Hi,

I understand the basic definition of sup and inf, but when it comes to proving the sup or inf of an infinite set where infS/supS is not an element of S, I am having trouble.

For example, given a problem of proving that

supS=0 where S={x|x<0},

I am able to prove the first part of the definition of supS (proving that 0 is an upper bound of S), but I always get stuck at the 2nd part of the definition

(

**proving that for any b, where b is an upper bound of S, 0 is less than or equal to b**).

Any help would be appreciated