Ultranumbers
We introduce a set of abstract objects, the so-called ultranumbers, in order to generalize different classes of numbers. The idea is to find equations with nonexistent solutions in the original set, and then use them to extend the numerical system.
https://doi.org/10.31219/osf.io/jrqax
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Void numbers
We present nonzero numbers whose square vanishes for pedagogical purposes.
https://doi.org/10.31219/osf.io/ur7me
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 5, Article 277, 2023 [KZ]
Lattices, Order
[knowledge base]
LATTICES, ORDER and their underlying definitions and theorems are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/fzpc4
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 4, Article 276, 2022 [KX]
Molecular construction in the relational quantum vacuum
We conjecture that the quantum vacuum fluctuations operate through abstract mathematical relations of relations. Then we show how to construct a number of molecules from simple rules. Although this is an application of the Wolfram model, the conjecture itself is more general and therefore does not restrict to its rules.
https://doi.org/10.31219/osf.io/n5rzy
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 4, Article 271, 2022 [KQ]
The qubit permutation semigroup
We propose the equivalence between one Wolfram model and the qubit permutation semigroup.
https://doi.org/10.31219/osf.io/qkdxv
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 4, Article 270, 2022 [KP]
The inner structure of time
Based on the idea that time is computation, we discuss one interpretation regarding the inner structure of time that explains quantum superposition.
https://doi.org/10.31219/osf.io/chmqy
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 4, Article 269, 2022 [KO]
LJ calculus with stoup: A pedagogical approach
We prove a theorem in calculus LJ and in LJT (LJ with stoup) as well. We show that while there are many proofs to one single theorem in LJ, there is exactly one proof in LJT.
https://doi.org/10.31219/osf.io/z6h4q
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 4, Article 268, 2022 [KN]
Proofs of Theorems in Topology
We prove some theorems in topology using the fewest number of symbols at each step. Our purpose is pedagogical.
https://doi.org/10.31219/osf.io/wn24y
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 4, Article 267, 2022 [KM]
Theorems in Topology
This is an introductory collection of theorems in topology.
https://doi.org/10.31219/osf.io/zm56w
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 4, Article 260, 2022 [KE]
Personal Handbook of Logic
This is a personal collection of definitions and results from first-order logic.
https://doi.org/10.31219/osf.io/8wck9
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 252, 2021 [JX]
Categories in symbols
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 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 247, 2021 [JR]
The undecidable dynamics generate quantum probabilities
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 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 242, 2021 [JM]
Lyapunov exponents for the Lorentz transformations
[microresearch]
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 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 239, 2021 [JJ]
Time is a discrete dynamical system
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 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 238, 2021 [JI]
The logistics of quantum spacetime
[conjecture]
We conjecture that quantum superposition is the result of the existence of different orbits in the logistic equation due to quantum interactions in spacetime.
https://doi.org/10.31219/osf.io/s2dnt
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 236, 2021 [JG]
Two non-isomorphic structures with the same number of elements
[white paper: pedagogical]
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 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 234, 2021 [JE]
The isomorphism between structures is an equivalence relation
[white paper: pedagogical]
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 5, Article 278, 2023 [LA]
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]
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 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 231, 2021 [JB]
The power set has 2^n elements
[white paper: pedagogical]
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 5, Article 278, 2023 [LA]
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]
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 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 229, 2021 [IZ]
A linear algebra
[knowledge base]
LINEAR ALGEBRA and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/8emp4
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 5, Article 278, 2023 [LA]
Op. J. Math. Phys.
Volume 3, Article 225, 2021 [IV]
Open Journal of Mathematics and Physics 