Counterexample (original) (raw)

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A counterexample is a form of counter proof.

Given a hypothesis stating that is true for all , show that there exists a such that is false, contradicting the hypothesis.

See also

Proof

This entry contributed by Wiktor K. Macura

Explore with Wolfram|Alpha

More things to try:

• 3,2 TM rule 2139050
• CNF (P && ~Q) || (R && S) || (Q && R && ~S)
• inflection points (x^5+x^9-x-1)^3

Cite this as:

Macura, Wiktor K. "Counterexample." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Counterexample.html

Subject classifications

• Calculus and Analysis
• Calculus
• Maxima and Minima
• MathWorld Contributors
• Macura