Cofinal (mathematics)
Mathematical property of subsets in order theory / From Wikipedia, the free encyclopedia
Not to be confused with cofinite.
In mathematics, a subset of a preordered set
is said to be cofinal or frequent[1] in
if for every
it is possible to find an element
in
that is "larger than
" (explicitly, "larger than
" means
).
Cofinal subsets are very important in the theory of directed sets and nets, where “cofinal subnet” is the appropriate generalization of "subsequence". They are also important in order theory, including the theory of cardinal numbers, where the minimum possible cardinality of a cofinal subset of is referred to as the cofinality of