Real Number Divided by Itself

Theorem

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


Proof

\(\ds \forall x \ne 0: \, \) \(\ds \frac x x\) \(=\) \(\ds x \times \frac 1 x\) Definition of Real Division
\(\ds \) \(=\) \(\ds 1\) Real Number Axiom $\R \text M4$: Inverses for Multiplication

$\blacksquare$


Sources

  • 2000: James R. Munkres: Topology (2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 4$: The Integers and the Real Numbers: Exercise $1 \ \text{(j)}$
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