Proof

Hampshire College
Low-Tech Computing

Prove: there are as many even numbers as there are natural numbers.

Proof: any even number can be divided by 2 and the result is one unique natural number, and any natural number can be multiplied by 2 and the result is an even number. Therefore, every even number has a corresponding natural number and there are no natural numbers that do not have a corresponding even number. If there were not as many even numbers as there are natural numbers, then there would have to be some natural number that could not be multiplied by 2 to get an even number, or an even number that, when divided by 2, produced more than one natural number. Neither of these are the case. Therefore, there are as many even numbers as there are natural numbers. ☺