Phrase guide

Hartogs number

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

For a given set X, the cardinality of the least ordinal number α such that there is no injection from α into X.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences, set-theory

Examples

  • 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).

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

After German-Jewish mathematician Friedrich Hartogs (1874–1943).