Cantor's ordinal numbers

Cantor's ordinal numbers are a way to describe the order type of well-ordered sets—sets arranged so every element has a unique position. Think of them as a way of extending counting beyond natural numbers to understand types of infinity and orderings. Each ordinal represents a unique "step" in an infinite hierarchy, with the smallest being zero, then the natural numbers, and larger ones like the first infinite ordinal called \(\omega\). These ordinals help mathematicians analyze different sizes and structures of infinity and organize concepts in set theory that go beyond finite counting.