Infinity

[Potatoman]

Obviously, numbers are infinate. At what point would two marbles touch each other, assuming that all distances can always be halved? ( 0.1mm, 0.01, 0.001, 0.00000001 etc) Its a maths homework problem!

[bernardo]

I'm not sure exactly what you mean. Can you give us the exact wording of the question? Physically speaking, there would be a limit to the closeness which two objects can come together due to the repulsion of the atoms - they have a natural distance between them which cannot be overcome without very strong compressive forces. e.g. if you put a large rock in the middle of the Sun, it would be squashed to the size of a pea because the weight is enough to squash out the empty space between the atoms. (I think).

[gazzawazza]

Surely the distance is zero? In all of your examples the distance is always greater than zero no matter how many noughts you put after the point.

[Hammer]

If it's supposed to be a relatively simple homework question, then gazzawazza is correct to say zero. Any other distance can be halved, so is not the smallest.

[karachele]

If the question says they are being moved together by 1/2 the distance each time, the answer is never.

[joe22]

This is an example of Zeno's paradox. Mathematically speaking, the marbles will never touch, because the distance (divided each time by half) is an infinite series that never reaches zero. In practice, as bernardo described, once the distance is small enough (< 10^-7 mm) strong repulsion occurs between atoms, at which point we would conventionaly consider the marbles to be "touching". FYI, Zeno tried to use this paradox to disprove the existance of infinite numbers. His argument fails, though, for reasons too detailed to go into here.