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[math] Loopace
Yi Taiyub at 2018-11-04 05:17
URL http://kallery.net/s.php?i=868

To get to a point in the space mentioned above, you have to travel half way to that point and half way to that halfway point and so on. There's no end to the halfway so you can't reach the point.
This paradox applies to all changes that are assumed to be continuous and the change of time is not an exception. To overcome this paradox, we assume that time and space are discrete and composed of elementary units that cannot be divided any more.
We also assume that the size of the unit space is not greater than the smallest particle in the universe and the length of the unit time is not longer than the time the fastest particle in the universe stays in one unit space.
This assumption prevents multiple particles from coexisting in one unit space at the same time and prevents one particle from being in multiple unit spaces at the same unit time.

We can go around the globe, but we can not find the end. The universe can be the same as the earth's surface but three-dimensional instead of two-dimensional. Then it would be endless and finite.
Suppose a looped space (for short, loopace) as follows:

At any point in the space, if you go straight in any possible direction, you will return to where you leave off.

Poincaré conjecture:
Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.

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