Related papers: An Elementary Proof of a Minimax Theorem

We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we…

We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

The aim of this article is to establish new two-functions minimax inequalities extending classical results such as Simons' minimax theorem. Our results will be proved in a non-compact setting. We also prove, under general conditions, that…

In this paper we prove a version of the Fountain Theorem for a class of nonsmooth functionals that are sum of a $C^1$ functional and a convex lower semicontinuous functional, and also a version of a theorem due to Heinz for this class of…

We present an optimization problem emerging from optimal control theory and situated at the intersection of fractional programming and linear max-min programming on polytopes. A na\"ive solution would require solving four nested, possibly…

The purpose of this note is to present my understanding of Tim Austin's proof of the multiple ergodic theorem for commuting transformations, emphasizing on the use of joinings, extensions and factors. The existence of a sated extension,…

A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…

It is shown that contrary to claims of Ref. [1] the formulated in the proper physical variables Low theorem [2] for soft photon emission does not require any modification. We also reject the criticism in Ref. [1] of the papers [3,4]. At the…

We give an elementary proof for new strict upper and lower bounds for the correction term in Ramanujan's approximation for the factorial function

The shortest known proof of the law of quadratic reciprocity (without supplements) is presented.

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau…

Novikov's theorem states that, given a taut (codimension-one) foliation on a closed 3-manifold M, the fundamental group of any leaf injects into the fundamental group of M. We use foliated branched covers to give a simple proof of this…

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

IIn the context of a weak formal theory called Basic Intuitionistic Mathematics $\mathsf{BIM}$, we study Brouwer's Fan Theorem and a strong negation of the Fan Theorem, Kleene's Alternative (to the Fan Theorem). We prove that the Fan…

We produce a new, shorter construction of a minor-universal planar graph.

An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.

We show that a simple and straightforward rational approximation to the Thomas-Fermi equation provides the slope at origin with unprecedented accuracy and that relatively small Pad\'e approximants are far more accurate than more elaborate…

We give a short and self-contained proof of the Marker-Steinhorn Theorem for o-minimal expansions of ordered groups, based on an analysis of linear orders definable in such structures.

We take the perspective of an advanced high school student trying to understand the proof of Fermat's Last Theorem for the first time. We collect definitions and statements needed to summarise how Fermat's Last Theorem was first proved in…