Related papers: An Elementary Proof of a Minimax Theorem
Real-world formal theorem proving often depends on a wealth of context, including definitions, lemmas, comments, file structure, and other information. We introduce miniCTX, which tests a model's ability to prove formal mathematical…
A new elementary proof of the prime number theorem presented recently in the framework of a scale invariant extension of the ordinary analysis is re-examined and clarified further. Both the formalism and proof are presented in a much more…
We provide a short proof of the 1-dimensional flat chain conjecture.
We provide an alternative, simpler proof of the existence of thick triangulations for noncompact $\mathcal{C}^1$ manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary…
We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…
We show that for a minimal system $(X,T)$, the set of saturated points along cubes with respect to its maximal $\infty$-step pro-nilfactor $X_\infty$ has a full measure. As an application, it is shown that if a minimal system $(X,T)$ has no…
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
We expose here a short proof of Cramer's theorem in R based on convex duality.
We give a new simple proof of Dehn's theorem by generalizing the notion of area. The method proposed in the present article is actually the "translation" of the method of additive functions into the elementary math language.
Minimax-based search algorithms with alpha-beta pruning and transposition tables are a central component of classical game-playing engines and remain widely used in practice. Despite their widespread use, these algorithms are subtle, highly…
In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup's generalised lower…
Chebotarev's theorem on roots of unity states that all minors of the Fourier matrix of prime size are non-vanishing. This result has been rediscovered several times and proved via different techniques. We follow the proof of Evans and…
Let X be a compact convex set and let ext X stand for the set of extreme points of X. We show that an affine function with the point of continuity property on X satisfies the minimum principle. As a corollary we obtain a generalization of a…
We give an undergraduate short and simple proof for Zariski's lemma.
This correspondence studies an estimator of the conditional support of a distribution underlying a set of i.i.d. observations. The relation with mutual information is shown via an extension of Fano's theorem in combination with a…
We present a new, elementary, dynamical proof of the prime number theorem.
In this note, we will give a short proof of an identity for cubic partitions.
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.
Consider a sum of convex functions, where the only information known about each individual summand is the location of a minimizer. In this work, we give an exact characterization of the set of possible minimizers of the sum. Our results…