# Finding an upper bound that is not the supremum

#### ver_mathstats

Problem Statement
Let S=(0,1), find a real number M which is an upper bound of S, but M is not the supremum of S.
Relevant Equations
S=(0,1)
I just want to see if I did this correctly, the interval (0,1) has 2 as an upper bound but the supremum of S is 1. So M would be equal to 2?

Thank you.

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#### PeroK

Homework Helper
Gold Member
2018 Award
Yes, any number greater than 1 would do.

#### ver_mathstats

Yes, any number greater than 1 would do.
Okay thank you.

#### WWGD

Gold Member
Just to expand a bit. The Supremum is , by definition/construction, the _Least_ Upper Bound. This implies any other upper bound should be greater than the Sup, as @PeroK wrote.

"Finding an upper bound that is not the supremum"

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