Related papers: The choosability version of Brooks' theorem -- a s…
We give a proof of the o-minimal version of the Whitney Extension Theorem simplified as compared to the original ones. A new simplifying ingredient is a definable variant of Urysohn's lemma for class $\mathcal{C}^q$ (see Section 3).
We give yet another proof of the list-color version of Brooks' theorem that is due, independently, to Vizing and to Erd\H{o}s, Rubin and Taylor, via a famous theorem of Dirac on chordal graphs.
It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.
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…
This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).
A short and simple proof of necessity in the McCullough-Quiggin characterization of positive semi-definite kernels with the complete Pick property is presented.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
In this paper we give an outline on the Bayesian Decision Theory.
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.
We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.
We obtain some results related to Romanoff's theorem.
In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
We provide a short proof of the 1-dimensional flat chain conjecture.
A short proof is given for the well-known Choi-Effros theorem on the structure of ranges of completely positive projections.
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
We show that Thompson's $A\times B$-Lemma can be obtained as a consequence of the Brauer pair version of Brauer's Third Main Theorem.
In this paper, we give a short proof of a relation generalizing many identities for Bernoulli numbers.
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.