Aleph Null

Aleph Null (ℵ₀) is the cardinality of the set of natural numbers, representing the smallest infinite cardinal number. It is used to describe the size of countably infinite sets, such as the integers and rational numbers.

Aleph Numbers

Aleph numbers are a sequence of cardinal numbers used to represent the sizes of infinite sets. ${\aleph }_0$ is the first aleph number, representing the cardinality of countably infinite sets. Higher aleph numbers, such as ${\aleph }_1$, ${\aleph }_2$, etc., represent larger infinities.

Aleph Null represents the smallest infinity, while ${\aleph }_1$ is the next larger cardinality, which is often associated with the cardinality of the continuum (the real numbers) under the Continuum Hypothesis.