Since this forum includes philosophy, I shall post this here.I will begin this thread with a brief synopsis of some relativistic concepts necessary to proceed in this thread.

Take your basic set of parallel lines. They can be curved in two ways: apart to create a hyperbola, or together to form an ellipse.

The lines themselves are of infinite length, and contained within that one dimension. The ellipse and hyperbola also are within one dimension, as they are of zero width or height. However they have curvature which can only be appreciated in two dimensions.

The same argument can be extended to that of two planes; they can bend gradually towards a spherical or a hyperbolic form which is impossible to perceive yet exists in two dimensions. Two volumes can similarly converge or diverge, despite our inability to see four dimensions.

If we extend the principle to our universe, we arrive at the fact that our universe must have negative (diverging) curvature, Euclidean (no) curvature, or positive (converging) curvature.

Let us set a two-dimensional man down on our sphere. If he walks steadily in the same direction, he eventually arrives back at the same place, and hence his universe is finite but unbounded. If a similar man walks along on a hyperbola, he can keep going and going, making his universe of infinite dimensions.

Since time is a dimension, it also must follow the rules of its universe's curvature, and thus a universe of negative curvature must never collapse, or time would end and dimensions don't end in negatively curved space.

Tests performed by curious scientists have yielded results which support the position that our universe will forever expand, including results on the density of matter in our universe, the rate of expansion, heavy hydrogen, and similar data.

If the amount of time and space available to our universe is infinite, than the number of random combinations yielded by quantum physics' uncertainty regarding the position of submolecular particles is also infinite and so must yield every potential combination. With that in mind, given enough raw material, a planet identical to the world of Pokémon must appear at some point in time.

Since there is a constant and unchanging availability of energy in our universe, it thus follows that it is impossible for Pokémon not to exist.