What does aleph-null mean?

Definitions for aleph-null
aleph-null

This dictionary definitions page includes all the possible meanings, example usage and translations of the word aleph-null.

Princeton's WordNet

  1. aleph-null, aleph-nought, aleph-zeronoun

    the smallest infinite integer

Wiktionary

  1. aleph-nullnoun

    The first of the transfinite cardinal numbers; corresponds to the number of positive integers, also called natural numbers. Georg Cantor showed that even all the rational numbers could be put in one-to-one correspondence with them, and are therefore countable, enumerable or denumerable.

Wikipedia

  1. aleph-null

    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.

ChatGPT

  1. aleph-null

    Aleph-null, also known as aleph-zero or aleph naught, is the smallest infinite cardinal number in set theory, a branch of mathematics. It represents the cardinality (size) of any set that can be put into a one-to-one correspondence with the set of natural numbers. This includes sets such as the set of integers, the set of rational numbers, and other countable sets. Aleph-null is denoted as ℵ₀ in mathematical notation.

Suggested Resources

  1. aleph-null

    The aleph-null symbol -- In this Symbols.com article you will learn about the meaning of the aleph-null symbol and its characteristic.

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Numerology

  1. Chaldean Numerology

    The numerical value of aleph-null in Chaldean Numerology is: 3

  2. Pythagorean Numerology

    The numerical value of aleph-null in Pythagorean Numerology is: 2


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"aleph-null." Definitions.net. STANDS4 LLC, 2024. Web. 29 Mar. 2024. <https://www.definitions.net/definition/aleph-null>.

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