# Writing an even number as an integer

## Statement

Every even number can be written as a multiple of two.

$$2k, \text{where} \space k \in \Z$$

## Proof

These are the even numbers:

$$..., -4, -2, 0, 2, 4, 6, 8, ...$$

Note that every even number is two more than the previous one.

So every even number can be written as two times a whole number $k$.

$$2 * k, \text{where} \space k \in \Z$$

## Proofs building upon this proof

### An even number plus an even number is even

This proofs shows that an even number plus another even number will always be even.

### An even number plus an odd number is odd

This proofs shows that an even number plus an odd number will always be odd.

### An even number times an even number is even

This proofs shows that an even number times an even number will always be even.

### An even number times an odd number is even

This proofs shows that an even number times an odd number will always be even.