[knowledge base]
SUBSTITUTIONS, SUBSTITUTABILITY, and their underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/k6w7u
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 212, 2021 [II]
We present a discussion on the definition of the positional argument and the continuum hypothesis.
https://doi.org/10.31219/osf.io/tvg64
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 211, 2021 [IH]
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]
[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]
[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]
[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]
[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]
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]
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]
[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]
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]
[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]
[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]
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]
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]
[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]
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]
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]
[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]
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 Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 138, 2020 [FI]
