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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 \(|X\times U|=|Y\times W|=|X|\cdot|U|=|Y|\cdot|W|\).
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2
Propositions: 3
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References
Bibliography
- Ebbinghaus, H.-D.: "Einführung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition
