How can there be more than 1 upper bound? Can't you use the same argument for showing that there is only 1 greatest lower bound?

That is, inf(A) is unique. Suppose s_1 and s_2 are both inf(A). Since s_1 is a greatest lower bound, s_2 <= s_1.

But, since s_2 is a greatest lower bound, s_1 <= s_2

This implies that s_1 = s_2.

Can't this argument be used for upper bounds...

Is it because of the notion that if you pick some "upper bound" you can always find something that's higher?