Definitions for aleph number
aleph num·ber

WiktionaryRate this definition:0.0 / 0 votes

1. aleph numbernoun

   Any of a sequence of numbers used to represent the cardinality of infinite sets, denoted by the Hebrew letter aleph.

WikipediaRate this definition:0.0 / 0 votes

1. Aleph number

   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.

WikidataRate this definition:0.0 / 0 votes

1. Aleph number

   In set theory, a discipline within mathematics, the aleph numbers are a sequence of numbers used to represent the cardinality of infinite sets. They are named after the symbol used to denote them, the Hebrew letter aleph. The cardinality of the natural numbers is, the next larger cardinality is aleph-one, then and so on. Continuing in this manner, it is possible to define a cardinal number for every ordinal number α, as described below. The concept goes back 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 commonly found in algebra and calculus. Alephs measure the sizes of sets; infinity, on the other hand, is commonly defined as an extreme limit of the real number line, or an extreme point of the extended real number line.

How to pronounce aleph number?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say aleph number in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of aleph number in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of aleph number in Pythagorean Numerology is: 7

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Aleph_Number
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Aleph_Number
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=aleph number