Zeno's Paradox

Consider a man who its purpose is to reach the wall that is 1 meter away. The ancient philosopher had proposed that if this man wants to reach the wall, first it must go the half of the distance. And then the half of the distance that is remaining, and so on.

Thus, because of this this man will not be able to reach this wall since this process can be extended into infinity. Thus, the argument in below is accepted:

It is impossible for infinitely divided over-lapping time intervals to all take place within a finite interval of time.

However, as we all know, this man is able to reach this wall (if he doesn’t have any physical disabilities). Since the term ‘infinity’ was not evaluated deeply in ancient times, this paradox will be resolved (or thought to be resolved) when the Cantorian set theory became an important part of the mathematics.  

With the Cantor’s potential infinity, we can reject this argument. You may ask how? Consider a hypersphere which has n dimensions. It can be understood that it is finite but unbounded. This unboundedness doesn’t make it an infinite thing, rather it becomes an endless.

When you thought the universe is rather infinitely expanding or there is some kind of bound which makes it finite, it doesn’t make sense when there is a bound which makes it finite since if there is a bound this doesn’t make the universe finite because there are remaining parts. However, if we assume the universe in a hypersphere, then this finiteness can be explained not with the existence of bound but by the endlessness of the universe. Which Aristo puts it ‘what is limited need not be limited with reference to something outside itself’.

From the perspective of physics, the paradox can be resolved with the idea of motion. As you might see, while math approaches the problem with a question of ‘Will this man reach the wall?’, the physics evaluates and examines the process of motion by asking ‘How does this man reach the wall?’.