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 builds on the principle of mathematical induction, which applies to natural numbers, by allowing for an infinite sequence of steps. In transfinite induction, one first proves a base case for the smallest element, often denoted as 0 or α for the least ordinal. Then, for any ordinal β, if the statement holds for all ordinals less than β, it is shown to hold for β itself, thus establishing the truth for all ordinals.