Wikipedia is actually a good place to go for Math help:

"In mathematics theinfimumof a subset of some set is the greatest element, not necessarily in the subset, that is less than or equal to all elements of the subset."

So basically, the infimum of the positive real numbers is 0 because 0 is the largest number you can find such that it is less than all the numbers in the positive real numbers.

You can try all you like, but you won't find a bigger number that's not a positive real number and which isn't greater than the greatest element (obviously the positive real numbers don't have a greatest element but this clause is relevant in some other cases).