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Glite Dictionary
aleph-zero

aleph-zero

1 9.9
The size of all whole numbers like 0, 1, 2 and so on, the smallest infinity
  • noun
  • /ˈɑːlɛf ˈzɪroʊ/
  • Specialized
translation icon : aleph-cero
  • Many mathematicians study aleph-zero to understand infinity.

Examples

  • The cardinality of the set of all natural numbers is denoted by aleph zero.

  • Set theory defines aleph-zero as the cardinality of all natural numbers.

  • No real-world collection can be said to have aleph-zero members, since it describes an abstract infinity.

  • The concept of aleph-zero is essential to understanding infinite sets in mathematics.

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

  • In set theory, aleph zero represents the smallest infinite quantity of natural numbers.

  • Mathematicians use aleph zero to describe levels of infinity in their proofs.

Synonyms

aleph-null
vsaleph-zero
  • Specialized
9.9

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

is identical in meaning but uses a different common spelling
aleph-nought
vsaleph-zero
  • UK
9.9

The number of all counting numbers that is the smallest kind of infinity

is the same concept but appears under an alternate spelling

How Large

aleph-zero
  • Specialized
1 9.9
finite
56 4.1

Surface Forms

aleph-zero singular
aleph-zeros plural

Morphology

aleph-zero = aleph + zero (opaque) = aleph + zero

Although built from 'aleph' and 'zero', the term is a conventional mathematical label (ℵ₀) whose meaning 'the smallest infinite cardinal' is not inferable from the ordinary meanings of its parts.

Etymology

Aleph-zero comes from the Hebrew letter aleph, which originally meant 'ox' and is used by mathematicians to name sizes of infinity, and the zero part marks it as the 'first' or smallest infinite size. So, aleph-zero means the size of the natural numbers, the smallest kind of infinity.