A linear algebra

[knowledge base]

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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]

Linear Transformations

[knowledge base]

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LINEAR TRANSFORMATION and its underlying definitions are presented in this white paper [knowledge base (http://omkb.org)].

doi.org/10.31219/osf.io/cjdwg

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 224, 2021 [IU]

Every group is isomorphic to a group of permutations

[knowledge base]

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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]

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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]

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]