aleph-nought (Meaning)

Wordnet

aleph-nought (n)

the smallest infinite integer

No Synonyms and anytonyms found

In mathematical notation, aleph-nought, also denoted as ℵ₀, represents the cardinality of countable infinity.
The concept of aleph-nought is fundamental in set theory, describing the size of countable sets.
Mathematicians often use aleph-nought to compare the sizes of different infinite sets.
The set of natural numbers, including 0, 1, 2, and so on, has an aleph-nought cardinality.
When studying infinite sequences or series, aleph-nought plays a crucial role in understanding convergence and divergence.
Cantor's groundbreaking work in the late 19th century laid the foundation for the exploration of aleph-nought and other transfinite numbers.
The mathematician explained the concept of aleph-nought to his students, emphasizing its significance in the field of mathematics.
Aleph-nought is a countable infinity, distinguishing it from larger infinities such as aleph-one or aleph-two.
The researcher's paper delved into the implications of aleph-nought in the context of mathematical logic.
Cantor's diagonal argument is a famous proof technique that demonstrates the uncountability of certain sets, challenging the intuitive understanding of aleph-nought.

the smallest infinite integer

No synonyms found.

No antonyms found.

In mathematical notation, aleph-nought, also denoted as ℵ₀, represents the cardinality of countable infinity.

The concept of aleph-nought is fundamental in set theory, describing the size of countable sets.

Mathematicians often use aleph-nought to compare the sizes of different infinite sets.

The set of natural numbers, including 0, 1, 2, and so on, has an aleph-nought cardinality.