Adjective
cofinal (not comparable)
(order theory) Of a subset of a partially ordered set; containing elements at least as late as any given element of the set, relative to the given partial order.
The Archimedean property of real numbers means that the natural numbers form a cofinal subset of ℝ.
An ordinal is called regular if it is cofinal with any smaller ordinal; otherwise it is singular. Source: Internet
Examples * The cofinality of a partially ordered set with greatest element is 1 as the set consisting only of the greatest element is cofinal (and must be contained in every other cofinal subset). Source: Internet
If two cofinal subsets of B have minimal cardinality (i.e. their cardinality is the cofinality of B), then they are order isomorphic to each other. Source: Internet
A subset is cofinal in the whole set if and only if it is unbounded in the whole set or it has a maximum which is also maximum of the whole set. Source: Internet
In more formal language, the set of all left-hand Riemann sums and the set of all right-hand Riemann sums is cofinal in the set of all tagged partitions. Source: Internet