counterexample

反例

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

Translation evidence: Literature usage

Meaning in context

An admissible instance satisfying a claim’s hypotheses but falsifying its asserted conclusion.

满足命题的假设而使其结论为假的一个具体实例。

Example

n=2n=2 refutes ∀n∈N  (n2=n)\forall n\in\mathbb N\;(n^2=n).

Usage and distinctions

An input violating the hypotheses is not a counterexample to the conditional theorem.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§7.2 The Universal Quantifier; §7.3 The Existential Quantifier · 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：§5.1 反例（名称证据，非正文定义证据） · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.