Writing an even number as an integer

Statement

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

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

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 $.

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

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

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

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

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