A transfinite number is a type of number that extends beyond the finite numbers we commonly use. Introduced by the mathematician Georg Cantor, transfinite numbers help describe sizes of infinite sets. For example, the set of natural numbers is infinite, and its size is represented by the smallest transfinite number, called aleph-null (ℵ₀). Transfinite numbers can also be used to compare different sizes of infinity. For instance, the set of real numbers is larger than the set of natural numbers, and its size is represented by a different transfinite number, known as the cardinality of the continuum. This concept allows mathematicians to explore the complexities of infinity in a structured way.