What is the math definition for 'counterexample'? When is counterexample used?

A counterexample is something that proves a statement, or equation, wrong. A counterexample is used in math when someone creates a theorem, writes an equation, or creates a new rule and someone proves it to be false.

For Example:

Let's say that I said an even number plus an odd number always equals an even number. A counterexample of that would be 4 + 5 = 9, because 9 is odd, therefore proving the statement wrong.