Cwangcisa ithiyori ngoku iyinxalenye yemathematics. Sonke siyazi ukuba ibizwa ngokuba siseti nakuphi na ukuqokelelwa kwezinto ezahlula ngokucacileyo omnye komnye, ezineempawu ezifanayo (okanye ezingaphezulu) ezifanayo. Cwangcisa izifundo zethiyori kwiipropathi kunye nobudlelwane beeseti; Le ntsimi yaphakanyiswa yiBolzano kunye noCantor, emva koko yagqitywa kwinkulungwane yama-20 ngezinye izibalo, ezinje ngoZermelo noFraenkel.
Kubalulekile ukuba iseti nganye ichazwe ngokugqibeleleyo, oko kukuthi, inokusekwa ngokuchanekileyo nokuba inikwe into, yeyayo okanye ayiyiyo iseti.
- Vula izibalo oku ngokuthe ngqo ngokuthe gca. Umzekelo, ukuba iseti yamanani angaphezulu kwe-1 nangaphantsi kwe-15 iyaqwalaselwa, kuyacaca ukuba le sethi iya kwenziwa ngamanani 2, 4, 6, 8, 10, 12 no-14 kuphela.
- Kwi Ulwimi oluqhelekileyo, ukuthetha ngeqela kunokuba yinto engacacanga ngakumbi, kuba ukuba sifuna ukwenza iqela leemvumi eziphambili, umzekelo, izimvo ziya kwahluka kwaye akukho kubambisana malunga nokuba ngubani oza kuba yinxalenye yeliqela kwaye ngubani . Ezinye iiseti ezizodwa ziiseti ezingenanto (zingenazinto) okanye iiseti zobunye (ezinento enye kuphela).
Inkqubo ye- izinto eziyinxalenye yeseti zibizwa ngokuba ngamalungu okanye izinto, kunye neeseti zimelwe kwizicatshulwa ezibhaliweyo ezifakwe kwizibiyeli. Ngaphakathi kumbhinqo, izinto zahlulwe ngeekoma. Banokumelwa yimizobo yeVenn, efaka ingqokelela yezinto ezenza iseti nganye kumgca oqinileyo ovaliweyo, ngokubanzi imilo yesangqa. Xa kukho imigca eliqela evaliweyo, nganye inikwa unobumba omkhulu (A, B, C, njl.
Ngeeseti onokuzenza imisebenzi; ezona ziphambili yimanyano, ukudibana, umahluko, ukuhambelana kunye nemveliso yeCartesian. Umdibaniso weeseti ezimbini A kunye no-B uchazwa njengeseti engu-A ∪ B kwaye oku kunento nganye ekwiyona inye kuzo. Inxaki ngokubanzi emele oku:
- UKUYA= {UJosé, uJerónimo}, B= {UMaría, uMabel, uMarcela}; AUB= {UJosé, uJerónimo, uMaría, uMabel, uMarcela}
- Iphe= {ipere, iapile}, C= {lemon, orenji}; F= {itsheri, currant};PUCUF = {ipere, iapile, ilamuni, iorenji, itsheri, currant}
- M={7, 9, 11}, U-N={4, 6, 8}; MUN={7, 9, 11, 4, 6, 8}
- R= {ibhola, skate, nesimbo}, UG= {phala, ibhola, skate}; RUG= {ibhola, isimbo, iskeyiti}
- C= {mnandi}, S= {ication}; CUS = {daisy, intyatyambo}
- C= {mnandi}, S= {ication}; T= {ibhotile}, CUSUT = {imargarita, ication, ibhotile}
- UG= {luhlaza, blowu, mnyama}, H= {mnyama}; GUH= {luhlaza, blowu, mnyama}
- UKUYA={ 1, 3, 5, 7, 9 }; B={ 10, 11, 12 }; AUB={ 1, 3, 5, 7, 9, 10, 11, 12 }
- D= {Lwesibini, Lwesine}, KUNYE= {NgoLwesithathu, ngoLwesihlanu}; NGOKO = {Lwesibini, Lwesithathu, Lwesine, Lwesihlanu}
- B= {iingcongconi, inyosi, ingcungcu}; C= {inkomo, inja, ihashe}; IBUC= {ingcongconi, inyosi, ingcungcu, inkomo, inja, ihashe}
- UKUYA={2, 4, 6, 8}, B={1, 2, 3, 4}; AUB={1, 2, 3, 4, 6, 8}
- Iphe= {itafile, isitulo}, Q= {itafile, isitulo}; PUQ= {itafile, isitulo}
- UKUYA= {isonka}, B = {itshizi}; AUB= {isonka, itshizi}
- UKUYA={20, 30, 40}, B= {5, 15}; AUB ={5, 15, 20, 30, 40}
- M= {Januwari, Februwari, Matshi, Epreli}, U-N= {Novemba, Disemba]; MUN= {Januwari, Februwari, Matshi, Epreli, Novemba, Disemba}
- F={12, 22, 32, 42}, UG= {a, e, i, o, u}; UKUGULA= {12, 22, 32, 42, a, e, i, o, u}
- UKUYA= {ihlobo}, B= {ubusika}; AUB= {ihlobo, ubusika}
- S= {imbadada, isiliphu, iflip flop}, R= {ihempe}; MAZANTSI= {imbadada, isiliphu, iflop flop, ihempe}
- H= {NgoMvulo, Lwesibini}, R= {NgoMvulo, Lwesibini}, D= {NgoMvulo, Lwesibini}; HURUD= {NgoMvulo, Lwesibini}
- Iphe= {bomvu, blowu}, Q= {luhlaza, tyheli}, PUQ= {bomvu, luhlaza, luhlaza, tyheli}
