Hartogs number
nounEtymology After German-Jewish mathematician Friedrich Hartogs (1874–1943).
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Mathematics, Sciences, Set theory For a given set X, the cardinality of the least ordinal number α such that there is no injection from α into X.
- 1973 [North-Holland], Thomas J. Jech, The Axiom of Choice, 2013, Dover, page 160, Let p be an infinite cardinal, |X|=p and let א=א(p) be the Hartogs number of p.
- 1995, The Bulletin of Symbolic Logic, Volume 1, Association for Symbolic Logic, page 139, If the Power Set Axiom is replaced by "א(x) is bound for every x" where א(x)={a|∃f(f is one-to-one function from a into x)}, then the theory is denoted by ZFH (H stands for Hartogs' Number).
1 more example
- Since the proof of Hartogs' Theorem does not appeal to the Axiom of Choice, the Hartogs number of a set X exists whether or not X has a well-ordering.2014, Barnaby Sheppard, The Logic of Infinity, Cambridge University Press, page 341:
- Related terms
- equipotent, Hartogs function