RINGS: Almost a ring, semiring, zero, integral domain

[knowledge base]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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]

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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

[white paper]

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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]

Is there a proof for the (non)existence of a formula for prime numbers?

[question]

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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

[white paper]

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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

[white paper]

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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]

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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]

A subgroup has equally many left and right cosets

[microreview]

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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]