Related papers: Th\'eor\`eme de de Smit et Lenstra, d\'emonstratio…

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

We present an elementary proof of Fermat's Last Theorem. No ancillary results are used, not even the most basic ones. The proof directly leads to a contradiction of the Fermat equation in the set of integers.

We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.

In this short note a new proof of the monotone con- vergence theorem of Lebesgue integral on \sigma-class is given.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

Herbrand's Theorem is a fundamental result in mathematical logic which provides a reduction of first-order formulas satisfied by a universal class to formulas free of existential quantifiers. In this work, a simpler and self-contained…

Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…

In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.

We give a constructive, metastable formulation of a theorem about the exchange of limits for convergent sequence $L^1$ functions. A crucial tool is a one-dimensional version of Szemeredi's regularity lemma for $L^1$ functions.

The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of symmetry.

A proof is given of Rosenthal's \(\ell_1\) theorem.

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.

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

Considering classical first-order logic with equality, we give a "fully syntactic" construction of the (weak) syntactic category $\text{Syn}(T)$ associated to a consistent theory $T$; we show it is a consistent coherent category; and we…

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

We present a new, elementary, dynamical proof of the prime number theorem.

We construct the geometric Langlands functor in one direction (from the automorphic to the spectral side) in characteristic zero settings (i.e., de Rham and Betti). We prove that various forms of the conjecture (de Rham vs Betti, restricted…

We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\omega_1, \omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense…

Due to the omission of a hypothesis from an elementary lemma in the author's paper "Gleason parts and point derivations for uniform algebras with dense invertible group", some of the proofs presented in that paper are flawed. We prove here…

We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.