Related papers: Constructive proof of the Carpenter's Theorem

Following suggestions of T. H. Koornwinder, we give a new proof of Kummer's theorem involving Zeilberger's algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater. The…

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…

We present in this work a new and simple proof of the false centre theorem.

Parikh's theorem is a fundamental result of the formal language's theory. There had been published many proofs and many papers claimed to provide a simplified proof, but most of them are long and still complicated. We provide the proof that…

A sequence of scalars is said to be admissible for a positive operator A on a Hilbert space if it is the diagonal of VAV* for some partial isometry V having as domain the closure of the range of A. When A is a projection, the celebrated…

We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…

Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.

The connections between the objects mentioned in the title are used to give a short proof of the Cartan--Helgason theorem and a natural construction of the compactifications.

This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.

We provide a constructive treatment of basic results in the theory of central simple algebras. One main issue is the fact that one starting result, Wedderburn's Theorem stating that a simple algebra is a matrix algebra over a skew field, is…

We prove a Khintchine type theorem for approximation of elements in the Cantor set, as a subset of the formal Laurent series over $\mathbb{F}_3$, by rational functions of a specific type. Furthermore we construct elements in the Cantor set…

In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…

We present a constructive proof of Tychonoff's fixed point theorem in a locally convex space for sequentially locally non-constant functions, As a corollary to this theorem we also present Schauder's fixed point theorem in a Banach space…

G\"odel's first and second incompleteness theorems are corner stones of modern mathematics. In this article we present a new proof of these theorems for ZFC and theories containing ZFC, using Chaitin's incompleteness theorem and a very…

We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.

We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.

A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…

In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…