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"compare": {
"fromid": 1,
"fromrevid": 1,
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"fromtitle": "Hlavn\u00ed strana",
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"tons": 0,
"totitle": "Matematika",
"*": "<tr><td colspan=\"2\" class=\"diff-lineno\" id=\"mw-diff-left-l1\">\u0158\u00e1dek 1:</td>\n<td colspan=\"2\" class=\"diff-lineno\">\u0158\u00e1dek 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\"><strong>MediaWiki byla \u00fasp\u011b\u0161n\u011b nainstalov\u00e1na</del>.<del class=\"diffchange diffchange-inline\"></strong></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">[[Soubor:Mathematicsgeneral.jpg|n\u00e1hled|Ilustrace \u0161\u00ed\u0159e matematick\u00fdch discipl\u00edn]]</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\">'''Matematika''' (z&nbsp;[[\u0159e\u010dtina|\u0159eck\u00e9ho]] {{Cizojazy\u010dn\u011b|el|\u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03cc\u03c2}} (''math\u00e9matikos'') = ''miluj\u00edc\u00ed pozn\u00e1n\u00ed''; {{Cizojazy\u010dn\u011b|el|\u03bc\u03ac\u03b8\u03b7\u03bc\u03b1}} (''math\u00e9ma'') = ''v\u011bda, v\u011bd\u011bn\u00ed, pozn\u00e1n\u00ed'') je [[v\u011bda]] zab\u00fdvaj\u00edc\u00ed se z&nbsp;form\u00e1ln\u00edho hlediska [[kvantita|kvantitou]], [[struktura|strukturou]], [[prostor (geometrie)|prostorem]] a zm\u011bnou. Matematika je t\u00e9\u017e popisov\u00e1na jako discipl\u00edna, je\u017e se zab\u00fdv\u00e1 vytv\u00e1\u0159en\u00edm [[abstrakce|abstraktn\u00edch]] [[entita (matematika)|entit]] a vyhled\u00e1v\u00e1n\u00edm z\u00e1konit\u00fdch vztah\u016f mezi nimi</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\">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/Help</del>:<del class=\"diffchange diffchange-inline\">Contents U\u017eivatelsk\u00e1 p\u0159\u00edru\u010dka] v\u00e1m napov\u00ed</del>, <del class=\"diffchange diffchange-inline\">jak pou\u017e\u00edvat MediaWiki</del>.</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Matematika je zalo\u017eena a budov\u00e1na jako </ins>[<ins class=\"diffchange diffchange-inline\">[exaktn\u00ed]] v\u011bda. Jej\u00ed exaktnost (podobn\u011b jako jin\u00fdch exaktn\u00edch v\u011bd) tkv\u00ed v&nbsp;tom \u017ee, jak matematick\u00e9 objekty, tak i operace nad nimi jsou exaktn\u011b vyty\u010deny (tj. s&nbsp;nulovou vnit\u0159n\u00ed [[v\u00e1gnost]]\u00ed)<ref> K\u0159emen, J.</ins>: <ins class=\"diffchange diffchange-inline\">''Modely a syst\u00e9my'' ACADEMIA, Praha 2007. <</ins>/<ins class=\"diffchange diffchange-inline\">ref>, tedy tak, \u017ee ka\u017ed\u00fd v&nbsp;matematice (v&nbsp;dan\u00e9 exaktn\u00ed v\u011bd\u011b) vzd\u011blan\u00fd \u010dlov\u011bk naprosto p\u0159esn\u011b (bez jak\u00fdchkoli pochyb) v\u00ed, co znamenaj\u00ed</ins>. <ins class=\"diffchange diffchange-inline\">To je podstata exaktnosti t\u00e9to discipl\u00edny</ins>. <ins class=\"diffchange diffchange-inline\">V&nbsp;r\u00e1mci matematiky existuje ale je\u0161t\u011b jinak ch\u00e1pan\u00e1 exaktnost, a to exaktnost pou\u017eit\u00fdch metod a jejich v\u00fdsledk\u016f</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\">\u00a0 </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\">P\u0159\u00edkladem m\u016f\u017ee b\u00fdt exaktn\u00ed a neexaktn\u00ed \u0159e\u0161en\u00ed</ins>: <ins class=\"diffchange diffchange-inline\">N\u011bkter\u00e9 aplikace jsou \u0159e\u0161iteln\u00e9 pouze opu\u0161t\u011bn\u00edm p\u0159\u00edsn\u00e9ho a omezuj\u00edc\u00edho po\u017eadavku exaktnosti v\u00fdsledku. Nap\u0159\u00edklad proto, \u017ee neexistuje matematick\u00e1 funkce, kter\u00e1 by byla (exaktn\u00edm) \u0159e\u0161en\u00edm dan\u00e9 diferenci\u00e1ln\u00ed rovnice. M\u016f\u017ee ale existovat posloupnost funkc\u00ed, kter\u00e1 s&nbsp;libovolnou p\u0159esnost\u00ed (nikoli v\u0161ak exaktn\u011b), \u0159e\u0161en\u00edm t\u00e9 rovnice je. Dosazen\u00edm exaktn\u00edho v\u00fdsledku (\u0159e\u0161en\u00ed) do v\u00fdchoz\u00edho vztahu (rovnice) dost\u00e1v\u00e1me identitu. Neexaktn\u00ed v\u00fdsledek se od exaktn\u00edho li\u0161\u00ed o \u201echybu \u201c</ins>, <ins class=\"diffchange diffchange-inline\">tak\u017ee po jeho dosazen\u00ed identitu nedostaneme</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\">Za\u010d\u00edn\u00e1me </del>==</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Charakteristickou vlastnost\u00ed matematiky je jej\u00ed d\u016fraz na absolutn\u00ed p\u0159esnost [[metoda|metod]] a nezpochybnitelnost v\u00fdsledk\u016f. Tyto vlastnosti, kter\u00e9 matematiku odli\u0161uj\u00ed od v\u0161ech ostatn\u00edch v\u011bdn\u00edch discipl\u00edn, maj\u00ed p\u016fvod ji\u017e v&nbsp;[[starov\u011bk\u00e9 \u0158ecko|antick\u00e9m \u0158ecku]]. Nejstar\u0161\u00edm dochovan\u00fdm p\u0159\u00edkladem tohoto p\u0159\u00edstupu je kniha \u0159eck\u00e9ho [[matematik]]a [[Eukleid\u00e9s|Euklida]] ''[[Eukleidovy Z\u00e1klady|Z\u00e1klady]]'' poch\u00e1zej\u00edc\u00ed z&nbsp;[[4. stolet\u00ed p\u0159. n. l.]]