Real Number Divided by Itself

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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

$\blacksquare$


Sources