👉 Continued math, also known as transfinite induction or ordinal induction, is a generalization of mathematical induction that extends beyond the finite realm to handle infinite sets. It's used to prove statements about all elements in a well-ordered set, such as the natural numbers, by demonstrating that if a property holds for the smallest element (the "0" in ordinal notation), and if it holds for each subsequent element (or an element immediately following the previous one) given that it holds for the immediate predecessor, then the property holds for all elements in the set. This method is crucial in set theory and advanced algebra, allowing mathematicians to rigorously establish properties across potentially infinite collections without explicitly listing every element.
