Proposition: Fundamental Counting Principle

Let \(S\) be a Cartesian product of a finitely many finite sets \[S=S_1\times S_2\times \ldots \times S_n.\] Then the cardinality of the set \(S\) is given by the product of cardinalities of its subsets. \[|S|=\prod_{i=1}^n |S_i|.\]

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9 10


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References

Bibliography

  1. Aigner, Martin: "Diskrete Mathematik", vieweg studium, 1993