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TEOREMA

TEOREMA (yunoni theoremma, az theoreo— muoina, tadqiq) dar matematika, jumla yo qaziyaero guyand, ki zimni isbot muqarrar meshavad (bar khilofi aksioma). Har yak, teorema az shart va khulosa iborat ast. Masalan, 1) agar khati rost ba yake az du hamvorihoi parallel perpendikulyar boshad, on goh vay ba hamvorii duyum ham pendikulyar ast. 2) Agar yake az kunjhoi sekunja rost bashad, on goh du kunji digar tez meboshad; bad az kalimai «agar» shart va bad az kalimai «on goh» khulosai teorema meoyad. Agar dar teorema joi shart va khulosaro ivaz namoem, teoremai aks hosil meshavad.

Teoreamai ba teoremai 1 aks chunin ast: du hamvorii ba yak khati rost perpendikulyar ba hamdigar paralleland. Teoremahoi ibtidoi (teoremai rost) va aks bayni khud baraksand. Na har guna teoremai aks haqiqist. Baroi misoli 1 teoremai aks haqiqi, ammo baroi misoli 2 gayrihaqiqist. Durustii teoremahoi bayni khud baraks chunin mano dorad: ijroi sharti har yaki on az tanho kofi, balki baroi durustii khulosa zarur ast (sharti zaruri va kofii teorema).

Agar shart va khulosai teoremaro bo inkori onho ivaz kunem, on goh teoremae hosil meshavad, ki ba teoremai dodashuda muqobil ast. Teoremai ba teoremai 1 muqobil in ast: agar khati rost ba yake az du hamvorii parallel perpendikulyar naboshad, on goh vay ba hamvorii digar ham perpendikulyar nameboshad. Teoremahoi aks va muqobil ba ham musoviand. Ba monandi hamin teoremai ba teoremai muqobil aks bo teoremai ibtidoi musovist.

T. Q. Juraev.

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