Transfinite induction is a mathematical technique used to prove statements about well-ordered sets, particularly those that extend beyond finite numbers, known as transfinite numbers. It operates similarly to mathematical induction but applies to infinite sets, allowing mathematicians to establish the truth of a statement for all ordinal numbers. The process involves three steps: first, proving the statement for the smallest ordinal; second, assuming it holds for an arbitrary ordinal; and third, demonstrating it holds for the next ordinal. This method is essential in set theory and is closely related to concepts like ordinal numbers and well-ordering.