</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\">* </del>[<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 Nastaven\u00ed konfigurace</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\">* </del>[<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 \u010casto kladen\u00e9 </del>ot\u00e1zky o <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\">\u0160irok\u00e9 ve\u0159ejnosti je zn\u00e1ma tzv. [[element\u00e1rn\u00ed matematika]], kter\u00e1 se zab\u00fdv\u00e1 operov\u00e1n\u00edm s&nbsp;[[\u010d\u00edslo|\u010d\u00edsly]], \u0159e\u0161en\u00edm praktick\u00fdch \u00faloh, jednoduch\u00fdch [[rovnice|rovnic]] a popisem z\u00e1kladn\u00edch [[geometrie|geometrick\u00fdch]] objekt\u016f. Ve [[fyzika|fyzice]], [[Informa\u010dn\u00ed v\u011bda|informatice]], [[chemie|chemii]], [[ekonomie|ekonomii]] a dal\u0161\u00edch oborech se \u010dasto vyu\u017e\u00edvaj\u00ed v\u00fdsledky [[aplikovan\u00e1 matematika|aplikovan\u00e9 matematiky]], kter\u00e1 je tak\u00e9 t\u011bmito obory zp\u011btn\u011b ovliv\u0148ov\u00e1na. Tzv. [[\u010dist\u00e1 matematika]] se zab\u00fdv\u00e1 pouze vysoce abstraktn\u00edmi pojmy, jejich\u017e definov\u00e1n\u00ed nen\u00ed p\u0159\u00edmo motivov\u00e1no praktick\u00fdm u\u017eitkem v&nbsp;re\u00e1ln\u00e9m sv\u011bt\u011b. N\u011bkter\u00e9 obory \u010dist\u00e9 matematiky se nach\u00e1zej\u00ed na pomez\u00ed s&nbsp;[[logika|logikou]] \u010di [[Filozofie|filozofi\u00ed]].</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\">* </del>[<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-announce</del>.<del class=\"diffchange diffchange-inline\">lists</del>.<del class=\"diffchange diffchange-inline\">wikimedia.org</del>/ <del class=\"diffchange diffchange-inline\">E</del>-<del class=\"diffchange diffchange-inline\">mailov\u00e1 konference ozn\u00e1men\u00ed MediaWiki</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>* [https://<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:MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Localisation#Translation_resources P\u0159eklad MediaWiki do va\u0161eho jazyka</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>== <ins class=\"diffchange diffchange-inline\">Charakteristika metod a&nbsp;c\u00edl\u016f matematiky </ins>==</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>* [https://<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.org/<del class=\"diffchange diffchange-inline\">wiki/Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage/Manual</del>:<del class=\"diffchange diffchange-inline\">Combating_spam Nau\u010dte se bojovat se spamem na va\u0161\u00ed wiki</del>]</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Mezi jin\u00fdmi v\u011bdami se matematika vyzna\u010duje nejvy\u0161\u0161\u00ed m\u00edrou [</ins>[<ins class=\"diffchange diffchange-inline\">abstrakce]] a p\u0159esnosti. D\u00edky t\u011bmto vlastnostem je \u010dasto ozna\u010dov\u00e1na za ''kr\u00e1lovnu v\u011bd''<ref>{{Citace elektronick\u00e9 monografie</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\"> | p\u0159\u00edjmen\u00ed = Dan\u00ed\u010dkov\u00e1</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\"> | jm\u00e9no = Sylva</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\"> | p\u0159\u00edjmen\u00ed2 = Houdek</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\"> | jm\u00e9no2 = Franti\u0161ek</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\"> | titul = O povaze kr\u00e1lovny v\u011bd aneb 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\"> | url = http</ins>://<ins class=\"diffchange diffchange-inline\">abicko</ins>.<ins class=\"diffchange diffchange-inline\">avcr</ins>.<ins class=\"diffchange diffchange-inline\">cz/archiv/2004/5</ins>/<ins class=\"diffchange diffchange-inline\">obsah</ins>/<ins class=\"diffchange diffchange-inline\">o-povaze-kralovny-ved-aneb-matematika.html</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\"> | datum vyd\u00e1n\u00ed = kv\u011bten 2004</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\"> | datum aktualizace =</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\"> | datum p\u0159\u00edstupu = 21.5.2013</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\"> | vydavatel = Akademick\u00fd bulletin [[Akademie v\u011bd \u010cR]]</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\"> | jazyk =</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\"></ref>. Tzv. [[matematick\u00fd d\u016fkaz]] je nejspolehliv\u011bj\u0161\u00ed zn\u00e1m\u00fd zp\u016fsob, jak ov\u011b\u0159ovat pravdivost tvrzen\u00ed. V&nbsp;matematice jsou za spolehliv\u00e1 pova\u017eov\u00e1na pouze ta [[Matematick\u00e1 v\u011bta|tvrzen\u00ed]] (naz\u00fdvan\u00e9 ''[[Matematick\u00e1 v\u011bta|v\u011bty]]''), ke kter\u00fdm je zn\u00e1m matematick\u00fd d\u016fkaz. Nov\u00e9 pojmy jsou vytv\u00e1\u0159eny jednozna\u010dn\u00fdmi [[definice]]mi z&nbsp;pojm\u016f ji\u017e zaveden\u00fdch.