadrati\u010bi indeterminati u ekwazzjonijiet simultanji.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Stampa:Diophantus-cover.jpg|thumb|right|200px| Pa\u0121na titulari ta\u2019 l-edizzjoni ta\u2019 1621 ta\u2019 l-''Arithmetica'' ta\u2019 Diofantu, maqluba g\u0127all-Latin minn de M\u00e9ziriac]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 150 AD: Il-matematiku E\u0121izzjan Ellenistiku [[Eroni ta\u2019 Lixandra]</ins>]<ins class=\"diffchange diffchange-inline\">, jittratta l-ekwazzjonijiet al\u0121ebrin fi tliet volumi tal-matematika.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>* <ins class=\"diffchange diffchange-inline\">\u010airka 200: Il-matematiku Babilonjan Ellenistiku, [</ins>[<ins class=\"diffchange diffchange-inline\">Diofantu]] li g\u0127ex fl-E\u0121ittu u li \u0127afna jikkunsidrawh b\u0127ala \"missier l-al\u0121ebra\", jikteb l-opra famu\u017ca tieg\u0127u, l-''Aritmetika'', li fiha soluzzjonijiet ta\u2019 ekwazzjonijiet al\u0121ebrin u xog\u0127ol fuq it-teorija tan-numri.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 499</ins>: <ins class=\"diffchange diffchange-inline\">Il-matematiku Indjan [[Arjabata]], fit-trattat tieg\u0127u ''Arjabatija'', jsib soluzzjonijiet interi g\u0127al xi ekwazzjonijiet linjari b\u2019metodu ekwivalenti g\u0127al dak li nu\u017caw illum, jiddeskrivi s-soluzzjoni integrali \u0121enerali ta\u2019 l-ekwazzjoni linjari indeterminata u jag\u0127ti soluzzjonijiet integrali ta\u2019 xi ekwazzjonijiet linjari simultanji indeterminati.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 625: Il-matematiku \u010aini\u017c, Wang [[Ksijaotong]],\u00a0 jsib soluzzjonijiet numeri\u010bi ta\u2019 ekwazzjonijiet kubi\u010bi.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 628: Il-matematiku Indjan, [[Brahmagupta]], fit-trattat tieg\u0127u ''Brahma Sputa Siddhanta'', jivvinta l-metodu ''\u010bakravala'' g\u0127as-soluzzjoni ta\u2019 xi ekwazzjonijiet kwadrati\u010bi simultanji indeterminati, fosthom l-ekwazzjoni ta\u2019 Pell, u jag\u0127ti regoli g\u0127as-soluzzjoni ta\u2019 l-ekwazzjonijiet linjari u kwadrati\u010bi.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 820: Il-matematiku Persjan, Muhammad ibn Musa [[al-Khwari\u017cmi]], jikteb it-trattat intitolat ''Al-Kitab al-\u0120abr wa-l-Muqabala'' (li tfisser \"Il-Ktieb tal-\u0121bir u t-tqabbil\") fuq is-soluzzjoni sistematika ta\u2019 l-ekwazzjonijiet linjari u kwadrati\u010bi. Il-kelma ''al\u0121ebra'' \u0121ejja minn ''al-\u0120abr'' fit-titlu ta\u2019 dal-ktieb. Al-Khwari\u017cmi hu kkunsidrat minn bosta b\u0127ala \"missier l-al\u0121ebra\" u \u0127afna mill-metodi tieg\u0127u ta\u2019 riduzzjoni jew \u2018\u2019\u0121bir\u2019\u2019 g\u0127adna\u00a0 nu\u017cawhom fl-al\u0121ebra sa llum.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 850:\u00a0 Il-matematiku Persjan, [[al-Ma\u0127ani]], ja\u0127seb fl-ideja ta\u2019 riduzzjoni ta\u2019 problemi \u0121ometri\u010bi, b\u0127ad-duplikazzjoni tal-kubu, g\u0127al problemi fl-al\u0121ebra.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 850 Il-matematiku, [[Mahavira]], jirri\u017colvi bosta ekwazzjonijiet kwadrati\u010bi, kubi\u010bi, kwarti\u010bi, kwinti\u010bi u ta\u2019 ordni og\u0127la kif ukoll xi ekwazzjonijiet indeterminati. kwadrati\u010bi, kubi\u010bi u ta\u2019 ordni og\u0127la. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 990:\u00a0 Il-Persjan [[Abu Bakr al-Kara\u0121i]], fit-trattat tieg\u0127u ''al-Fakhri'', ji\u017cviluppa l-al\u0121ebra i\u017cjed billi jestendi l-metodolo\u0121ija ta\u2019 Al-Khwari\u017cmi biex tinkludi poteri integrali u radi\u010bi integrali ta\u2019 kwantitajiet mhux mag\u0127rufa. Jissostwixxi l-operazzjonijiet gometri\u010bi ta\u2019 l-al\u0121ebra b\u2019operazzjonijiet aritmeti\u010bi moderni, u jiddefinixxi il-monomjali x, x<sup>2<</ins>/<ins class=\"diffchange diffchange-inline\">sup>, x<sup>3<</ins>/<ins class=\"diffchange diffchange-inline\">sup>, </ins>..