Is there a symbol for the idea of the smallest value greater than zero? I know that it isn't actually a number but I do think it's a concept in mathematics. So the question is, is there a symbol representing this concept? I thought maybe it was Phi but I couldn't find it for sure anywwhere.
Answer I was looking for (but inadvertantly phrased in such a way that caused much distress to this community):
"In floating-point computing that would be epsilon." –  uncle brad

Before you can give something a name you must make sure there is something to name. You claim (correctly) that it (whatever it is) is not a number. Then before running off to try and find a name for it, start by stipulating what it might be. Some of the comments to your question mention infinitesimals (in the form of the hyperreal numbers) and an algebraic version (in the form nilpotent elements in a ring (e.g., the ring of dual numbers)). Whatever it is you are looking for won't be found there, as (for pretty much the same reason that there isn't a smallest positive real number) there is no smallest positive element in those number systems. 
The fact is that the ordering of the reals simply does not allow for such entities and no known useful extension of the real numbers does either. You are always free to invent and ideal new entity, declare it to be a smallest positive element and see what kind of system you get. It won't be pretty or particularly useful. But once you've done that, you can give that entity any name you like. In mathematics there is no concept of smallest positive number. 
