Ordinal arithmetic is a branch of mathematics that deals with the manipulation of ordinal numbers, which represent the order of elements in a set. Unlike cardinal numbers that indicate quantity, ordinals focus on the position or rank of items. For example, in the sequence of natural numbers, 1st, 2nd, and 3rd are ordinal numbers that show the order of elements. In ordinal arithmetic, operations such as addition, multiplication, and exponentiation are defined differently than with regular numbers. For instance, when adding ordinals, the order matters; 2 + 3 is not the same as 3 + 2. This unique approach allows mathematicians to explore concepts of infinity and order in set theory, particularly in relation to Cantor's work on transfinite numbers.