<ins class=\"diffchange diffchange-inline\">. u 1</ins>/<ins class=\"diffchange diffchange-inline\">x, 1</ins>/<ins class=\"diffchange diffchange-inline\">x<sup>2<</ins>/<ins class=\"diffchange diffchange-inline\">sup>, 1/x<sup>3</sup>, ... u jag\u0127ti\u00a0 l</ins>-<ins class=\"diffchange diffchange-inline\">prodott ta\u2019 kull par minn dawn</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 1050: Il-matematiku \u010aini\u017c, [[\u0120ija Ksijan]], jsib soluzzjonijiet numeri\u010bi ta\u2019 ekwazzjonijiet polinomjali</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1072:\u00a0 Il-matematiku Persjan, [[Omar Khajjam]], ji\u017cviluppa l-\u0121ometrija al\u0121ebrija, u fit-''Trattat fuq Dimostrazzjoni ta\u2019 Problemi fl-Al\u0121ebra'',\u00a0 jag\u0127ti klassifikazzjoni ta\u2019 ekwazzjonijiet kubi\u010bi permezz ta\u2019soluzzjonijiet \u0121ometri\u010bi \u0121enerali misjuba bis-sezzjonijiet koni\u010bi ntlaqqin.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1114: Il-matematiku Indjan, [[Bhaskara]], fil- ''Bi\u0121aganita'' (''Al\u0121ebra''), jinduna li numru po\u017cittiv g\u0127andu radi\u010bi kwadrata po\u017cittiva u o\u0127ra negattiva, u jirri\u017colvi bosta ekwazzjonijiet kubi\u010bi, kwarti\u010bi, kwinti\u010bi u ta\u2019 ordni polinomjali, kif ukoll l-ekwazzjoni kwadratika \u0121enerali indeterminata.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1202: L-al\u0121ebra tid\u0127ol l-Ewropa l-iktar im\u0127abba x-xog\u0127ol ta\u2019 [[Leonardo Fibonacci]] ta\u2019 Pisa fil-ktieb tieg\u0127u ''[[Liber Abaci]]''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 1300: Il-matematiku \u010aini\u017c, [[\u017bhu Xi\u0121je]], jittratta l-al\u0121ebra polinomjali, jirri\u017colvi ekwazzjonijiet kwadrati\u010bi, ekwazzjonijiet simultanji u ekwazzjonijiet b\u2019sa erbg\u0127a kwantitajiet mhux mag\u0127rufa, u jirri\u017colvi numerikament xi ekwazzjonijiet kwarti\u010bi, kwinti\u010bi u polinomjali ta\u2019 ordni og\u0127la.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Stampa:Evariste galois.jpg|thumb|right|200px| \u00c9variste Galois t</ins>.<ins class=\"diffchange diffchange-inline\">1811 m.1832]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* \u010airka 1400: </ins>Il-<ins class=\"diffchange diffchange-inline\">matematiku Indjan, [[Madhava ta\u2019 Sangamagramma]], jiskopri metodi iterattivi g\u0127as-soluzzjoni approssima ta\u2019 ekwazzjonijiet mhux linjari.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1535: Nicolo Fontana [[Tartaglia]] u\u00a0 matemati\u010bi o\u0127ra fl-Italja independentement\u00a0 jirri\u017colvu l-ekwazzjoni kubika \u0121enerali.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1545: Girolamo [[Cardano]] jippublika ''Ars magna'' (''L-Arti l-Kbira'') fejn jag\u0127ti s-soluzzjoni ta\u2019 Fontana g\u0127all-ekwazzjoni kwartika \u0121enerali.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1572: Rafael [[Bombelli]] jsib ir-radi\u010bi komplessa </ins>tal-<ins class=\"diffchange diffchange-inline\">kubiku u jtejjeb in-notazzjoni kurrenti.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1591: [[Fran\u00e7ois Vi\u00e8te]] ji\u017cviluppa u jtejjeb in-notazzjoni simbolika g\u0127all-poteri fil-ktieb ''In artem analyticam isagoge''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1682: [[Gottfried Leibniz|Gottfried Wilhelm Leibniz]] ji\u017cviluppa l-manipulazzjoni simbolika b\u2019regoli formali li jg\u0127idilhom ''characteristica generalis''.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1680s: Il-matematiku \u0120appuni\u017c, [[Kowa Seki]], fil-''Metodu g\u0127as-soluzzjoni ta\u2019 problemi dissimulati'', jiskopri d-determinant u n-[[numri ta\u2019 Bernoulli]].</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1750: [[Gabriel Cramer]], fit-trattat tieg\u0127u\u00a0 '</ins>'<ins class=\"diffchange diffchange-inline\">Introduzzjoni g\u0127all-analisi ta\u2019 kurvi al\u0121ebrin'', jipproponi r-[[regola ta\u2019 Cramer]] u jistudja </ins>l<ins class=\"diffchange diffchange-inline\">-kurvi al\u0121ebrin, il-matri\u010bi u d-determinanti.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1824: [[Niels Henrik Abel]] jipprova li ma nistg\u0127ux nirri\u017colvu l-ekwazzjoni kwintika \u0121enerali bir-radi\u010bi.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* 1832: It-teorija ta\u2019 Galois ji\u017cviluppha [[\u00c9variste Galois]] fix-xog\u0127ol tieg\u0127u fuq l-al\u0121ebra astratta.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">{{Portal Matematika}}</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Kategorija:Matematika| ]]</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Kategorija:10 artikli essenzjali]</ins>]</div></td></tr>\n"
}
}