I have a hard time understanding the following statement from my textbook (Apostol Calculus Vol.1) :

" Example 1: Let S be the set of all positive real numbers. This set is unbounded above. It has no upper bounds and it has no maximum element.

In example 1, the set of all positive real numbers, the number 0 is the infimum of S. This set has no minimum element."

I understand the first part of the proof about the upper bounds. But why is zero the infimum. Is zero consider a positive real number? Also, in order to be the minimum element, zero has to be included in the set, which I thought it is.