Related papers: A double-inductive proof of Moessner's theorem

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…

We give a new simpler proof of a theorem of Jayne and Rogers.

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in the limit of small probabilities. The…

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…

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.

We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.

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 give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.

We use the Terwilliger algebra to provide a new approach to the Assmus-Mattson theorem. This approach also includes another proof of the minimum distance bound shown by Martin as well as its dual.

An elementary proof of the two-sidedness of the matrix-inverse is given using only linear independence and the reduced row-echelon form of a matrix. In addition, it is shown that a matrix is invertible if and only if it is row-equivalent to…

We study induction on the program structure as a proof method for bisimulation-based compiler correctness. We consider a first-order language with mutually recursive function definitions, system calls, and an environment semantics. The…

We present a nonstandard simple elementary proof of Szemer\'{e}di's theorem by a straightforward induction with the help of three levels of infinities and four different elementary embeddings in a nonstandard universe.

We offer a proof of a summation formula equivalent to one due to Berndt. Our proof uses the M$\ddot{u}$ntz formula and the Poisson summation formula. By utilizing known properties of Mellin inversion, we give an example from a discontinuous…

This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…

We prove a conjecture of Meszaros and Morales on the volume of a flow polytope. Independently from our work, Zeilberger sketched a proof of their conjecture. In fact, our proof is the same as Zeilberger's proof. The purpose of this note is…

A very short proof of Kneser's theorem via transversal is given.