Related papers: Realizing Infinity
We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$-bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$. We exhibit examples…
In this article we discuss the transcendence of certain infinite sums and products by using the Subspace theorem. In particular we improve the result of Han\v{c}l and Rucki \cite{hancl3}.
In this article we want to answer the cosmologically relevant question what, with some good semantic and physical reason, could be called the mass of an infinitely extended, homogeneously matter-filled and expanding universe. To answer this…
A century ago, discoveries of a serious kind of logical error made separately by several leading mathematicians led to acceptance of a sharply enhanced standard for rigor within what ultimately became the foundation for Computer Science. By…
Given a finite dimensional algebra $\Lambda$, we show that a frequently satisfied finiteness condition for the category ${\cal P}^{\infty}(\Lambda\rm{-mod})$ of all finitely generated (left) $\Lambda$-modules of finite projective dimension,…
Is a logicist bound to the claim that as a matter of analytic truth there is an actual infinity of objects? If Hume's Principle is analytic then in the standard setting the answer appears to be yes. Hodes's work pointed to a way out by…
The discovery of the infinite integer leads to a partition between finite and infinite numbers. Construction of an infinitesimal and infinitary number system, the Gossamer numbers. Du Bois-Reymond's much-greater-than relations and…
The evolution of matter in the expanding FRW universe during the time interval between the end of inflation and the beginning of the radiation-dominated era is studied. A constraint between the global geometry and total amount of matter in…
Measurement outcomes provide data for a physical theory. Unless they are objective they support no objective scientific knowledge. So the outcome of a quantum measurement must be an objective physical fact. But recent arguments purport to…
In this article we investigate some "unexpected" properties of the "Infinite Power Tower". \[y = f(x) = {x^{{x^{{x^{{x^ {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} }}}}}}}\] The…
A fundamental problem of Einstein's theory of classical general relativity is the existence of singularities such as the big bang. All known laws of physics end at these boundaries of classical space-time. Thanks to recent developments in…
We present a characterization of the completeness of the field of real numbers in the form of a \emph{collection of ten equivalent statements} borrowed from algebra, real analysis, general topology and non-standard analysis. We also discuss…
The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern…
Courses in mathematical methods for physics students are not known for including too much in the way of mathematical rigour and, in some ways, understandably so. However, the conditions under which some quite commonly used mathematical…
This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
In our previous articles ("The Information and the Matter", v1, v5; more systematically the informational conception is presented in arXiv paper "The Information as Absolute", 2010) it was rigorously shown that the Matter is some…
Do we have two kinds of reality: physical and mathematical? What is the role of mathematics in physics? These fundamental questions have intrigued original and brilliant minds since ancient times. A recent article (Aharonov, Cohen and…
We study regularity properties of solutions to reaction-diffusion equations ruled by the infinity laplacian operator. We focus our analysis in models presenting plateaus, i.e. regions where a non-negative solution vanishes identically. We…
We present two tools, which could be useful in determining whether or not a non-Homogenous Linear Recurrence can reach a desired rational. First, we derive the determinant that is equal to the ith term in a non-Homogenous Linear Recurrence.…