stylistic:style_transfer, information:filtering
Formal definition

A lower bound of a subset S {\displaystyle S} of a partially ordered set (P, ≤) {\displaystyle (P,\leq)} is an element a {\displaystyle a} of P {\displaystyle P} such that

A lower bound a {\displaystyle a} of S {\displaystyle S} is called an infimum (or greatest lower bound, or meet) of S {\displaystyle S} if

Similarly, an upper bound of a subset S {\displaystyle S} of a partially ordered set (P, ≤) {\displaystyle (P,\leq)} is an element b {\displaystyle b} of P {\displaystyle P} such that

An upper bound b {\displaystyle b} of S {\displaystyle S} is called a supremum (or least upper bound, or join) of S {\displaystyle S} if