Transfinite numbers are a type of number that extends beyond the finite numbers we commonly use. They were introduced by the mathematician Georg Cantor in the late 19th century to describe sizes of infinite sets. For example, the set of all natural numbers is infinite, and its size is represented by the transfinite number aleph-null (ℵ₀). There are different types of transfinite numbers, including ordinal numbers and cardinal numbers. Ordinal numbers describe the position of elements in a well-ordered set, while cardinal numbers measure the size of sets. Transfinite numbers help mathematicians understand and compare different infinities, revealing a rich structure within the concept of infinity.