Related papers: An Elementary Proof for the Basel Problem
We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.
We provide a simple proof of the completeness of arbitrary public announcement logic APAL. The proof is an improvement over the proof found in the publication Knowable as Known after an Announcement.
Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.
We give a new proof of Lucas' Theorem in elementary number theory.
We consider the k-th order statistic from unit exponential distribution and show that it can be represented as a sum of independent exponential random variables. Our proof is simple and different. It readily proves that the standardized…
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
While it is widely agreed that Bell's theorem is an important result in the foundations of quantum physics, there is much disagreement about what exactly Bell's theorem shows. It is agreed that Bell derived a contradiction with experimental…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
We discuss an earlier application of the Ritz variational method for strongly nonlinear problems. We clearly prove that the results derived for several extremely simple problems of supposedly physical and mathematical interest do not…
We prove an elementary lemma concerning primitive amalgams and use it to greatly simplify the proof of the Sims conjecture in the case of almost simple groups.
We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.
In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…
In this paper, we develop the method of circle of partitions and associated statistics. As an application we prove conditionally the binary Goldbach conjecture. We develop a series of steps to prove the binary Goldbach conjecture in full.…
Leibniz algebras generated by one element, called cyclic, provide simple and illuminating examples of many basic concepts. It is the purpose of this paper to illustrate this fact.
The Collatz conjecture is a famous math problem that was introduced by Lothar Collatz in 1937, and nobody has yet succeeded in proving or disproving it. In this article, I will analyze this problem with a new approach and I will discuss my…
The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
In 1914, Felix Hausdorff published an elegant proof that almost all numbers are simply normal in base 2. We generalize this proof to show that almost all numbers are normal. The result is arguably the most elementary proof for this theorem…