</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\">Pro sou\u010dasnou matematiku je typick\u00e1 vysok\u00e1 p\u0159esnost, zaji\u0161\u0165ovan\u00e1 [[Axiomatick\u00e1 teorie mno\u017ein|\u00faplnou formalizac\u00ed]]. Je-li stanoveno n\u011bkolik z\u00e1kladn\u00edch tvrzen\u00ed (tzv. [[axiom]]y), je z&nbsp;nich mo\u017en\u00e9 s&nbsp;pou\u017eit\u00edm odvozovac\u00edch pravidel zalo\u017een\u00fdch na logice odvodit dal\u0161\u00ed pravdiv\u00e1 tvrzen\u00ed pomoc\u00ed [[Hilbertovsk\u00fd kalkulus|form\u00e1ln\u00edch d\u016fkaz\u016f]]. V\u00fdklad matematick\u00fdch poznatk\u016f tak spo\u010d\u00edv\u00e1 v&nbsp;definov\u00e1n\u00ed nov\u00fdch pojm\u016f, formulov\u00e1n\u00ed platn\u00fdch v\u011bt o&nbsp;nich (p\u0159\u00edpadn\u011b takov\u00fdch v\u011bt, kter\u00e9 je d\u00e1vaj\u00ed do souvislosti s&nbsp;pojmy star\u0161\u00edmi) a dokazov\u00e1n\u00ed pravdivosti t\u011bchto v\u011bt. Matematick\u00e9 pr\u00e1ce maj\u00ed proto \u010dasto strukturu \u201edefinice \u2013 v\u011bta \u2013 d\u016fkaz\u201c s&nbsp;minimem dopl\u0148uj\u00edc\u00edho textu \u010di zcela bez n\u011bj. Stejn\u011b jako v&nbsp;jin\u00fdch v\u011bdn\u00edch discipl\u00edn\u00e1ch se tak\u00e9 m\u016f\u017ee objevit formulace neov\u011b\u0159en\u00e9 [[hypot\u00e9za|hypot\u00e9zy]] - p\u0159edpokladu (jako v\u00fdzva k&nbsp;jej\u00edmu dok\u00e1z\u00e1n\u00ed \u010di vyvr\u00e1cen\u00ed) nebo polo\u017een\u00ed dosud nezodpov\u011bzen\u00e9 ot\u00e1zky.</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\">N\u011bkter\u00e9 z&nbsp;matematikou vytv\u00e1\u0159en\u00fdch abstraktn\u00edch [[pojem|pojm\u016f]] slou\u017e\u00ed k&nbsp;vysv\u011btlen\u00ed \u010di snadn\u011bj\u0161\u00edmu uchopen\u00ed pojm\u016f dal\u0161\u00edch, jin\u00e9 slou\u017e\u00ed v&nbsp;jin\u00fdch v\u011bdn\u00edch oborech jako n\u00e1stroj k&nbsp;popisu ur\u010dit\u00fdch [[Fenom\u00e9n|jev\u016f]] nebo jako idealizovan\u00fd [[V\u011bdeck\u00e9 modelov\u00e1n\u00ed|model]] re\u00e1ln\u00fdch objekt\u016f \u010di syst\u00e9m\u016f, dal\u0161\u00ed pak umo\u017e\u0148uj\u00ed precizaci a rozvoj koncept\u016f a my\u0161lenek n\u011bkter\u00fdch discipl\u00edn [[filozofie]]. Z\u00e1konitosti objeven\u00e9 mezi t\u011bmito pojmy lze p\u0159i vhodn\u00e9 aplikaci zp\u011btn\u011b p\u0159eformulovat jako pravidla a vlastnosti skute\u010dn\u00e9ho sv\u011bta nebo jako obecn\u011b platn\u00e9 [[teze]]. To v\u0161ak ji\u017e nen\u00ed \u00fakolem matematiky, n\u00fdbr\u017e p\u0159\u00edslu\u0161n\u00e9 jin\u00e9 discipl\u00edny.</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\">== Jazyk matematiky je um\u011bl\u00fd form\u00e1ln\u00ed jazyk ==</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\">Je t\u0159eba p\u0159ipomenout, \u017ee jazyk matematiky je um\u011bl\u00fd [[form\u00e1ln\u00ed jazyk]], pro kter\u00fd plat\u00ed kategorick\u00fd po\u017eadavek exaktn\u00ed (tj. s&nbsp;nulovou vnit\u0159n\u00ed v\u00e1gnost\u00ed) [[interpretace]] v\u0161ech jeho jazykov\u00fdch konstrukc\u00ed. Um\u011bl\u00fdmi form\u00e1ln\u00edmi jazyky jsou i jazyky v\u0161ech typ\u016f form\u00e1ln\u00edch logik a programovac\u00ed jazyky. Nelze tedy nap\u0159. v&nbsp;jak\u00e9koli form\u00e1ln\u00ed logice pou\u017e\u00edt p\u0159irozen\u00fd jazyk, nebo\u0165 ten m\u00e1 inherentn\u011b v\u00e1gn\u00ed, a tak i emocion\u00e1ln\u00ed interpretaci (\u0159\u00edk\u00e1me j\u00ed [[konotace]]) v\u0161ech sv\u00fdch jazykov\u00fdch konstrukc\u00ed.<ref> K\u0159emen, J.</ins>: <ins class=\"diffchange diffchange-inline\">'' Nov\u00fd pohled na mo\u017enosti automatizovan\u00e9ho (po\u010d\u00edta\u010dov\u00e9ho) odvozov\u00e1n\u00ed. Slaboproud\u00fd obzor. Ro\u010d. 68 (2013), \u010d. 1., str. 7 \u2013 11. '' <</ins>/<ins class=\"diffchange diffchange-inline\">ref>. S&nbsp;t\u00edmto omylem se m\u016f\u017eeme setkat v&nbsp;n\u011bkter\u00fdch u\u010debnic\u00edch form\u00e1ln\u00ed logiky nebo um\u011bl\u00e9 inteligence viz [[reprezentace znalost\u00ed]]. Je to p\u0159ekro\u010den\u00ed hranic exaktn\u00edho sv\u011bta poru\u0161en\u00edm podm\u00ednky exaktn\u00ed interpretace. Pro hlub\u0161\u00ed pochopen\u00ed probl\u00e9mu</ins>: <ins class=\"diffchange diffchange-inline\">P\u0159irozen\u00fd jazyk nem\u016f\u017ee b\u00fdt sou\u010d\u00e1st\u00ed exaktn\u00edho sv\u011bta, nem\u00e1 exaktn\u00ed interpretaci sv\u00fdch jazykov\u00fdch konstrukc\u00ed. Nap\u0159\u00edklad pokud n\u011bjak\u00fd objekt exaktn\u00edho sv\u011bta, t\u0159eba veli\u010dinu \u201eRychlost pohybu t\u011blesa\u201c, m\u00edsto (obvykl\u00e9ho) symbolu&nbsp;V (jedno\u010dlenn\u00e9ho \u0159et\u011bzce symbol\u016f), ozna\u010d\u00edme konstrukc\u00ed p\u0159irozen\u00e9ho jazyka (v\u011btou): Marj\u00e1nka se na n\u011bj usm\u00edvala, nelze tuto v\u011btu ch\u00e1pat jako v\u011btu p\u0159irozen\u00e9ho jazyka (a p\u0159i\u0159azovat j\u00ed obvykl\u00fd v\u00fdznam), ale nutn\u011b jen jako \u0159et\u011bzec symbol\u016f dost\u00e1vaj\u00edc\u00ed v&nbsp;exaktn\u00edm sv\u011bt\u011b nov\u00fd v\u00fdznam, a to jm\u00e9no t\u00e9 veli\u010diny. Ona v\u011bta dost\u00e1v\u00e1 tedy stejn\u00fd v\u00fdznam, jako m\u011bl p\u016fvodn\u011b symbol&nbsp;V. P\u0159i\u0159azen\u00ed v\u00fdznamu t\u00e9 v\u011bt\u011b je pak exaktn\u00ed, jak odpov\u00edd\u00e1 statutu veli\u010diny jako elementu exaktn\u00edho sv\u011bta. Je\u0161t\u011b poznamenejme, \u017ee pokud um\u011bl\u00e9 form\u00e1ln\u00ed jazyky maj\u00ed vypov\u00eddat o znalostech v re\u00e1ln\u00e9m sv\u011bt\u011b, mus\u00ed se tak d\u00edt prost\u0159ednictv\u00edm veli\u010din viz [[Exaktn\u00ed v\u011bda]], jinak nelze. [[Veli\u010dina]] je jedin\u00fdm prost\u0159edn\u00edkem mezi re\u00e1ln\u00fdm a exaktn\u00edm sv\u011btem.