Related papers: Yet another elementary proof of Morley's theorem
We give an elementary, self-contained, and purely combinatorial proof of the Rayleigh monotonicity property of graphs.
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.
In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.
In this note, a simple proof Jordan normal form and rational form of matrices over a field is given.
We give a counting based proof of the Graham Pollak Theorem
We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.
We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.
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.
I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
We present an elementary proof for Ljunggren equation
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
We give a one-sentence elementary proof of the combinatorial Fa\`a di Bruno's formula.
We give an elementary proof of the group law for elliptic curves using explicit formulas.
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
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.
A simple proof of Egorov's theorem for infinite measure is given
We present a new proof of the existence of Morley sequences in simple theories. We avoid using the Erd\H{o}s-Rado theorem and instead use only Ramsey's theorem and compactness. The proof shows that the basic theory of forking in simple…