nLab counterexample

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Contents

Idea

In mathematics, a counterexample is an example for the negation of a statement.

A counterexample to a conjecture is a way to satisfy the hypotheses of the conjecture such that the conclusion is a contradiction.

In constructive mathematics one considers also “weak counterexamples”. See there for more.

Examples

References

Examples of counterexamples in topology:

See also:

Last revised on May 31, 2022 at 07:57:36. See the history of this page for a list of all contributions to it.