Wellfoundedness

Wellfoundedness is a concept primarily used in mathematical logic and set theory, particularly in the context of order relations and transfinite induction. A relation \( R \) on a set \( S \) is said to be well-founded if every non-empty subset of \( S \) has a minimal element with respect to the relation \( R \). In simpler terms, this means that there are no infinite descending chains of elements.