Last Updated：2025/11/26

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(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.

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Hartogs number

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Source Word

Hartogs number

Noun

Japanese Meaning

(集合論) 任意の集合 X に対して、X への単射が存在しない最小の順序数 α の濃度

What is this buttons?

To compare the sizes of infinite sets, set theorists often examine the Hartogs number of a given set, which is the cardinality of the least ordinal that cannot be injected into that set.

Google Translation / DeepL Translation

無限集合の大きさを比較するために、集合論者はしばしば与えられた集合に対して、その集合へ単射が存在しない最小の順序数の基数を調べる。

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Sense（1）

Let p be an infinite cardinal, |X|=p and let א=א(p) be the Hartogs number of p.

Google Translation / DeepL Translation

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Hartogs numbers

（ plural ）

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Hartogs number

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Hartogs number

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