This is a tricky question?

Question

Please try and use your imagination. Lets say you have two objects on a table. You then move them half the distance towards each other. you then do it again and again. How many times can you do this before they touch. If you keep moving the objects half the distance to each other, they would never touch...right?

Answer 1

This is a variant of an old philosophical conundrum called Xeno's Paradox. It involves a tortoise and a hare in a race in which the hare has given the tortoise a head start. Each time the hare reaches a point that the tortoise has been, the tortoise has moved a bit further on. The paradox is that it is not clear how the hare can ever catch the tortoise. In your variant, you imply a system which is a set of discrete movements and not the dynamic moving system of the tortoise and the hare. Since each move of half the distance towards each other is a separate and discrete move, they would theoretically never touch.

Answer 2

At some point, the distance would be small enough for the gravitational attraction of the two objects to overcome inertia and friction and they would move together.

Answer 3

At some point you would have to pass each other. No matter how small space is, It's still there. All matter is accounted for.
Try this one!

What happens to the objects if you remove the space between them? do they become closer?

Answer 4

I think they would never touch. I'm just not sure you'd be able to continue to measure half the distance when it gets reallly close.

Answer 5

nope they would never touch because they would always be half apart

Answer 6

move them once and they reach each other

Answer 7

Yes. it seems me you are right

Answer 8

right. in theory. but not in practice