# Binary Subtraction

Subtraction is made by the operation of -1 defined to be the inverse or opposite of +1, so that for two natural numbers m and n:

• m = n – 1 is the same as n = m + 1.

Given m you get n = m + 1  by adding 1 to m (doing +1), and then you get back m = n – 1 back by subtracting 1 from n (doing -1).

Watch this example and play with the code.

Then take a look this subtraction machine.

Repeating -1 starting from 0 constructs the negative numbers -1, -2, -3, -4,…,. which together with the natural numbers created by repeating +1, constructs the

• integers $0,\,\pm 1,\,\pm 2,\,\pm 3,...,$.

The negative numbers is a wonderful gift to humanity by the heavens, or simply constructed by the human mind.