</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\">[[Soubor:Image-Al-Kit\u0101b al-mu\u1e2bta\u1e63ar f\u012b \u1e25is\u0101b al-\u011fabr wa-l-muq\u0101bala.jpg|n\u00e1hled|Str\u00e1nka z&nbsp;knihy [[Al-Kit\u0101b al-mu\u1e2bta\u1e63ar f\u012b \u1e25is\u0101b al-\u011fabr wa-l-muq\u0101bala]] od [[Persie|persk\u00e9ho]] matematika [[Al-Chorezm\u00ed]]ho, v&nbsp;n\u00ed\u017e jsou polo\u017eeny z\u00e1klady [[algebra|algebry]]]]</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\">== Historie ==</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\">{{Podrobn\u011b|D\u011bjiny matematiky}}</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\">Vznik matematiky byl zap\u0159\u00ed\u010din\u011bn p\u0159edev\u0161\u00edm pot\u0159ebou \u0159e\u0161it praktick\u00e9 \u00falohy, jako nap\u0159\u00edklad r\u016fzn\u00e9 [[obchod]]n\u00ed \u00falohy, vym\u011b\u0159ov\u00e1n\u00ed a d\u011blen\u00ed pozemk\u016f, [[stavebnictv\u00ed]] a m\u011b\u0159en\u00ed [[\u010das]]u. [[D\u011bjiny matematiky|Historie matematiky]] sah\u00e1 a\u017e do [[prav\u011bk]]u, kdy vznikly prvn\u00ed abstraktn\u00ed matematick\u00e9 pojmy \u2013 [[p\u0159irozen\u00e9 \u010d\u00edslo|p\u0159irozen\u00e1 \u010d\u00edsla]]. Velk\u00fd rozvoj prod\u011blala v&nbsp;[[starov\u011bk\u00e9 \u0158ecko|antick\u00e9m \u0158ecku]], kde v\u00fdrazn\u00fdch \u00fasp\u011bch\u016f dos\u00e1hla zejm\u00e9na [[geometrie]]. Dal\u0161\u00ed etapou prudk\u00e9ho rozvoje matematiky byl ran\u00fd novov\u011bk, kdy byly p\u0159edev\u0161\u00edm Descartem ustaveny z\u00e1klady [[matematick\u00e1 anal\u00fdza|matematick\u00e9 anal\u00fdzy]]. Pot\u00e9 se d\u00edky pr\u00e1ci Newtona, Leibnize, Eulera, Gausse a dal\u0161\u00edch matematik\u016f poda\u0159ilo dos\u00e1hnout z\u00e1sadn\u00edch v\u00fdsledk\u016f v&nbsp;oblasti anal\u00fdzy zejm\u00e9na polo\u017een\u00edm z\u00e1klad\u016f diferenci\u00e1ln\u00edho a integr\u00e1ln\u00edho po\u010dtu.</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\">Jin\u00fdm v\u00fdznamn\u00fdm obdob\u00edm d\u011bjin matematiky byl p\u0159elom [[19. stolet\u00ed|19.]] a [[20. stolet\u00ed]], kdy zkoum\u00e1n\u00ed dokazatelnosti tvrzen\u00ed bylo postaveno na solidn\u00ed a form\u00e1ln\u00ed z\u00e1klad, objevy v&nbsp;[[matematick\u00e1 logika|matematick\u00e9 logice]] a zaveden\u00edm [[axiomatick\u00e1 teorie mno\u017ein|axiomatick\u00e9 teorie mno\u017ein]]. Touto dobou za\u010daly b\u00fdt t\u00e9\u017e zkoum\u00e1ny [[Abstraktn\u00ed algebra|abstraktn\u00ed struktury]], co\u017e umo\u017e\u0148uje jedn\u00edm d\u016fkazem ov\u011b\u0159it matematick\u00e9 tvrzen\u00ed pro [[Abstraktn\u00ed algebra#V\u00fdznam abstraktn\u00ed algebry|\u0161irokou skupinu]] matematick\u00fdch objekt\u016f. Vyvrcholen\u00edm tohoto trendu byl v&nbsp;polovin\u011b 20.&nbsp;stolet\u00ed vznik [[teorie kategori\u00ed]], kter\u00e1 je pokl\u00e1d\u00e1na za nejobecn\u011bj\u0161\u00ed a nejabstraktn\u011bj\u0161\u00ed matematickou discipl\u00ednu.</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\">== Matematick\u00e9 discipl\u00edny ==</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\">{{podrobn\u011b|text=Strukturovan\u00fd seznam v\u0161ech z\u00e1kladn\u00edch obor\u016f matematiky|Seznam matematick\u00fdch discipl\u00edn}}</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\">Hlavn\u00ed klasick\u00e9 discipl\u00edny matematiky se vyvinuly ze \u010dty\u0159 praktick\u00fdch lidsk\u00fdch pot\u0159eb&nbsp;\u2013&nbsp;pot\u0159eby po\u010d\u00edtat p\u0159i [[obchod]]ov\u00e1n\u00ed, porozum\u011bt vztah\u016fm mezi \u010d\u00edseln\u011b vyj\u00e1d\u0159en\u00fdmi mno\u017estv\u00edmi, vym\u011b\u0159ov\u00e1n\u00ed pozemk\u016f a staveb a p\u0159edpov\u00edd\u00e1n\u00ed [[astronomie|astronomick\u00fdch]] jev\u016f. Z&nbsp;t\u011bchto \u010dty\u0159 pot\u0159eb vznikly \u010dty\u0159i klasick\u00e9 matematick\u00e9 discipl\u00edny&nbsp;\u2013&nbsp;po \u0159ad\u011b [[aritmetika]], [[algebra]], [[geometrie]] a&nbsp;[[matematick\u00e1 anal\u00fdza]], kter\u00e9 se zab\u00fdvaj\u00ed zhruba \u0159e\u010deno \u010dty\u0159mi z\u00e1kladn\u00edmi oblastmi z\u00e1jmu matematiky&nbsp;\u2013&nbsp;[[kvantita|kvantitou]], [[struktura|strukturou]</ins>]<ins class=\"diffchange diffchange-inline\">, [[prostor (geometrie)|prostorem]] a zm\u011bnou. Pozd\u011bji se d\u00edky snah\u00e1m zast\u0159e\u0161it tyto \u010dty\u0159i discipl\u00edny jednotnou matematickou teori\u00ed a dos\u00e1hnout co nejv\u011bt\u0161\u00ed p\u0159esnosti a nezpochybnitelnosti v\u00fdsledk\u016f rozvinulo n\u011bkolik vz\u00e1jemn\u011b prov\u00e1zan\u00fdch discipl\u00edn naz\u00fdvan\u00fdch souhrnn\u011b [[z\u00e1klady matematiky]]. Tyto discipl\u00edny krom\u011b v\u00fd\u0161e zm\u00edn\u011bn\u00e9ho umo\u017enily tak\u00e9 hlub\u0161\u00ed propojen\u00ed matematiky s&nbsp;[[Filozofie|filozofi\u00ed]] \u010di rozvoj [[teoretick\u00e1 informatika|teoretick\u00e9 informatiky]]. Ve [[20. stolet\u00ed|20.&nbsp;stolet\u00ed]] zaznamenaly ohromn\u00fd rozvoj discipl\u00edny [[aplikovan\u00e1 matematika|aplikovan\u00e9 matematiky]], kter\u00e9 slou\u017e\u00ed jako d\u016fle\u017eit\u00e9 n\u00e1stroje v&nbsp;nejr\u016fzn\u011bj\u0161\u00ed oborech lidsk\u00e9 \u010dinnosti.