Prewellordering
In set theory, a prewellordering on a set X {\displaystyle X} is a preorder ≤ {\displaystyle \leq } on X {\displaystyle X} (a transitive and reflexive relation on X {\displaystyle X} ) that is strongly connected (meaning that any two points are comparable) and well-founded in the sense that the induced relation x < y {\displaystyle x<y} defined by x ≤ y and y ≰ x {\displaystyle x\leq y{\text{ and }}y\nleq x} is a well-founded relation. == Prewellordering on a set == A prewellordering on a set X {\displaystyle X} is a homogeneous binary relation ≤ {\displaystyle \,\leq \,} on X {\displaystyle X} that satisfies the following conditions: Reflexivity: x ≤ x {\displaystyle x\leq x} for all x ∈ X .