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.

In the Vinony graph

Vinony's link graph records 799 inbound references to 定理, and connects out to logic, semantic theory of truth and theory.

Vinony files it under Concepts in logic, Logical consequence and Logical expressions.

Vinony links it to 92 Wikipedia language editions.

Wikidata facts

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

Show 7 more facts

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。

Abstract from DBpedia / Wikipedia · CC BY-SA