A counterexample is a special kind of example that disproves a statement or proposition. Counterexamples are often used in math to prove the boundaries of possible theorems. ... Counterexamples are helpful because they make it easier for mathematicians to quickly show that certain conjectures, or ideas, are false.

What is the purpose of a counterexample?

A counterexample to a mathematical statement is an example that satisfies the statement's condition(s) but does not lead to the statement's conclusion. Identifying counterexamples is a way to show that a mathematical statement is false.

How does counterexample help in problem solving?

Counterexamples are often used to prove the limitations of possible theorems. By using counterexamples to display that definite estimations are false, mathematical researchers avoid going down blind paths and learn how to modify estimations to produce demonstrable theorems.