A semigroup with a left identity and left inverse is a group

[pedagogical]

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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]

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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]

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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]

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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]

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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]

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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]

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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

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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

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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

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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

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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

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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]

Advanced ceramics: Intrinsic and extrinsic factors

[microreview]

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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]

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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]