theorem

theorem — noun

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

1.名詞C1
釋義

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.

proved + famous theorem + about [topic]

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

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.