Real Division by One
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Theorem
- $\forall x \in \R: \dfrac x 1 = x$
Proof
| \(\ds \frac x 1\) | \(=\) | \(\ds x \times \frac 1 1\) | Definition of Real Division | |||||||||||
| \(\ds \) | \(=\) | \(\ds x \times 1\) | Real Number Divided by Itself | |||||||||||
| \(\ds \) | \(=\) | \(\ds x\) | 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 $1 \ \text{(k)}$