counterexample

A counterexample is an example which is used to prove that a statement is false.

For instance, to disprove that the statement “For all $n$, $2^{2^n}+1$ is prime.”, one could exhibit $5$ as a counterexample; since $2^{2^5}+1=641\times 6700417$, the statement is false.

Title	counterexample
Canonical name	Counterexample
Date of creation	2013-03-22 14:43:00
Last modified on	2013-03-22 14:43:00
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	5
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 00A20