Related papers: A new proof of a theorem of Jayne and Rogers
We provide a simple proof of a computable analogue to the Jayne Rogers Theorem from descriptive set theory. The difficulty of the proof is delegated to a simulation result pertaining to non-deterministic type-2 machines. Thus, we…
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
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.
In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.
In this note we give a detailed proof of a theorem of Aubin.
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
I present a simple derivation of the de Gennes narrowing phenomenon.
We prove the Aharoni Berger Conjecture
A proof is given of Rosenthal's \(\ell_1\) theorem.
A very simple but useful almost sure convergence theorem of probability is given.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.
Here is present short proofing of Jordan's theorem about dividing of flat on two disjoint subsets by one closed curve.
Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.