[knowledge base]
LINEAR ALGEBRA and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/8emp4
Op. J. Math. Phys.
Volume 3, Article 225, 2021 [IV]
Author: Matheus Lobo, PhD
Open Scientist.
Linear Transformations
[knowledge base]
LINEAR TRANSFORMATION and its underlying definitions are presented in this white paper [knowledge base (http://omkb.org)].
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 224, 2021 [IU]
Every group is isomorphic to a group of permutations
[knowledge base]
CAYLEY’s THEOREM, the SYMMETRIC GROUP THEOREM, and their underlying definitions are presented in this white paper (knowledge base = http://omkb.org).
https://doi.org/10.31219/osf.io/63pmy
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 223, 2021 [IT]
A semigroup with a left identity and left inverse is a group
[pedagogical]
We translate the proof of the theorem stated in the title, accomplished by Prover9, into a human readable form.
https://doi.org/10.31219/osf.io/wsbne
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 222, 2021 [IS]
The membership relation
[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]
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
[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]
A proof for Cantor-Schröder-Bernstein Theorem using the diagonal argument
[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]
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
[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]
On the arithmetics of theorem proving
[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]
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]