</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\">=== Kvantita ===</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\">Studium kvantity je v\u016fbec nejstar\u0161\u00ed oblast\u00ed matematiky. Jeho po\u010d\u00e1tky se objevuj\u00ed ji\u017e v&nbsp;[[prav\u011bk]]u, kdy doch\u00e1z\u00ed k&nbsp;porozum\u011bn\u00ed pojmu [[p\u0159irozen\u00e9 \u010d\u00edslo|p\u0159irozen\u00e9ho \u010d\u00edsla]]. Postupem \u010dasu n\u00e1sleduje vytv\u00e1\u0159en\u00ed z\u00e1kladn\u00edch aritmetick\u00fdch [[operace (matematika)|operac\u00ed]] a roz\u0161i\u0159ov\u00e1n\u00ed \u010d\u00edseln\u00e9ho oboru p\u0159es \u010d\u00edsla [[cel\u00e9 \u010d\u00edslo|cel\u00e1]], [[racion\u00e1ln\u00ed \u010d\u00edslo|racion\u00e1ln\u00ed]], [[re\u00e1ln\u00e9 \u010d\u00edslo|re\u00e1ln\u00e1]] a&nbsp;[[komplexn\u00ed \u010d\u00edslo|komplexn\u00ed]] a\u017e k&nbsp;r\u016fzn\u00fdm specializovan\u00fdm \u010d\u00edseln\u00fdm obor\u016fm jako jsou [[hyperkomplexn\u00ed \u010d\u00edslo|hyperkomplexn\u00ed \u010d\u00edsla]], [[kvaternion]]y, [[oktonion]]y, [[ordin\u00e1ln\u00ed \u010d\u00edslo|ordin\u00e1ln\u00ed]] a [[kardin\u00e1ln\u00ed \u010d\u00edslo|kardin\u00e1ln\u00ed \u010d\u00edsla]] nebo [[Nadre\u00e1ln\u00e9 \u010d\u00edslo|surre\u00e1ln\u00e1 \u010d\u00edsla]].</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\">I&nbsp;v&nbsp;[[teorie \u010d\u00edsel|teorii p\u0159irozen\u00fdch \u010d\u00edsel]] z\u016fst\u00e1v\u00e1 dosud mnoho snadno formulovateln\u00fdch otev\u0159en\u00fdch [[probl\u00e9m (matematika)|probl\u00e9m\u016f]], nap\u0159. [[Prvo\u010d\u00edseln\u00e1 dvojice|hypot\u00e9za prvo\u010d\u00edseln\u00fdch dvojic]] nebo [[Goldbachova hypot\u00e9za]]. Z\u0159ejm\u011b nejslavn\u011bj\u0161\u00ed probl\u00e9m cel\u00e9 matematiky, [[velk\u00e1 Fermatova v\u011bta]], byl vy\u0159e\u0161en v&nbsp;roce [</ins>[<ins class=\"diffchange diffchange-inline\">1995]] po 350&nbsp;letech marn\u00fdch pokus\u016f.</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\">:{| style=\"border:1px solid #ddd; text-align:center; margin</ins>: <ins class=\"diffchange diffchange-inline\">auto;\" cellspacing=\"20\"</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>1; 2; 3\\,\\!</math> || <math>-2; -1; 0; 1; 2\\,\\!<</ins>/<ins class=\"diffchange diffchange-inline\">math> || <math>-2; \\frac{2}{3}; 1{,}21\\,\\!<</ins>/<ins class=\"diffchange diffchange-inline\">math> || <math>-e; \\sqrt{2}; 3; \\pi\\,\\!</math> || <math>2; i; -2+3i; 2e^{i\\frac{4\\pi}{3}}\\,\\!</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><ins class=\"diffchange diffchange-inline\">|[[P\u0159irozen\u00e9 \u010d\u00edslo|P\u0159irozen\u00e1 \u010d\u00edsla]]||[[Cel\u00e9 \u010d\u00edslo|Cel\u00e1 \u010d\u00edsla]] ||[[Racion\u00e1ln\u00ed \u010d\u00edslo|Racion\u00e1ln\u00ed \u010d\u00edsla]]||[[Re\u00e1ln\u00e9 \u010d\u00edslo|Re\u00e1ln\u00e1 \u010d\u00edsla]] ||[[Komplexn\u00ed \u010d\u00edslo|Komplexn\u00ed \u010d\u00edsla]]</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\">=== Struktura ===</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\">Mnoho matematick\u00fdch objekt\u016f jako [[mno\u017eina|mno\u017einy]] \u010d\u00edsel \u010di [[funkce (matematika)|funkc\u00ed]] vykazuj\u00ed jistou vnit\u0159n\u00ed strukturu. Abstrahov\u00e1n\u00edm n\u011bkter\u00fdch z&nbsp;t\u011bchto struktur\u00e1ln\u00edch vlastnost\u00ed vznikly pojmy [[grupa]] (skupina), [[okruh (algebra)|okruh]], [[t\u011bleso (algebra)|t\u011bleso]] a dal\u0161\u00ed. Studiem t\u011bchto abstraktn\u00edch koncept\u016f se zab\u00fdv\u00e1 [[algebra]]</ins>. <ins class=\"diffchange diffchange-inline\">Jej\u00ed d\u016fle\u017eitou sou\u010d\u00e1st\u00ed je [[line\u00e1rn\u00ed algebra]], kter\u00e1 se zab\u00fdv\u00e1 studiem [[vektorov\u00fd prostor|vektorov\u00fdch prostor\u016f]], je\u017e v&nbsp;sob\u011b kombinuj\u00ed t\u0159i ze \u010dty\u0159 okruh\u016f z\u00e1jmu matematiky \u2013 kvantitu, strukturu a prostor. Diferenci\u00e1ln\u00ed a integr\u00e1ln\u00ed po\u010det p\u0159id\u00e1v\u00e1 k&nbsp;t\u011bmto t\u0159em okruh\u016fm i&nbsp;\u010dtvrt\u00fd \u2013 zm\u011bnu</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\">:{| style=\"border:1px solid #ddd; text-align:center; margin: auto;\" cellspacing=\"15\"</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\">| [[Soubor:Elliptic curve simple.png|96px]] || [[Soubor:Rubik's cube.svg|96px]] || [[Soubor:Group diagdram D6.svg|96px]] || [[Soubor:Lattice of the divisibility of 60.svg|96px]]</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\">| [[Teorie \u010d\u00edsel]] || [[Algebra]] || [[Teorie grup]] || [[Teorie uspo\u0159\u00e1d\u00e1n\u00ed]]</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\">=== Prostor ===</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\">Studium prostoru za\u010d\u00edn\u00e1 v&nbsp;matematice ji\u017e ve [[starov\u011bk]]u [[geometrie|geometri\u00ed]] \u2013&nbsp;konkr\u00e9tn\u011b [[Eukleidovsk\u00e1 geometrie|euklidovskou]]. [[Trigonometrie]] p\u0159ib\u00edr\u00e1 do hry fenom\u00e9n kvantity. Z\u00e1kladn\u00edm tvrzen\u00edm t\u00e9to kvantitativn\u00ed geometrie je [[Pythagorova v\u011bta]]. V&nbsp;pozd\u011bj\u0161\u00edch dob\u00e1ch doch\u00e1z\u00ed k&nbsp;zobec\u0148ov\u00e1n\u00ed sm\u011brem k&nbsp;[[Dimenze vektorov\u00e9ho prostoru|v\u00edcedimenzion\u00e1ln\u00edm]] prostor\u016fm, [[Neeukleidovsk\u00e1 geometrie|neeuklidovsk\u00fdm geometri\u00edm]] a&nbsp;[[topologie|topologii]]. Uva\u017eov\u00e1n\u00edm v&nbsp;kvantitativn\u00edch sf\u00e9r\u00e1ch se dost\u00e1v\u00e1me k&nbsp;[[analytick\u00e1 geometrie|analytick\u00e9]], [[diferenci\u00e1ln\u00ed geometrie|diferenci\u00e1ln\u00ed]] a&nbsp;[[algebraick\u00e1 geometrie|algebraick\u00e9 geometrii]]. Diferenci\u00e1ln\u00ed geometrie se zab\u00fdv\u00e1 studiem hladk\u00fdch [[k\u0159ivka|k\u0159ivek]] a&nbsp;[[varieta (matematika)|ploch]] v&nbsp;prostoru, algebraick\u00e1 pak geometrickou reprezentac\u00ed mno\u017ein [[Ko\u0159en polynomu|ko\u0159en\u016f]] [[polynom]]\u016f v\u00edce [[prom\u011bnn\u00e1|prom\u011bnn\u00fdch]]. [[Topologick\u00e1 grupa|Topologick\u00e9 grupy]] v&nbsp;sob\u011b kombinuj\u00ed fenom\u00e9ny prostoru a&nbsp;struktury, [[Lieova grupa|Lieovy grupy]] p\u0159id\u00e1vaj\u00ed nav\u00edc je\u0161t\u011b zm\u011bnu.