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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

1. Ebbinghaus, H.-D.: "Einführung in die Mengenlehre", BI Wisschenschaftsverlag, 1994, 3th Edition