von Neumann ordinals

Von Neumann ordinals are a way to represent and organize different types of numbers, particularly in set theory. Each ordinal number is defined by the set of all smaller ordinals. For example, the ordinal for 3 is the set containing 0, 1, and 2, written as {0, 1, 2}. This structure allows us to compare sizes of infinite sets and understand their arrangement. In essence, von Neumann ordinals help mathematicians study sequences and order in a logical, structured way, facilitating discussions about infinite and finite numbers alike.