aleph-null

9.9

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

noun
/ˈɑːlɛf nʌl/

Specialized

: aleph-cero

The set of natural numbers has cardinality aleph-null in set theory.

Examples

You cannot reach aleph-null by simply adding one to a finite number.
Mathematicians often use aleph-null to describe the size of infinite countable sets.
The concept of aleph-null is fundamental in set theory.
Is aleph-null truly the smallest infinity?
Mathematicians often use aleph-null to describe the size of infinite countable sets.
The concept of aleph-null is fundamental in set theory.
The set of natural numbers has cardinality aleph-null in mathematics.

Synonyms

aleph-zero

vsaleph-null

Specialized

1 9.9

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

is the same concept but uses an alternative name form

aleph-nought

vsaleph-null

9.9

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

has identical meaning but uses a different traditional name

How Large

aleph-null

Specialized

9.9

finite

56 4.1

Surface Forms

aleph-null singular

aleph-nulls plural

Morphology

aleph-null = aleph + null (opaque) = aleph + null

Formally a compound of the lexical items 'aleph' (the Hebrew letter used to label cardinals) and 'null' (zero), but understanding it as the smallest infinite cardinal requires specialized mathematical knowledge.

Etymology

Aleph-null comes from two parts: aleph, the first letter of the Hebrew alphabet, like 'alpha' in Greek, and null, meaning 'nothing' or 'zero'. So aleph-null names the 'first' kind of infinity, the size of all counting numbers, and that's why you cannot reach it by adding one to any finite number.