| 释义 |
cardinal arithmetic Given two (possibly infinite) cardinal numbers |X|, |Y|, where X, Y are sets, it is possible to define sums, products, and powers. The sum |X| + |Y| is defined as |X⊔Y|, the cardinality of the disjoint union. The product |X||Y| is defined as |X×Y|, the cardinality of the Cartesian product. The power |X||Y| is defined as the cardinality of the set of functions from Y to X. In particular, 2|Y| is the cardinality of the power set of Y. All these definitions are theorems for finite sets, so it makes sense to extend these definitions to infinite sets. Cantor showed that 2|ℕ| = |R|. See also Cantor-Schröder-Bernstein theorem, continuum hypothesis.
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