theorem 定理 — 中文意思、英文定義、例句

1.名詞C1

釋義

定理

經邏輯證明為真的數學命題

In mathematics and logic, a statement whose truth has been established by a valid chain of reasoning, working step by step from agreed-upon starting points (definitions and axioms) and previously proven results.

例句

Pythagoras proved his famous theorem about right-angled triangles more than two thousand years ago.

Pythagoras 在兩千多年前證明了關於直角三角形的著名定理。

proved + famous theorem + about [topic]

Every student in the advanced maths class had to prove the theorem using basic algebra.

高階數學課上的每個學生都必須用基礎代數證明同一個定理。

prove a theorem using [method]

同義詞

proposition
A broader term for any statement put forward for consideration; a proposition becomes a theorem only after it has been proved.
lemma
A minor theorem proved as a stepping stone toward a larger, more important theorem.
corollary
A statement that follows directly from a theorem with little or no additional proof needed.

反義詞

conjecture
A statement believed to be true but not yet proved; the opposite status of a theorem.

用法筆記

Used primarily in formal mathematics and logic contexts. A theorem is distinct from a hypothesis (an unproven guess) and an axiom (a starting assumption that is accepted without proof). Common verbs used with this sense include prove, state, apply, and demonstrate.

常見錯誤

❌Einstein's theory of relativity is just a theorem.

✅Einstein's theory of relativity is a scientific theory, not a theorem.

💡A scientific theory is a broad explanatory framework supported by evidence, while a theorem is a specific statement proved within a formal system such as mathematics.

❌The scientist made a theorem about the weather.

✅The scientist proposed a hypothesis about the weather.

💡Theorem is almost never used for natural or social sciences; use hypothesis or theory instead.

theorem

theorem — 名詞

1. In mathematics and logic, a statement whose truth has been established by a vali

用法筆記

常見錯誤