Aleph numbers are a concept in set theory used to describe the sizes of infinite sets. The smallest aleph number, denoted as ℵ₀ (aleph-null), represents the cardinality of the set of natural numbers, indicating that it is the smallest type of infinity. Higher aleph numbers, such as ℵ₁, ℵ₂, and so on, represent larger infinities. For example, ℵ₁ is often associated with the cardinality of the set of all countable ordinal numbers. Aleph numbers help mathematicians understand and compare different sizes of infinity in a structured way.