Subset Product/Examples/Subsets of Reals under Multiplication
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Example of Subset Product
Let $\struct {\R, \times}$ be the multiplicative group of (non-zero) real numbers.
Let $S = \set {-1, 2}$.
Let $T = \set {1, 2, 3}$.
Then the subset product $S T$ is:
- $ST = \set {-1, -2, -3, 2, 4, 6}$
Proof
Taking each ordered pair $\tuple {s, t}$ from $S \times T$:
\(\ds -1 \times 1\) | \(=\) | \(\ds -1\) | ||||||||||||
\(\ds -1 \times 2\) | \(=\) | \(\ds -2\) | ||||||||||||
\(\ds -1 \times 3\) | \(=\) | \(\ds -3\) | ||||||||||||
\(\ds 2 \times 1\) | \(=\) | \(\ds 2\) | ||||||||||||
\(\ds 2 \times 2\) | \(=\) | \(\ds 4\) | ||||||||||||
\(\ds 2 \times 3\) | \(=\) | \(\ds 6\) |
$\blacksquare$
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Subgroups