What does aleph-one mean?
Definitions for aleph-one
aleph-one
This dictionary definitions page includes all the possible meanings, example usage and translations of the word aleph-one.
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Wiktionary
aleph-onenoun
The second of the transfinite cardinal numbers; according to the continuum hypothesis, it corresponds to the number of real numbers.
Wikipedia
aleph-one
In mathematics, particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets that can be well-ordered. They were introduced by the mathematician Georg Cantor and are named after the symbol he used to denote them, the Semitic letter aleph ( ℵ {\displaystyle \,\aleph \,} ).The cardinality of the natural numbers is ℵ 0 {\displaystyle \,\aleph _{0}\,} (read aleph-nought or aleph-zero; the term aleph-null is also sometimes used), the next larger cardinality of a well-orderable set is aleph-one ℵ 1 , {\displaystyle \,\aleph _{1}\;,} then ℵ 2 {\displaystyle \,\aleph _{2}\,} and so on. Continuing in this manner, it is possible to define a cardinal number ℵ α {\displaystyle \,\aleph _{\alpha }\,} for every ordinal number α , {\displaystyle \,\alpha \;,} as described below. The concept and notation are due to Georg Cantor, who defined the notion of cardinality and realized that infinite sets can have different cardinalities. The aleph numbers differ from the infinity ( ∞ {\displaystyle \,\infty \,} ) commonly found in algebra and calculus, in that the alephs measure the sizes of sets, while infinity is commonly defined either as an extreme limit of the real number line (applied to a function or sequence that "diverges to infinity" or "increases without bound"), or as an extreme point of the extended real number line.
Suggested Resources
aleph-one
The aleph-one symbol -- In this Symbols.com article you will learn about the meaning of the aleph-one symbol and its characteristic.
Numerology
Chaldean Numerology
The numerical value of aleph-one in Chaldean Numerology is: 3
Pythagorean Numerology
The numerical value of aleph-one in Pythagorean Numerology is: 4
Translations for aleph-one
From our Multilingual Translation Dictionary
- алеф-одинRussian
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"aleph-one." Definitions.net. STANDS4 LLC, 2024. Web. 26 Apr. 2024. <https://www.definitions.net/definition/aleph-one>.
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