AQA GCSE Mathematics · 8300
Specification A6 · Paper 1, Paper 2, Paper 3
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GCSE Mathematics · key term
A value or example that shows a general claim is false.
Used by AQA and Edexcel
Specification A6 · Paper 1, Paper 2, Paper 3
Specification A6 · Paper 1, Paper 2, Paper 3
A single example that shows a general claim is false.
Revise: Equations and ProofSubstitution is useful for disproving an alleged identity: one value for which the two sides differ is a counterexample. Testing several values cannot prove an identity, however, because untested values remain. A proof requires valid algebra that works generally.
One counterexample is enough to show that a proposed identity is false, but it does not identify every value that satisfies the resulting equation.
One counterexample is enough to disprove a universal claim, but one successful example cannot prove it.
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