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

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]

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]

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]

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

[white paper]

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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

[white paper]

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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]

A billion dollar idea

[original idea]

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A peer to peer open science app for crowd co-authorship is described. It would allow citizens to participate in the main steps of the scientific research.

https://doi.org/10.31219/osf.io/3ny8k

Open Collaboration

Op. J. Math. Phys.
Volume 2, Article 139, 2020 [FJ]

Roads to the Planck scale

[white paper]

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A summary of a few roads exploring the Planck scale is presented. We consider both Newtonian and relativistic systems.

https://doi.org/10.31219/osf.io/2cdwb

Open Quantum Collaboration

Op. J. Math. Phys.
Volume 2, Article 138, 2020 [FI]

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]