Lemma: Finite Cardinal Numbers and Set Operations

Let \(X, Y, U\) and \(W\) be finite sets. The following properties of cardinal numbers are fulfilled:

(1) From \(|X|=|Y|, |U|=|W|\) and \(X\cap U=\emptyset, Y\cap W=\emptyset\) it follows that \(|X\cup U|=|Y\cup W|=|X| + |U|=|Y| + |W|\).

(2) From \(|X|=|Y|\) and \(|U|=|W|\) it follows that \(|X\times U|=|Y\times W|=|X|\cdot|U|=|Y|\cdot|W|\).

Proofs: 1

Proofs: 1 2
Propositions: 3


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References

Bibliography

  1. Ebbinghaus, H.-D.: "Einf├╝hrung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition