Counterexample

How it is used

You find, give or construct a counterexample. Questions often say 'prove or disprove' or 'give a counterexample to show the statement is false'. One counterexample is enough to disprove a claim, but no number of examples can prove one.

Example sentences

1. Give a counterexample to the claim that x² > x for every real number x.

2. x = 0.5 is a counterexample, because 0.25 is less than 0.5.

Common collocations

• give a counterexample
• find a counterexample
• counterexample to the claim
• prove or disprove

Related terms

• proofA logical argument that shows, step by step from accepted facts, that a mathematical statement is always true.
• theoremAn important mathematical statement that has been proved to be true, such as the Pythagorean theorem.
• converseThe statement you get by swapping the 'if' part and the 'then' part of a conditional; the converse of 'if p, then q' is 'if q, then p'.
• proof by contradictionA method of proof in which you assume the statement is false and show that this leads to something impossible, so the statement must be true.

This word in other fields

The same English word can have a different meaning in another field:

• counterexample · Philosophy

More terms: Proofs and Mathematical Writing

• let x be
• lemma
• proof by induction
• QED
• without loss of generality
• it follows that