08.5 Counterexamples and Edge Cases
8.5 Counterexamples and Edge Cases A counterexample is a single instance that shows a statement is false. An edge case is a boundary or extreme situation where a statement is most likely to fail or require adjustment. Together, they form one of the most reliable tools in problem solving. A universal statement has the form: $$ \text{for all } x,\ P(x). $$ To disprove it, one example with $\neg P(x)$...