Real Division by One

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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

$\blacksquare$


Sources