Ordinal arithmetic is a branch of mathematics that deals with the manipulation of ordinal numbers. Ordinal numbers extend the concept of natural numbers to describe the order of elements in a set. For example, while natural numbers can count items, ordinals indicate positions, such as first, second, or third. In ordinal arithmetic, operations like addition and multiplication are defined differently than with regular numbers. For instance, when adding ordinals, the order matters; 3 + 2 is not the same as 2 + 3. This unique approach helps mathematicians understand and work with infinite sets and their properties.