Related papers: A really simple elementary proof of the uniform bo…

We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.

We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.

We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.

I give a relatively elementary proof of the symmetric space theorem, due to Goddard, Nahm and Olive \cite{GNO}. Unlike their original proof, which involves the quark-model construction, I only use elementary algebraic techniques.

We present a new and direct proof of Grothendieck's generic freeness lemma in its general form. Unlike the previously published proofs, it does not proceed in a series of reduction steps and is fully constructive, not using the axiom of…

We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.

We present a short elementary proof of the Gearhart-Pr\"uss theorem for bounded $C_0$-semigroups on Hilbert spaces.

The paper gives a unified and simple proof of both theorems and Cousin's theorem.

We prove Union-Closed sets conjecture.

We give a simple proof of Chebotarev's theorem: Let $p$ be a prime and $\omega $ a primitive $p$th root of unity. Then all minors of the matrix $(\omega^{ij})_{i,j=0}^{p-1}$ are non-zero.

We provide an elementary proof that subgroups of free groups are free via group actions.

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

We provide a short proof for the Figiel, Lindenstrauss and Milman inequality regarding the number of vertices and faces of certain polytope, with an explicit bound on the universal constant involved. The proof is completely elementary and…

We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.

Let $I=[0,1)$ and $\mathcal{PC}(I)$ [resp. $\mathcal{PC}^+(I)$] be the quotient group of the group of all piecewise continuous [resp. piecewise continuous and orientation preserving] bijections of $I$ by its normal subgroup consisting in…

The aim of this note is to provide an intrinsic proof of the Gauss--Bonnet theorem without invoking triangulations, which is achieved by exploiting complex structures.

In this paper, we present a simple analytic proof of Siegel's theorem that concerns the lower bound of $L(1,\chi)$ for primitive quadratic $\chi$. Our new method compares an elementary lower bound with an analytic upper bound obtained by…

We give a new proof of Lucas' Theorem in elementary number theory.

We give a direct analytic proof of the classical Boundary Harnack inequality for solutions to linear uniformly elliptic equations in either divergence or non-divergence form.