Definition:Cardinal Number
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Definition
Let $S$ be a set.
The cardinal number of $S$ is defined as follows:
- $\card S = \displaystyle \bigcap \set {x \in \On : x \sim S}$
where $\On$ is the class of all ordinals.
Compare cardinality.
Also see
- Definition:Cardinal, where cardinal numbers are defined as equivalence classes of sets rather than as ordinal numbers.
Sources
- 1939: E.G. Phillips: A Course of Analysis (2nd ed.) ... (previous) ... (next): Chapter $\text {I}$: Number: $1.1$ Introduction
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 10.7$
- 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): Appendix $\text{A}$: Set Theory: Cardinal Numbers
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: cardinal number