定理

Also known as mathematical theorem, mathematical sentence

基於既定陳述之上所證明出的陳述

AI overview

A theorem is a mathematical statement that has been proven to be true based on logical reasoning and previously established facts. The Pythagorean theorem, which describes the relationship between the sides of a right triangle, is a famous example that mathematicians have verified through hundreds of different proofs, showing how important and useful such proven statements are.

AI-generated from the Wikipedia summary — may contain errors.

Wikidata facts

Subclass of: conclusion
Part of: formal proof
Has part: mathematical proof
Based on: axiomatic system

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Commons category: Theorems
topic's main category: Category:Theorems
uses: deductive reasoning
has characteristic: existence
on focus list of Wikimedia project: Wikipedia:Vital articles/Level/4
maintained by WikiProject: WikiProject Mathematics
has list: list of theorems

Sources (3)

via Wikidata · CC0

Article · 中文

定理（英語：Theorem）是經過受邏輯限制的證明為真的陈述。一般來說，在數學中，只有重要或有趣的陳述才叫定理。證明定理是數學的中心活動。一个定理陈述一个给定类的所有（全称）元素一种不变的关系，这些元素可以是无穷多，它们在任何时刻都无区别地成立，而没有一个例外。（例如：某些是，某些是，就不能算是定理）。猜想是相信為真但未被證明的數學敘述，或者叫做命题，當它經過證明後便是定理。猜想是定理的來源，但並非唯一來源。一個從其他定理引伸出來的數學敘述可以不經過成為猜想的過程，成為定理。如上所述，定理需要某些邏輯框架，繼而形成一套公理（公理系統）。同時，一個推理的過程，容許從公理中引出新定理和其他之前發現的定理。在命題邏輯，所有已證明的敘述都稱為定理。

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