proof by contraposition

逆否法证明

Foundations & Logic · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A classical proof of $P\to Q$ by deriving $\neg P$ from $\neg Q$.

通过证明逆否命题 ¬Q→¬P 来确立原命题 P→Q 的经典证明方法。

Example

To show $n^2$ odd implies $n$ odd, show even $n=2k$ has even square $4k^2$.

Usage and distinctions

The converse Q→P is not the contrapositive; reversing an implication alone is invalid.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§5.1 Proof by Contradiction; §5.2 Some Classical Principles · Checked 2026-10-14

Translation sources

1. 高等教育出版社 — 数学证明 通往高等数学的阶梯（第4版）影印版，官方中文目录官方中文目录：§3.3 逆否法证明（名称证据，非正文定义证据） · Checked 2026-10-14

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