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]
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 277, 2023 [KZ]
[question]
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]
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]
We propose a model to assign prime numbers to axioms and theorems, then by comparing equivalent numbers, it results in new equivalent theorems.
https://doi.org/10.31219/osf.io/wbf85
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 132, 2020 [FC]
[original idea]
We apply an analogous setting from Gödel’s numbering system to automatic theorem proving.
https://doi.org/10.31219/osf.io/g7usc
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 119, 2020 [EP]
[original idea]
We apply in the complex numbers the same line of thought that led to the very creation of the complex themselves. In addition, we consider multiple imaginary numbers and generalize both ideas altogether.
https://doi.org/10.31219/osf.io/485kj
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 105, 2020 [EB]
[original insight]
We present two cycle decompositions for the permutations of an infinite set.
https://doi.org/10.31219/osf.io/u6zwt
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 92, 2020 [DO]
Open Journal of Mathematics and Physics 