Functions and Analysis

2104 Submissions

[3] viXra:2104.0141 [pdf] submitted on 2021-04-22 21:22:50

An Elementary Proof of $0.999\dots=1$

Authors: O. Kurwa
Comments: 2 Pages.

One of the properties distinguishing irrational and rational numbers is the uniqueness (or the lack thereof) of their decimal representations. For example, the numbers $\pi$ and $1$ can be used as specimens of this phenomenon, as $\pi$ has precisely one expression as decimals, but $1=1.0=1.00=\dots$. In this paper, we provide an elementary proof for the fact that $0.999\dots$ is also a decimal representation of $1$, using the Lebesgue measure.
Category: Functions and Analysis

[2] viXra:2104.0078 [pdf] submitted on 2021-04-12 21:45:08

The Complex Curvature Is the Inverse of the Complex Radius

Authors: Abel Cavasi
Comments: 2 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

I don't know if anyone else has noticed, but if we consider that the radius and pitch of the helix is a complex number, then the curvature and torsion can be JUST THE INVERSE of this complex number.
Category: Functions and Analysis

[1] viXra:2104.0048 [pdf] submitted on 2021-04-09 11:22:07

A Formula of Integration

Authors: Antoine Balan
Comments: 1 page, written in french

We propose a formula which characterizes the integral.
Category: Functions and Analysis