Aleph-null (ℵ₀) is a mathematical concept that represents the smallest infinite cardinal number. It is used to describe the size of sets that can be put into a one-to-one correspondence with the natural numbers, such as the set of all natural numbers itself. This means that even though the set is infinite, it can still be counted in a way. In set theory, Georg Cantor introduced the concept of cardinality, which helps compare the sizes of different sets. Aleph-null is significant because it shows that not all infinities are equal; for example, the set of real numbers is larger than aleph-null, indicating that there are different "sizes" of infinity.