# Real Number Divided by Itself

## Theorem

$\forall x \in \R_{\ne 0}: \dfrac x x = 1$

## Proof

 $\, \displaystyle \forall x \ne 0: \,$ $\displaystyle \frac x x$ $=$ $\displaystyle x \times \frac 1 x$ Definition of Real Division $\displaystyle$ $=$ $\displaystyle 1$ Real Number Axioms: $\R M 4$: Inverses

$\blacksquare$