# Writing an odd number as an integer

## Statement

Every odd number can be written as a multiple of two plus one.

$$2k + 1, \text{where} \space k \in \Z$$

## Proof

These are the even numbers:

$$..., -3, -1, 1, 3, 5, 7, 9$$

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

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

$$2 * k + 1, \text{where} \space k \in \Z$$

## Proofs building upon this proof

### 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 odd number is even

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

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

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

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

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