# Real Number Subtracted from Itself leaves Zero

## Theorem

Let $x \in \R$ be a real number.

Then:

$x - x = 0$

where $x - x$ denotes the operation of real subtraction.

## Proof

 $\ds x - x$ $=$ $\ds x + \paren {-x}$ Definition of Real Subtraction $\ds$ $=$ $\ds 0$ Inverse for Real Addition

$\blacksquare$