Word Pronunciation & Dictionary

hartogs number

Word Rarity Very rare

Frequency: Zipf frequency 0.00 in modern English

Syllables: har-togs num-ber
IPA

21

Scrabble Score

13

Letters

3

Syllables

12

Unique Chars

Meaning

noun

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

Example Sentences

"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)."
"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."

Etymology

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

Inflected Forms

Hartogs numbers (plural) Hartogs' number (alternative)

Phrases

Hartogs function

Frequently Paired Words

equipotent Hartogs function

Questions

What does hartogs number mean?: For a given set X, the cardinality of the least ordinal number α such that there is no injection from α into X.
Where does hartogs number come from?: After German-Jewish mathematician Friedrich Hartogs (1874–1943).

How to pronounce hartogs number

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