</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\">:{| style=\"border:1px solid #ddd; text-align:center; margin: auto;\" cellspacing=\"15\"</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\">| [[Soubor:Illustration to Euclid's proof of the Pythagorean theorem.svg|96px]] || [[Soubor:Sine cosine plot.svg|96px]] || [[Soubor:Hyperbolic triangle.svg|96px]] || [[Soubor:Torus.png|96px]] || [[Soubor:Koch curve.svg|96px]]</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\">|[[Geometrie]] || [[Trigonometrie]] || [[Diferenci\u00e1ln\u00ed geometrie]] || [[Topologie]] || [[Frakt\u00e1l|Frakt\u00e1ln\u00ed geometrie]]</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\">=== Zm\u011bna ===</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\">Pochopen\u00ed a popis zm\u011bny je z\u00e1kladn\u00ed snahou [[p\u0159\u00edrodn\u00ed v\u011bdy|p\u0159\u00edrodn\u00edch v\u011bd]]. Mocn\u00fdm n\u00e1strojem k&nbsp;uchopen\u00ed fenom\u00e9nu zm\u011bny je kalkulus [[matematick\u00e1 anal\u00fdza|matematick\u00e9 anal\u00fdzy]], kter\u00fd vyu\u017e\u00edv\u00e1 konceptu [[funkce (matematika)|funkce]]. Studiem funkc\u00ed na oboru [[re\u00e1ln\u00e9 \u010d\u00edslo|re\u00e1ln\u00fdch \u010d\u00edsel]] se zab\u00fdv\u00e1 [[re\u00e1ln\u00e1 anal\u00fdza]], obdobnou discipl\u00ednou pro [[komplexn\u00ed \u010d\u00edslo|komplexn\u00ed]] p\u0159\u00edpad je [[komplexn\u00ed anal\u00fdza]]. Jej\u00ed sou\u010d\u00e1st\u00ed je pravd\u011bpodobn\u011b nejslavn\u011bj\u0161\u00ed i&nbsp;nejt\u011b\u017e\u0161\u00ed nevy\u0159e\u0161en\u00fd probl\u00e9m sou\u010dasn\u00e9 matematiky \u2013 [[Riemannova hypot\u00e9za]]. [[Funkcion\u00e1ln\u00ed anal\u00fdza]] se zab\u00fdv\u00e1 studiem p\u0159irozen\u011b vznikaj\u00edc\u00edch prostor\u016f funkc\u00ed, jednou z&nbsp;mnoha aplikac\u00ed tohoto oboru je [[kvantov\u00e1 mechanika]]. Pomoc\u00ed [[diferenci\u00e1ln\u00ed rovnice|diferenci\u00e1ln\u00edch rovnic]] je mo\u017en\u00e9 studovat problematiku zm\u011bn kvantitativn\u00edch veli\u010din. Vysoce slo\u017eit\u00e9 p\u0159\u00edrodn\u00ed syst\u00e9my slou\u017e\u00ed jako inspirace pro studium [[dynamick\u00e9 syst\u00e9my|dynamick\u00fdch syst\u00e9m\u016f]] a&nbsp;[[teorie chaosu]].</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\">{| style=\"border:1px solid #ddd; text-align:center; margin: auto;\" cellspacing=\"20\"</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\">| [[Soubor:Integral as region under curve.svg|96px]]\u00a0 || [[Soubor:Vector field.svg|96px]] || [[Soubor:Airflow-Obstructed-Duct.png|96px]] || [[Soubor</ins>:<ins class=\"diffchange diffchange-inline\">Limitcycle.svg|96px]] || [[Soubor</ins>:<ins class=\"diffchange diffchange-inline\">Lorenz attractor.svg|96px]]</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\">| [[Matematick\u00e1 anal\u00fdza]] ||[[Tenzorov\u00fd po\u010det|Vektorov\u00fd po\u010det]]||[[Diferenci\u00e1ln\u00ed rovnice]] || [[Dynamick\u00e9 syst\u00e9my]] || [[Teorie chaosu]]</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\">=== Z\u00e1klady matematiky a filozofie ===</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\">Ve snaze objasnit a zp\u0159esnit z\u00e1kladn\u00ed kameny matematiky byly na konci [[19. stolet\u00ed|19.&nbsp;stolet\u00ed]] polo\u017eeny z\u00e1klady discipl\u00edn\u00e1m [[teorie mno\u017ein]] a [[matematick\u00e1 logika|matematick\u00e9 logiky]], je\u017e b\u00fdvaj\u00ed souhrnn\u011b ozna\u010dov\u00e1ny jako [[z\u00e1klady matematiky]]. Na pomez\u00ed z\u00e1klad\u016f matematiky a abstraktn\u00ed [[algebra|algebry]] le\u017e\u00ed [[teorie kategori\u00ed]].</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\">Matematick\u00e1 logika poskytuje pevn\u00fd [[axiom]]atick\u00fd r\u00e1mec cel\u00e9 matematice a svoj\u00ed maxim\u00e1ln\u00ed p\u0159esnost\u00ed za\u0161ti\u0165uje nezpochybnitelnost v\u0161ech matematick\u00fdch v\u00fdsledk\u016f. [[Teorie d\u016fkazu]] precizuje a matematizuje z\u00e1kladn\u00ed principy rozumov\u00e9ho odvozov\u00e1n\u00ed a nutn\u00e9ho vypl\u00fdv\u00e1n\u00ed. [[Teorie model\u016f]] studuje logick\u00e9 koncepty pomoc\u00ed algebraick\u00fdch metod. Form\u00e1ln\u00ed studium aritmetick\u00fdch teori\u00ed jako jsou [[Robinsonova aritmetika|Robinsonova]] \u010di [[Peanova aritmetika]] m\u00e1 velk\u00fd v\u00fdznam i&nbsp;pro [[Filozofie|filozofick\u00e9]] </ins>ot\u00e1zky <ins class=\"diffchange diffchange-inline\">t\u00fdkaj\u00edc\u00ed se hranic [[dedukce|deduktivn\u00ed]] metody. Odpov\u011bd\u00ed na v\u011bt\u0161inu t\u011bchto ot\u00e1zek je nejslavn\u011bj\u0161\u00ed v\u00fdsledek cel\u00e9 [[logika|logiky]] \u2013&nbsp;[[G\u00f6delovy v\u011bty </ins>o<ins class=\"diffchange diffchange-inline\">&nbsp;ne\u00faplnosti</ins>]<ins class=\"diffchange diffchange-inline\">]. [[Teorie rekurze]] m\u00e1 velk\u00fd v\u00fdznam pro teoretick\u00e9 z\u00e1klady [[Informa\u010dn\u00ed v\u011bda|informatiky]].