Suprema and Infima (Sups and Infs) Lie at the Heart of Real Analysis. The Range of Cos(n) is an Interesting Example.
Study Help for Baby Rudin, Part 1.3
and 
which is bounded above, the supremum of 
, when it exists in , is also called the least upper bound of in .
with 
. The directed line segments are not part of the set. They only indicate the order.
is more than just a set. As