Supremum of an Increasing Bounded Sequence
Supremum of an Increasing Bounded Sequence
The supremum (or least upper bound) of a sequence is a number fulfilling the following conditions.1. For all , ≤M.2. For all , there exists an such that >M-ϵ.In the case of an increasing bounded sequence, .
a
n
sup()=M
a
n
n
a
n
ϵ>0
m
a
m
sup()=
a
n
lim
n∞
a
n