ʻO kahi theorem kahi huaʻōlelo Helene i hoʻomaka ʻia a kuhi e hōʻike ana i kahi ʻoiaʻiʻo no kekahi kahua o ka ʻepekema, ka mea nona ka kikoʻī o ka hōʻike ʻia e ka ʻimi ʻana i nā manaʻo i hōʻike ʻia ma mua, i kapa ʻia nā axioms. ʻO ka maʻamau kākoʻo nā theorems i nā ʻepekema i kapa ʻia ʻo 'kikoʻī’, ʻo ia hoʻi ka 'formal' (makemakika, ka noʻonoʻo), ʻo ia nā mea e hoʻohana i nā mea kūpono e huki ai i nā hopena maʻamau.
ʻO ka noʻonoʻo ma hope o ka manaʻo o kahi theorem ʻo ia, ke hoʻokumu ʻia kēia mau mea ma nā manaʻo maoli i haʻi ʻia me ke kūpono a me ka pololei, ʻo ka mea a ka theorem e hōʻike ai he ʻoiaʻiʻo o ka paʻa loa.. ʻO kēia ka mea e ʻae iā lākou e lawelawe ma ke ʻano he kākoʻo no ka hoʻomohala ʻana i kekahi ʻepekema ʻepekema, me ka ʻole o ka hōʻoia e hōʻoia hou.
ʻO ke kiko waena o nā theorems ko lākou ʻano o kūpono. Ma ka laulā, a ke hoʻohālikelike hou ʻia me nā ʻano ʻepekema ʻē aʻe (e like me nā mea i hana ʻia ma o ka inferensi a i ʻole ka nānā ʻana), ʻo ke kumu mai kahi hana o kahi hana kūpono e hiki ke kauoha maʻalahi. I kēia ʻano, hoʻomaka nā theorems mai a kuhiakau paʻa, ʻo ia ka mea āu e makemake ai e hōʻike; kahi palapala kākau, ʻo ia nō ka hōʻike hōʻikeʻike, a he corollary, ʻo ia ka hopena hōʻea ʻia i ka pau ʻana o ka hōʻike.
E like me ka mea i ʻōlelo ʻia, ʻo ka manaʻo nui o nā theorems ka nīnau no ka hiki mau a me ka hiki ke helu inoa ʻia a ʻae hou ʻia i nā manawa āpau. Eia naʻe, inā kū mai kahi hanana kahi i nalowale ka theorem i kona universally, lilo koke ka theorem i mea ʻole.
Ua lawe ʻia ka manaʻo o ka theorem e ʻepekema ʻē aʻe (economics, psychology a i ʻole ʻepekema politika, a me nā mea ʻē aʻe) e koho i kekahi mau manaʻo nui a hoʻokumu paha e hoʻomalu i kēlā mau māla, ʻoiai ʻaʻole ala kēia mau mea ma o ka hana i wehewehe ʻia. I kēia mau hihia, ʻaʻole hoʻohana ʻia nā axioms akā ua hana ʻia nā hana e nā kaʻina hana e like me ka nānā ʻana a i ʻole ka ʻikepili helu.
Hōʻiliʻili ka papa inoa aʻe i nā laʻana o ka theorems a me kahi wehewehe pōkole o ka mea e postulate ai:
- Theorem ʻo Pythagoras: ka pilina ma waena o ke ana o ka hypotenuse a me nā wāwae, i ka hihia o nā triangles pono.
- Theorem helu helu: Ke ulu nei ka laina helu, e emi ana a emi mai nā helu mai kēlā hui.
- ʻO Theorem Binomial: ʻano hana no ka hoʻoponopono ʻana i nā mana o nā binomial (nā hoʻohui a i ʻole nā unuhi o nā mea).
- Theorem ʻo Frobenius: ka hoʻonā ʻana i nā kumuhana no nā ʻōnaehana o nā kaulike kaulike.
- Thales theorem: nā ʻano e pili ana i nā huina a me nā ʻaoʻao o nā huinakolu like, a me nā waiwai ʻē aʻe o lākou.
- ʻO ke kumu mele a Euler: ʻo ka helu o nā piko a me ka helu o nā helehelena e like me ka helu o nā kihi hoʻohui 2.
- ʻO kā Ptolemy haʻi'ōlelo: ʻO ka huina o nā huahana o nā diagonal ua like ia me ka huina o nā huahana o nā ʻaoʻao ʻaoʻao.
- Cauchy-Hadamard theorem: Ka hoʻokumu ʻana i ka radius o ka hoʻohui ʻana o kahi mana o nā mana e hoʻokokoke i kahi hana a puni kahi kiko.
- ʻO kā Rolle haʻi'ōlelo: I kahi wā i loiloi ʻia nā mea ʻoi loa i kahi hana ʻokoʻa i like, aia ma laila kahi kiko kahi e nalo ai ka derivative.
- ʻO ke kumu manaʻo waiwai: Inā hoʻomau a ʻano ʻokoʻa kekahi hana ma waena o kahi wā, e loaʻa kahi kiko i kēlā wā i kahi e kūlike ai ke ʻano o ka mea paʻa me ke kekona.
- ʻO Cauchy Dini's theorem: Nā kūlana no ka helu ʻana i nā derivatives i ka hihia o nā hana implicit.
- Helu mele: ʻO ka derivation a me ka hoʻopili ʻana o kahi hana he hana i hoʻohuli ʻia.
- ʻOrlelo aʻoaʻo Arithmetic: Hiki ke hōʻike i kēlā me kēia helu helu maikaʻi ma ke ʻano he huahana o nā kumu nui.
- Bayes theorem (helu helu): Ke kiʻina e loaʻa ai nā hopena kūlana.
- ʻO Theorema Cobweb (economics): Ke wehewehe e wehewehe i ka hoʻokumu ʻia ʻana o nā huahana i hoʻokumu ʻia ma muli o ke kumukūʻai mua.
- ʻO Theorem (economics) ʻo Marshall Lerner: Ka Ikepili o ka hopena o ka hoʻoliʻiliʻi kālā ma nā ʻano o nā nui a me nā kumukūʻai.
- Coor theorem (economics): ʻO ka hopena no nā hihia o waho, e mālama nei i ka hoʻopau ʻana.
- Theorem koho koho Median (ʻepekema politika): Mālama ka ʻōnaehana koho balota i ka balota waena.
- ʻO kā Thelete Baglini (ʻepekema politika, Argentina): Hoʻolālā ka mea politika i kāna mau noi i ke kikowaena ke hoʻokokoke ʻo ia i nā kūlana o ka mana.
- ʻO kā Thomas theorem (sociology): Inā wehewehe ka poʻe i nā kūlana he maoli, lilo lākou i maoli i kā lākou hopena.
