Given a
set S with a
partial order <=, an
infinite descending chain is a
chain V, that is, a subset of
S upon which <= defines a
total order, such that
V has no
minimal element, that is, an element
m such that for all elements
n in
V it holds that
m <=
v.
As an example, in the set of Integers, the chain -1,-2,-3,... is an infinite descending chain, but there exists no infinite chain on the Natural numbers, every chain of natural numbers has a minimal element.
![[Home]](wikipedia.png)