We prove Cantor-Schröder-Bernstein theorem using the diagonal argument.
https://doi.org/10.31219/osf.io/2qkpx
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 210, 2021 [IG]
Author: Matheus Lobo, PhD
Open Scientist.
Model
[knowledge base]
MODEL (mathematical logic) and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/vs6j9
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 209, 2021 [IF]
Supremum and infimum
[knowledge base]
SUPREMUM (least upper bound), INFIMUM (greatest lower bound) and their underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/6fhrn
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 207, 2021 [ID]
Partial and total order relations on a set
[knowledge base]
PARTIAL and TOTAL ORDER relations and their underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/zx8ua
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 206, 2021 [IC]
Metrizable Topological Space
[knowledge base]
METRIZABLE TOPOLOGICAL SPACE and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/f8vez
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 205, 2021 [IB]
Scientific Autobiography
I present the references of my scientific publications divided into categories.
https://doi.org/10.31219/osf.io/zdxh3
Matheus Pereira Lobo, PhD
Op. J. Math. Phys.
Volume 3, Article 203, 2021 [ML]
On the arithmetics of theorem proving
We present the arithmetization of strings in order to be deployed as an alternative model for automatic theorem proving.
https://doi.org/10.31219/osf.io/ega6t
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 202, 2021 [HZ]
Presheaf (of abelian groups) on a topological space
[knowledge base]
PRESHEAF and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/2y5s4
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 201, 2021 [HY]
Searching for new theorems in M: a pure mathematical programming language
We present a project to be deployed in Python to serve as a powerful auxiliar tool for theorem proving. In the future, it can be turned into a programming language in its own right.
https://doi.org/10.31219/osf.io/6gyq4
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 195, 2020 [HR]
Advanced ceramics: Intrinsic and extrinsic factors
[microreview]
The efficiency of devices based on advanced ceramics is related to the optimization of material properties. In this paper, we discuss the intrinsic and extrinsic factors that influence the properties of advanced ceramics.
https://doi.org/10.31219/osf.io/xt7h6
Open Engineering Collaboration
Op. J. Math. Phys.
Volume 2, Article 186, 2020 [HH]
Is there a proof for the (non)existence of a formula for prime numbers?
[question]
We discuss about whether it is possible or not to prove or disprove the existence of a formula for the prime numbers.
https://doi.org/10.31219/osf.io/sb7td
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 167, 2020 [GO]
Transdenumerability of the reals
We show that the real numbers are transdenumerable by setting a one to one map with the set of the transfinite ordinals introduced by Cantor.
https://doi.org/10.31219/osf.io/fu7bx
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 156, 2020 [GD]
A unidimensional windmill in the plane with varying pivot points
We show that we can choose a point in the plane such that the resulting windmill process with varying pivot uses each point of the plane infinitely many times.
https://doi.org/10.31219/osf.io/mwkaf
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 148, 2020 [FT]
Generating finitely many circles from one circle using Banach-Tarski decomposition paradox
[microreview]
We prove the Banach-Tarski decomposition paradox applied to a circle.
https://doi.org/10.31219/osf.io/mh5gx
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 142, 2020 [FN]
Call for co-signing a paper: Increasing collaboration, fostering open science, and sharing the Article Processing Charge (APC)
We argue that sharing one’s research with citizens and other scientists is a win-win crowd science strategy.
https://doi.org/10.31219/osf.io/62x8h
Open Collaboration
Op. J. Math. Phys.
Volume 2, Article 141, 2020 [FM]
Open Science TV
Open Science done right
A chain of simultaneous actions to foster open science is proposed.
https://doi.org/10.31219/osf.io/sa28u
Open Collaboration
Op. J. Math. Phys.
Volume 2, Article 140, 2020 [FL]
A billion dollar idea
[original idea]
A peer to peer open science app for crowd co-authorship is described. It would allow citizens to participate in the main steps of the scientific research.
https://doi.org/10.31219/osf.io/3ny8k
Open Collaboration
Op. J. Math. Phys.
Volume 2, Article 139, 2020 [FJ]
Roads to the Planck scale
A summary of a few roads exploring the Planck scale is presented. We consider both Newtonian and relativistic systems.
https://doi.org/10.31219/osf.io/2cdwb
Open Quantum Collaboration
Op. J. Math. Phys.
Volume 2, Article 138, 2020 [FI]
A subgroup has equally many left and right cosets
[microreview]
We prove that a subgroup has the same number of left and right cosets.
https://doi.org/10.31219/osf.io/t4snh
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 137, 2020 [FH]
The multiverse equation: a toy model
[conjecture]
We present a toy model for the multiverse equation built upon a single cosmic variable encompassing information of all universes, all spaces, and all times.
https://doi.org/10.31219/osf.io/dg7b2
Open Physics Collaboration
Op. J. Math. Phys.
Volume 2, Article 136, 2020 [FG]
