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So, me and my dad were talking the other day, and he proposed the following... If there is an infinate number of possible distances between my hand and this table, then surely, as I bring my hand to touch the table, it passes through an infinate number of distances, so how is it that i can touch the table?

After quite some thinking, I concluded that this must indicate that there isn't an infinate number of distances between his hand and the table, and that infact "distance" is not infinately divisable, that is, that there is a distance (smaller than any sub-atomic particle) whereby there can be no smaller distance.

And, I thought, if this is so for distances, then surely (since time and space are relative) it is so for time too. So, I concluded, does this show that time and space are not infinately divisable?

I appreciate any comments on this. I am probably wrong in every possible corner here (lol), but I think it makes sense.