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Glite Dictionary
aleph-nought

aleph-nought

9.9
The number of all counting numbers that is the smallest kind of infinity
  • noun
  • /ˈɑːlɛf noʊt/
  • UK
translation icon : aleph-cero
  • Cantor proved that the set of natural numbers has a cardinality of aleph-nought.

Examples

  • No finite number can equal aleph-nought, as it represents the smallest infinity.

  • The concept of aleph-nought is central in set theory and the study of infinite sets.

  • The concept of aleph-nought is fundamental in set theory.

  • Many mathematicians study aleph-noughts to understand infinity.

  • Cantor proved that the set of natural numbers has a cardinality of aleph-nought.

  • No finite number can equal aleph-nought, as it represents the smallest infinity.

  • The concept of aleph-nought is central in set theory and the study of infinite sets.

Synonyms

aleph-zero
vsaleph-nought
  • Specialized
1 9.9

The size of all whole numbers like 0, 1, 2 and so on, the smallest infinity

is identical in meaning but differs only in written form or notation
aleph-null
vsaleph-nought
  • Specialized
9.9

The size of the smallest infinity, the number of counting numbers like 1, 2, 3

is identical in meaning but differs only in written form or notation

How Large

aleph-nought
  • UK
9.9
finite
56 4.1

Surface Forms

aleph-nought singular
aleph-noughts plural

Morphology

aleph-nought = aleph + nought (opaque) = aleph + nought

Although built from 'aleph' + 'nought', the specific mathematical meaning (the smallest infinite cardinal) is technical and not derivable by a typical learner from the component meanings.

Etymology

Aleph-nought joins the Hebrew letter aleph and the English word nought, which means 'zero' or 'nothing', so you can imagine a 'first nothing' as a picture for the first level of infinity. That's why aleph-nought means the smallest infinite size, the number of counting numbers 1, 2, 3 and so on.