In mathematics, a binary relation R is called well-founded on a set or, more generally, a class X if every non-empty subset S ⊆ X has a minimal element with respect to R; that is, there exists an m ∈ S such that for every s ∈ S, one does not have s R m. More formally, a relation is well-founded if: Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set.