Hi

My question has to do with the completeness property of the group R (real numbers)

It seems to be a basic question but I have no idea how to formally prove what i need.

I need to prove that infimums and supremums exist.

Let there be group A(a,b) which is a subgroup of R. Prove that group A has a supremum and an infimum. Meaning - Prove that there is a smallest upper bound, and largest lower bound.

I know they exist, but don't know how to prove it