Inverse Element/Examples/Rational Multiplication
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Examples of Inverse Elements
Consider the multiplicative group of positive rational numbers $\struct {\Q_{> 0}, \times}$.
- $\tfrac 4 {23}$ and $5 \tfrac 3 4$ are inverses of each other.
Proof
\(\ds 5 \tfrac 3 4\) | \(=\) | \(\ds \dfrac {5 \times 4 + 3} 4\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \tfrac {23} 4\) |
Then we have: | |||||||||||
\(\ds \tfrac 4 {23} \times \tfrac {23} 4\) | \(=\) | \(\ds \dfrac {4 \times 23} {23 \times 4}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 1\) |
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inverse: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inverse: 2.