What do the statements 2 + 2 = 4 and "the sky is blue" have in common? One might say that they are both true. The statement about the sky can be confirmed by going outside and observing the color of the sky. How, then, can one confirm the truth of the statement 2 + 2 = 4? A statement in mathematics is considered true, or valid, on the basis of whether or not the statement can be proved within its mathematical system.

What does it mean to prove something mathematically? A mathematical proof is a convincing argument that is made up of logical steps, each of which is a valid deduction from a beginning statement that is known to be true. The reasons used to validate each step can be definitions or assumptions or statements that have been previously proved.

As an example of a proof, look at finding the sum of the first n whole numbers...