Related papers: An Elementary Proof of a Minimax Theorem
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
In this paper, we present an elementary proof of the Bhatia-\v{S}emrl Theorem, utilizing the Minimax Theorem for bounded linear operators by Asplund and Ptak [1]. Some related results are also discussed.
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 present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.
The goal of this expository article is to present a proof that is as direct and elementary as possible of the fundamental theorem of complex multiplication (Shimura, Taniyama, Langlands, Tate, Deligne et al.). The article is a revision of…
We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…
Theorem 1 of [14], a minimax result for functions $f:X\times Y\to {\bf R}$, where $Y$ is a real interval, was partially extended to the case where $Y$ is a convex set in a Hausdorff topological vector space ([15], Theorem 3.2). In doing…
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.
The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary…
If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on…
We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.
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.
In this paper, we establish two minimax theorems for functions $f:X\times I\to {\bf R}$, where $I$ is a real interval, without assuming that $f(x,\cdot)$ is quasi-concave. Also, some related applications are presented.
For the analytic function f(z), H. Shiraishi and S. Owa (Stud. Univ. Babes-Bolyai Math. 55(2010), 207-211) have shown a theorem for the minimum value of |f(z)|. In this paper, we discuss an application of this theorem and some corollaries.
Hanner's theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanner's original proof of the theorem is quite simple for separable spaces, it is rather…
We present a short proof of Jin's theorem which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. The given proof provides the explicit…
Using nonstandard analysis, an intuitive and very short proof of the Radon-Nikodym theorem is provided
We give a proof of Fermat's little theorem which does not use nor arithmetic(Euclidean algorithm) neither algebra (group theory), but it rather employs the field of the formal power series Q((x)). The note is an example of a mathematical…
We present a short proof, relaying on the divergence theorem, verifying that minimal sets in the plane are trivial.
In this technical note, we give two extensions of the classical Fano inequality in information theory. The first extends Fano's inequality to the setting of estimation, providing lower bounds on the probability that an estimator of a…