Cofinal (mathematics)
In mathematics, a subset B ⊆ A {\displaystyle B\subseteq A} of a preordered set ( A , ≤ ) {\displaystyle (A,\leq )} is said to be cofinal or frequent in A {\displaystyle A} if for every a ∈ A , {\displaystyle a\in A,} it is possible to find an element b {\displaystyle b} in B {\displaystyle B} that dominates a {\displaystyle a} (formally, a ≤ b {\displaystyle a\leq b} ). Cofinal subsets are very important in the theory of directed sets and nets, where “cofinal subnet” is the appropriate generalization of "subsequence".