Related papers: Hasse theorem -- an elementary approach
In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.
We give an elementary introduction to the theory of supermembranes.
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.
In this paper we show an index theorem for gerbes
An technically interesting proof of a known theorem.
A very simple but useful almost sure convergence theorem of probability is given.
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.
We prove the Aharoni Berger Conjecture
This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.
An elementary proof of Bertrand's theorem is given by examining the radial orbit equation, without needing to solve complicated equations or integrals.
We give a new simpler proof of a theorem of Jayne and Rogers.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
We present in this work a new and simple proof of the false centre theorem.
An elementary proof of an identity by Lyons, Paule and Riese is given. It is simpler than all the 3 published proofs.
We prove the decidability of the elementary theory of a free group.
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
We establish an equivalent condition to the validity of the Collatz conjecture, using elementary methods. We derive some conclusions and show several examples of our results. We also offer a variety of exercises, problems and conjectures.
I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.
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.
A proof is given of Rosenthal's \(\ell_1\) theorem.