We obtain that Universe space has to be flat, but also, at the same time, it has to be finite, homogeneous (on global scale) and isotropic. So rays of light can be observed moving along parallel trajectories in an expanding finite hypersphere. We show this implies an accelerated expansion of the Universe. Considering the energy conservation problem, also we argue about the necessity of matter-antimatter asymmetry.

A contradiction is obtained, considering the axiom of infinity, then ℕ and Peano axioms, together a list of ℕ subsets and with inclusion relation and union operation. Natural numbers constitute an infinite set, ℕ, but we show the union of its proper subsets, with a specific form, isn’t an infinite set. Also we get a simpler explanation and a symbolic representation. Lastly, inconsistency of Peano successor axiom is a consequence of rejecting infinity.

In the article ”Inconsistency of N from a not-finitist point of view” we have shown the inconsistency of N, going through a denial. Here we delete this indirect step and essentially repeat the same proof. Contextually we find a contradiction about natural number definition. Then we discuss around the rejection of infinity.

From classical mechanics, in particular the motion in a straight line, together set theory and ordinal number theory, we prove a not-classical behaviour, a discontinuous motion and emission.

From time involved in pair production process, in the photon-photon collision, we consider energy and then mass uncertainty. Taking the latter as the mass of a particle, we repeat pair production process obtaining another mass uncertainty, then another particle mass, and so on. Starting with the heaviest charged elementary particle that is possible using Planck length for electromagnetic mass, we obtain a mass value close to electron mass. It is supposed exactly electron mass, considering the presence of uncertainties in the (...) process. Then plausible neutrino mass and other particles masses are obtained. (shrink)

Considering the set of natural numbers ℕ, then in the context of Peano axioms, starting from inequalities between finite sets, we find a fundamental contradiction, about the existence of ℕ, from a not-finitist point of view.