Partially Ordered Set
A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially
ordered set is defined as an ordered pair 
, where
is called the ground
set of 
and 
is the partial
order of 
.
An element 
in a partially ordered set 
is said
to be an upper bound for a subset 
of 
if for every 
, we have 
. Similarly,
a lower bound for a subset 
is an element 
such that for every 
, 
. If there
is an upper bound and a lower bound for 
, then the poset
is said to be bounded.
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30-sided polyhedron