WOLFRAM|DEMONSTRATIONS PROJECT

Supremum of an Increasing Bounded Sequence

m

1

zoom

1

ϵ

0

The supremum (or least upper bound) of a sequence

a

n

is a number

sup(

a

n

)=M

fulfilling the following conditions.1. For all

n

,

a

n

≤M

.2. For all

ϵ>0

, there exists an

m

such that

a

m

>M-ϵ

.In the case of an increasing bounded sequence,

sup(

a

n

)=

lim

n∞

a

n

.