# Real Division by One

## Theorem

$\forall x, y \in \R: \dfrac x 1 = x$

## Proof

 $\displaystyle \frac x 1$ $=$ $\displaystyle x \times \frac 1 1$ Definition of Division $\displaystyle$ $=$ $\displaystyle x \times 1$ Real Number Divided by Itself $\displaystyle$ $=$ $\displaystyle x$ Real Number Axioms: $\R M 4$: Identity

$\blacksquare$