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Lets see...
I'll try to approach this by thinking about distance as it is easier for me. So, half the distance of two spots in space. Now do it again. If you half the distance all the time the two points will always get closer to each other, but you can't really say that they reach each other, since they don't. And there's a big difference in "it is so close that it practically reaches it" and "the two points have touched each other".
So, this leads to a question: can there be a distance so small that it cannot be divided into two anymore? Is there some kind of minimum unit for distance? And similarly: can there be a number so small that it cannot be any smaller?
Okay, of course when it's about numbers you can always add another digit, but how can you add a digit to a series of numbers that goes forever?
Hope these thoughts make some kind of sense.