00A20-Counterexample.tex

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A \emph{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.
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