Cardinality of Cartesian Product of Finite Sets/Corollary/Proof 1
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Corollary to Cardinality of Cartesian Product of Finite Sets
- $\card {S \times T} = \card {T \times S}$
Proof
| \(\ds \card {S \times T}\) | \(=\) | \(\ds \card S \times \card T\) | Cardinality of Cartesian Product of Finite Sets | |||||||||||
| \(\ds \) | \(=\) | \(\ds \card T \times \card S\) | Integer Multiplication is Commutative | |||||||||||
| \(\ds \) | \(=\) | \(\ds \card {T \times S}\) | Cardinality of Cartesian Product of Finite Sets |
$\blacksquare$