Finding an upper bound that is not the supremum

[ver_mathstats]

Homework 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.

 

[PeroK]

Yes, any number greater than 1 would do.

 

[ver_mathstats]

Yes, any number greater than 1 would do.

Okay thank you.

 

[WWGD]

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.