</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\">Teorie mno\u017ein je \u010dasto ozna\u010dov\u00e1na jako \u201esv\u011bt matematiky\u201c. Ka\u017ed\u00e1 jin\u00e1 matematick\u00e1 discipl\u00edna m\u016f\u017ee b\u00fdt pova\u017eov\u00e1na za sou\u010d\u00e1st teorie mno\u017ein. Krom\u011b toho m\u00e1 teorie mno\u017ein vlastn\u00ed obor studia zam\u011b\u0159en\u00fd z&nbsp;v\u011bt\u0161\u00ed \u010d\u00e1sti na pochopen\u00ed a&nbsp;popis fenom\u00e9nu [[nekone\u010dno|nekone\u010dna]] v&nbsp;jeho aktu\u00e1ln\u00ed podob\u011b. Slavn\u00fdm probl\u00e9mem teorie mno\u017ein byla [[hypot\u00e9za kontinua]], filozofick\u00e9 dopady m\u00e1 ot\u00e1zka [</ins>[<ins class=\"diffchange diffchange-inline\">axiom v\u00fdb\u011bru|axiomu v\u00fdb\u011bru]].</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\">:{| style=\"border:1px solid #ddd; text-align:center; margin</ins>: <ins class=\"diffchange diffchange-inline\">auto;\" cellspacing=\"15\"</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> P \\Rightarrow Q \\,<</ins>/<ins class=\"diffchange diffchange-inline\">math>|| [[Soubor:Venn A intersect B.svg|128px]] || [[Soubor:Commutative diagram for morphism.svg|96px]]</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\">| [[Matematick\u00e1 logika]] || [[Teorie mno\u017ein]] || [[Teorie kategori\u00ed]]</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\">=== Diskr\u00e9tn\u00ed 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\">Jako [[diskr\u00e9tn\u00ed matematika]] se ozna\u010duj\u00ed oblasti matematiky, kter\u00e9 se zab\u00fdvaj\u00ed studiem kone\u010dn\u00fdch diskr\u00e9tn\u00edch syst\u00e9m\u016f. Jej\u00ed podobory maj\u00ed obvykle velk\u00fd praktick\u00fd v\u00fdznam v&nbsp;[[Informatika|informatice]] a [[programov\u00e1n\u00ed]]. Pat\u0159\u00ed sem discipl\u00edny jako [[teorie slo\u017eitosti]], [[teorie informace]] nebo studium teoretick\u00fdch model\u016f [[po\u010d\u00edta\u010d]]\u016f, jak\u00fdm je [[Turing\u016fv stroj]]. Teorie v\u00fdpo\u010detn\u00ed slo\u017eitosti se zab\u00fdv\u00e1 \u010dasovou n\u00e1ro\u010dnost\u00ed [[algoritmus|algoritm\u016f]] zpracov\u00e1van\u00fdch v&nbsp;po\u010d\u00edta\u010d\u00edch, teorie informace mo\u017enostmi efektivn\u00edho skladov\u00e1n\u00ed informac\u00ed na z\u00e1znamov\u00fdch m\u00e9di\u00edch \u2013&nbsp;studuje pojmy [[komprese dat]], [[entropie]] apod. Nejslavn\u011bj\u0161\u00edm probl\u00e9mem t\u011bchto discipl\u00edn je \u201e[[Probl\u00e9m P versus NP|probl\u00e9m P = NP]]\u201c. Dal\u0161\u00edmi sou\u010d\u00e1stmi diskr\u00e9tn\u00ed matematiky jsou [[kombinatorika]], [[teorie graf\u016f]] nebo [[kryptografie]].</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\">:{| style=\"border:1px solid #ddd; text-align:center; margin: auto;\" cellspacing=\"15\"</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} (1,2,3) & (1,3,2) \\\\ (2,1,3) & (2,3,1) \\\\ (3,1,2) & (3,2,1) \\end{matrix}<</ins>/<ins class=\"diffchange diffchange-inline\">math> || [[Soubor:DFAexample.svg|96px]] || [[Soubor:Caesar3</ins>.<ins class=\"diffchange diffchange-inline\">svg|96px]] || [[Soubor:6n-graf</ins>.<ins class=\"diffchange diffchange-inline\">svg|96px]]</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\">| [[Kombinatorika]] || [[Teorie v\u00fdpo\u010dt\u016f]] || [[Kryptografie]] || [[Teorie graf\u016f]]</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\">=== Aplikovan\u00e1 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\">[[Aplikovan\u00e1 matematika]] pou\u017e\u00edv\u00e1 abstraktn\u00ed matematick\u00e9 n\u00e1stroje k&nbsp;\u0159e\u0161en\u00ed praktick\u00fdch probl\u00e9m\u016f z&nbsp;jin\u00fdch oblast\u00ed v\u011bdy, [[obchod]]u apod. [[Statistika]] pou\u017e\u00edv\u00e1 [[teorie pravd\u011bpodobnosti|teorii pravd\u011bpodobnosti]] k&nbsp;popisu, anal\u00fdze a p\u0159edpov\u00edd\u00e1n\u00ed jev\u016f, v&nbsp;nich\u017e hraje d\u016fle\u017eitou roli [[n\u00e1hoda]]. [[Numerick\u00e1 matematika]] vytv\u00e1\u0159\u00ed a teoreticky za\u0161ti\u0165uje po\u010d\u00edta\u010dov\u00e9 v\u00fdpo\u010detn\u00ed metody pro \u0159e\u0161en\u00ed \u0161irok\u00e9ho spektra \u00faloh p\u0159\u00edli\u0161 n\u00e1ro\u010dn\u00fdch pro \u010dlov\u011bka. Vyu\u017e\u00edv\u00e1 ji [[po\u010d\u00edta\u010dov\u00e9 modelov\u00e1n\u00ed]] s&nbsp;mnoha aplikacemi p\u0159i popisu a p\u0159edpov\u011bdi [[fyzika|fyzik\u00e1ln\u00edch]], [[meteorologie|meteorologick\u00fdch]], [[sociologie|sociologick\u00fdch]], [[chemie|chemick\u00fdch]] a jin\u00fdch jev\u016f. Ve sv\u011bt\u011b obchodu a [[bankovnictv\u00ed]] hraje d\u016fle\u017eitou roli [[finan\u010dn\u00ed matematika]]. K&nbsp;popisu [[ekonomie|ekonomick\u00fdch]] fenom\u00e9n\u016f slou\u017e\u00ed \u010dasto jazyk a v\u00fdsledky [[teorie her]].