Writing an odd number as an integer

Statement

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

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

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.

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

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

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

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

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