A cofinal subset of a partially ordered set 
is a subset 
such that, for every 
, there is an 
with 
. Thus no element of 
lies strictly above all the elements
of 
.
For an ordinal number 
, a subset 
is cofinal in 
precisely when it is unbounded in 
. The least cardinal number
of a cofinal subset is the cofinality of the partially
ordered set or ordinal number.
