Shay's Maths and Art

A simple proof that two wrongs make a right

Actually this is a simple proof that two negative numbers when multiplied make a positive number. ( Multiplication between $a$ and $b$ is denoted $a\cdot b$ ).

We will prove that $-1\cdot -1 = 1$

Firstly we need to agree on a few rules

$-1\cdot 1 = 1 \cdot -1$
$1\neq0$
$1-1 = 0$
$-1\cdot 1 = -1$
$a\cdot(b+c) = a\cdot b + a\cdot c$

That final rule is called distributivity and is the key to understanding the following.

And we are done.

2019.12.07