[knowledge base]
The MEMBERSHIP RELATION and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/r9p2m
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 221, 2021 [IR]
Author: Matheus Lobo, PhD
Open Scientist.
Modules over Rings
[knowledge base]
MODULES over RINGS and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/xjsc7
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 220, 2021 [IQ]
Vector space over a field
[knowledge base]
VECTOR SPACE OVER A FIELD and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/g6ux5
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 219, 2021 [IP]
Field, commutative ring, integral domain
[knowledge base]
FIELD, three propositions, and their underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/wmjst
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 217, 2021 [IN]
RINGS: Almost a ring, semiring, zero, integral domain
[knowledge base]
RING, commutative ring, almost a ring, semiring, zero ring, zero property, zero divisors, domain, integral domain, and their underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/bzugr
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 216, 2021 [IM]
Cyclic Group
[knowledge base]
CYCLIC GROUP and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/nvkab
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 215, 2021 [IL]
Strong Induction
[knowledge base]
STRONG INDUCTION and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/jysg5
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 213, 2021 [IJ]
Substitutions and Substitutability
[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]
The positional argument and the continuum hypothesis
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]
A proof for Cantor-Schröder-Bernstein Theorem using the diagonal argument
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]
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]
Open Journal of Mathematics and Physics 