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Hartogs number

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

Noun

Hartogs number (plural Hartogs numbers)

  1. 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.
    • 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).1995, The Bulletin of Symbolic Logic, Volume 1, Association for Symbolic Logic, page 139

Forms of Hartogs number

pluralHartogs numbers
alternative formHartogs' number

Origin of Hartogs number

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

Questions about Hartogs number

What does Hartogs number mean?
Hartogs number means for a given set X, the cardinality of the least ordinal number α such that there is no injection from α into X.
What part of speech is Hartogs number?
Hartogs number is a noun.
What is the plural of Hartogs number?
The plural of Hartogs number is Hartogs numbers.

Words near Hartogs number in the dictionary

  1. Hartneys
  2. Hartnup disease
  3. Hartnup disorder
  4. Hartog
  5. Hartogs
  6. Hartogs number
  7. Hartogs numbers
  8. Hartoin
  9. Hartola
  10. Harton
  11. Hartons

Source and license

Adapted from Wiktionary: Hartogs number (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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