Related papers: An Elementary proof for Bertrand's Postulate
This essay offers a brief biography of Paul Erd\H{o}s and summarizes his approach to mathematics. This is further elucidated by a discussion of Erd\H{o}s' simple proof of Bertrand's Postulate.
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
We present an astonishingly simple and elegant proof of the celebrated Basel problem.
In this article we present Pickands theorem and his double sum method. We follow Piterbarg's proof of this theorem. Since his proof relies on general lemmas we present a complete proof of Pickands theorem using Borell inequality and Slepian…
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
We derive an expression for the determination of the apsidal angles that holds good for arbitrary central potentials. Then we discuss under what conditions the apsidal angles remain independent of the mechanical energy and angular momentum…
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
Chang's lemma is a useful tool in additive combinatorics and the analysis of Boolean functions. Here we give an elementary proof using entropy. The constant we obtain is tight, and we give a slight improvement in the case where the…
An error in the proof of Bell's Theorem is identified and a semiclassical model of the EPRB experiment is presented
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
We prove an infinitary version of the Brauer-Schur theorem.
We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.
We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.
This note offers an elementary proof of the Siegel-Walfisz theorem for primes in arithmetic progressions.
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
In this note we generalise a method of Perott to give new proofs that there are infinitely many prime numbers.
We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…
We give a new simpler proof of a theorem of Jayne and Rogers.