Categories in symbols

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An introduction to the language of category theory is presented in a very minimalistic fashion, using the fewest number of symbols as possible. In this white paper, the focus is on the main concepts underlying categories.

https://doi.org/10.31219/osf.io/k9fbc

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 247, 2021 [JR]

The undecidable dynamics generate quantum probabilities

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We conjecture a new approach to quantum mechanics that, if confirmed, will explain the wave function from a fundamentally deeper level.

https://doi.org/10.31219/osf.io/hfc82

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 242, 2021 [JM]

Lyapunov exponents for the Lorentz transformations

[microresearch]

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We calculate the Lyapunov exponents of the complex stretch factor $f^-(z)=(1-z^2)^{-1/2}$ from the Lorentz transformations and of its reciprocal $f^+(z)=(1-z^2)^{+1/2}$ as well.

https://doi.org/10.31219/osf.io/jsncm

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 239, 2021 [JJ]

Time is a discrete dynamical system

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We conjecture that quantum vacuum operates its discrete dynamics in a superposition of a class of iterating functions such that each physical system operates within a distinct function.

https://doi.org/10.31219/osf.io/8f4yg

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 238, 2021 [JI]

Two non-isomorphic structures with the same number of elements

[white paper: pedagogical]

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For pedagogical purposes, we define a simple language to show that two different structures with the same number of elements in their universes are not isomorphic.

https://doi.org/10.31219/osf.io/ytcru

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 234, 2021 [JE]

The isomorphism between structures is an equivalence relation

[white paper: pedagogical]

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We present a pedagogical proof that the function of an isomorphism between two structures is an equivalence relation.

https://doi.org/10.31219/osf.io/7uwnh

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 233, 2021 [JD]

The terms of a language with one constant, one binary function, and one 4-ary function have an odd number of symbols

[white paper: pedagogical]

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We show using induction on complexity that all terms of a language with one constant, one binary function, and one 4-ary function have an odd number of symbols.

https://doi.org/10.31219/osf.io/ue32a

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 231, 2021 [JB]

The power set has 2^n elements

[white paper: pedagogical]

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We prove that if A is a set consisting of n elements, then A has 2^n subsets.

https://doi.org/10.31219/osf.io/mptx7

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 230, 2021 [JA]

Goldbach Conjecture, Twin Primes Conjecture, and Bounded Gap Theorem in the language of number theory

[white paper: pedagogical]

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We write the formulas of the theorem and the conjectures highlighted in the title of this white paper in the language of number theory for pedagogical purpose in first-order logic.

https://doi.org/10.31219/osf.io/u45y3

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 229, 2021 [IZ]

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]

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]

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]

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]

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

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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

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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]

Call for co-signing a paper: Increasing collaboration, fostering open science, and sharing the Article Processing Charge (APC)

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We argue that sharing one’s research with citizens and other scientists is a win-win crowd science strategy.

https://doi.org/10.31219/osf.io/62x8h

Open Collaboration

Op. J. Math. Phys.
Volume 2, Article 141, 2020 [FM]

Open Science done right

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A chain of simultaneous actions to foster open science is proposed.

https://doi.org/10.31219/osf.io/sa28u

Open Collaboration

Op. J. Math. Phys.
Volume 2, Article 140, 2020 [FL]