How do you prove that a statement is not true?

In mathematics proving can be a very difficult process. In fact, some statements remain unproven to this day.

That said, usually the easiest way to prove that a statement is not true is by finding a counterexample.

Example:

Statement: Multiplying two numbers will always result in a bigger number.

Counterexample: 0.5*0.5 = 0.25

I have proven that the statement is not true by demonstrating that multiplying two numbers can in fact lead to a smaller number; 0.25 < 0.5