</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\">:{| style=\"border:1px solid #ddd; text-align:center; margin: auto;\" cellspacing=\"15\"</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\">| [[Soubor:Gravitation space source.png|96px]] || [[Soubor:BernoullisLawDerivationDiagram.png|96px]] || [[Soubor:Composite trapezoidal rule illustration small.png|96px]] || [[Soubor:Maximum boxed.png|96px]] || [[Soubor:Two red dice 01.svg|96px]] || [[Soubor:Oldfaithful3.png|96px]] || [[Soubor:Market Data Index NYA on 20050726 202628 UTC.png|96px]] || [[Soubor:Arbitrary-gametree-solved.png|96px]]</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\">| [[Matematick\u00e1 fyzika]] || [[Mechanika tekutin|Matematick\u00e9 modelov\u00e1n\u00ed tekutin]] || [[Numerick\u00e1 matematika]] || [[Optimalizace (matematika)|Optimalizace]] || [[Teorie pravd\u011bpodobnosti]] || [[Statistika]] || [[Finan\u010dn\u00ed matematika]] || [[Teorie her]]</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\">== Odkazy ==</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\">=== Reference ===</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\"><references </ins>/<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\">=== Literatura ===</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\">* {{Citace elektronick\u00e9 monografie</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\"> | p\u0159\u00edjmen\u00ed = Pavl\u00edkov\u00e1 Pavla, Schmidt Oskar</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\"> | titul = Z\u00e1klady matematiky, 1. vyd\u00e1n\u00ed</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\"> | url = http:</ins>//<ins class=\"diffchange diffchange-inline\">vydavatelstvi</ins>.<ins class=\"diffchange diffchange-inline\">vscht</ins>.<ins class=\"diffchange diffchange-inline\">cz/knihy/uid_isbn-80-7080-615-X</ins>/<ins class=\"diffchange diffchange-inline\">pages</ins>-<ins class=\"diffchange diffchange-inline\">img/</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\"> | datum vyd\u00e1n\u00ed = 2006</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\"> | isbn = 80-7080-615-X</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\"> | vydavatel = V\u0160CHT v Praze</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\">* {{Citace monografie</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\"> | p\u0159\u00edjmen\u00ed = Men\u0161\u00edk</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\"> | jm\u00e9no = Miroslav</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\"> | titul = Matematika a geometrie pro technickou praxi</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\"> | url = </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\"> | m\u00edsto = Praha</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\"> | rok = 1945</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\"> | po\u010det stran = 329</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\"> | vydavatel = \u00dastav pro u\u010debn\u00e9 pom\u016fcky pr\u016fmyslov\u00fdch a odborn\u00fdch \u0161kol</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\">=== Souvisej\u00edc\u00ed \u010dl\u00e1nky ===</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\">* [[Exaktn\u00ed]]</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\">* [[Logika]</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\">* [[Fyzika]]</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\">* [[Informa\u010dn\u00ed v\u011bda]]</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\">* [[Matematik]]</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\">=== Extern\u00ed odkazy ===</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\">* {{Commonscat|Mathematics}}</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\">* {{Otto|heslo=Mathematika}}</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\">* {{Wikicit\u00e1ty|t\u00e9ma=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\">* {{Wikislovn\u00edk|heslo=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\">* {{Wikiknihy|kniha=Kategorie: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>* [https://<ins class=\"diffchange diffchange-inline\">mathworld</ins>.<ins class=\"diffchange diffchange-inline\">wolfram</ins>.<ins class=\"diffchange diffchange-inline\">com/ Wolfram MathWorld] \u2013 matematick\u00e1 encyklopedie (anglicky)</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\">* [https:</ins>//<ins class=\"diffchange diffchange-inline\">isibalo.com</ins>/<ins class=\"diffchange diffchange-inline\">matematika Isibalo</ins>] <ins class=\"diffchange diffchange-inline\">\u2013 matematick\u00fd vzd\u011bl\u00e1vac\u00ed videoport\u00e1l</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>* [https://<ins class=\"diffchange diffchange-inline\">cs</ins>.<ins class=\"diffchange diffchange-inline\">khanacademy</ins>.org/<ins class=\"diffchange diffchange-inline\">math Matematika na Khan Academy]</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\">{{Polozam\u010deno}}</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\">{{Autoritn\u00ed data}}</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\">{{Port\u00e1ly|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\">{{1000 nejd\u016fle\u017eit\u011bj\u0161\u00edch \u010dl\u00e1nk\u016f}}</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\">[[Kategorie: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\">[[Kategorie:P\u0159\u00edrodn\u00ed v\u011bdy]]</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\">[[Kategorie</ins>:<ins class=\"diffchange diffchange-inline\">Studijn\u00ed p\u0159edm\u011bty]]</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\">[[Kategorie</ins>:<ins class=\"diffchange diffchange-inline\">Form\u00e1ln\u00ed v\u011bdy]</ins>]</div></td></tr>\n"
}
}