Definitions for aleph-nought
aleph-nought

Princeton's WordNetRate this definition:0.0 / 0 votes

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

   the smallest infinite integer

WikipediaRate this definition:0.0 / 0 votes

1. aleph-nought

   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.

ChatGPTRate this definition:0.0 / 0 votes

1. aleph-nought

   Aleph-naught (also known as aleph-null or aleph-zero) is the concept in mathematics that represents the cardinality (size) of infinite sets which can be paired off one-to-one with the set of natural numbers, such as integers or rational numbers. It is the smallest cardinal number of infinity in set theory. Named after the first letter of the Hebrew alphabet, "aleph", it was introduced by mathematician Georg Cantor.

Matched Categories

1. • Large Integer

How to pronounce aleph-nought?

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-nought in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of aleph-nought in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of aleph-nought in Pythagorean Numerology is: 1

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=aleph-nought
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Aleph-Nought
3. ^ ChatGPT
   https://chat.openai.com