Cartesian Product/Examples/Product of Arbitrary Sets 1
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Examples of Cartesian Products
Let $S = \set {1, 2, 3}$.
Let $T = \set {a, b}$.
Then:
\(\ds S \times T\) | \(=\) | \(\ds \set {\tuple {1, a}, \tuple {1, b}, \tuple {2, a}, \tuple {2, b}, \tuple {3, a}, \tuple {3, b} }\) | ||||||||||||
\(\ds T \times S\) | \(=\) | \(\ds \set {\tuple {a, 1}, \tuple {a, 2}, \tuple {a, 3}, \tuple {b, 1}, \tuple {b, 2}, \tuple {b, 3} }\) |
Sources
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 1.7$. Pairs. Product of sets: Exampe $22$