counterexample

Thân thiện

A student presents a counterexample on the whiteboard.

Definition

1. Noun:
   • A specific example that disproves a general statement or theory: A "counterexample" is an instance or case that demonstrates a proposed rule, claim, or hypothesis is false. It is a fundamental tool in logic, mathematics, and argumentation for refuting universal statements.

Examples of Usage

• Noun:
  • The mathematician found a single counterexample that invalidated the long-standing conjecture.
  • His claim that "all birds can fly" is easily disproven by the counterexample of a penguin.
  • A good counterexample is often more valuable than many supporting examples in logical proof.

Advanced Usage

• "To serve as a counterexample to": To function as evidence that refutes a claim.
  • The discovery of a planet orbiting a pulsar served as a counterexample to the theory that only single stars could host planets.
• "To construct/bring forward a counterexample": To deliberately create or present an instance to disprove something.
  • In the debate, she skillfully constructed a counterexample to her opponent's sweeping generalization.

Variants and Related Words

• Counterevidence (n): Evidence that contradicts or opposes a claim.
• Refutation (n): The act of proving a statement or theory to be wrong or false.

Synonyms

• Disproof: Evidence or argument that establishes the falsity of something.
• Exception: A case that does not follow a rule or pattern.

Related Phrases

• Proof by counterexample: A logical method of proving a statement false by providing a single instance where it fails.
  • The theorem was dismissed through a simple proof by counterexample.

Học thuật

Noun

1. refutation by example