Let (X,≤)(X,\leq)(X,≤) be a poset and let S⊆XS\subseteq XS⊆X. The infimum of this subset, if it exists, is a lower bound aaa of SSS in XXX such that for all lower bounds yyy of SSS in XXX, y≤ay\leq ay≤a. That is, the infimum is the greatest lower bound.