[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]
[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]
[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]
[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]
[white paper]
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]
[white paper]
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]
[white paper]
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]
[white paper]
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]
[white paper]
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]
[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]
[white paper]
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]
[white paper]
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]
[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]
