Originally Posted by
laserlight
My point is that if you give me the "smallest possible non-zero number", I can give you a smaller non-zero number, simply by dividing it by a number greater than 1. Clearly, there is no smallest non-zero number, or more accurately, there is no smallest positive real number. I assumed that you were aware of the concept of countable and uncountable sets, so I expressed my point indirectly.
If you can map a set (as in a one to one mapping, possibly with some natural numbers left unmapped as in the case of a finite set) to the set of natural numbers (or some other countable set), then that set is countable.