Let S={2−(1/n) :n∈N}. Prove that sup S=2.

Homework Statement

Let S={2−(1/n) :n∈N}.Prove that sup S=2.

Homework Equations

I have a hard time proving sups and all the examples that I have do not ask you to prove it to an actual number

I have started something but do not know how to complete it.

The Attempt at a Solution

Let b=sup S. The s<= b for all s in S. So b is an upper bound for S. (Next, I know that I need to prove that b is the least upper bound by proving that something else cannot be the least upper bound. But, how do I get the 2 into the proof?) Thanks