Category:Counterexamples
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This category contains results about Counterexamples.
Let $X$ be the universal statement:
- $\forall x \in S: \map P x$
That is:
Such a statement may or may not be true.
Let $Y$ be the existential statement:
- $\exists y \in S: \neg \map P y$
That is:
- There exists at least one element $y$ of the set $S$ such that the property $P$ does not hold.
It follows immediately by De Morgan's laws that if $Y$ is true, then $X$ must be false.
Such a statement $Y$ is referred to as a counterexample to $X$.
Pages in category "Counterexamples"
The following 3 pages are in this category, out of 3 total.