Inverse of Subset/Group/Examples/Subset of Reals under Multiplication
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Example of Inverse of Subset of Group
Let $\struct {\R, \times}$ be the multiplicative group of (non-zero) real numbers.
Let $S = \set {-1, 2}$.
Then the inverse $S^{-1}$ of $S$ is:
- $S^{-1} = \set {-1, \dfrac 1 2}$
Proof
Taking each element of $S$:
\(\ds \paren {-1}^{-1}\) | \(=\) | \(\ds -1\) | ||||||||||||
\(\ds 2^{-1}\) | \(=\) | \(\ds \dfrac 1 2\) |
$\blacksquare$
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Subgroups