Functions and Analysis

2310 Submissions

[4] viXra:2310.0144 [pdf] submitted on 2023-10-30 20:45:29

Inversions (Mirror Images) With Respect to the Unit Circle and Division by Zero

Authors: Saburou Saitoh
Comments: 6 Pages.

In this note, we will consider the interesting inversion formula that was discovered by Yoichi Maeda with respect to the unit circle on the complex plane from the viewpoint of our division by zero: $1/0=0/0=0$.
Category: Functions and Analysis

[3] viXra:2310.0074 [pdf] replaced on 2023-11-05 04:00:45

The Infinite Series 1+2+3+4+⋯ is Strictly Divergent

Authors: Amisha Oufaska
Comments: 2 Pages.

In this paper , I prove that the infinite series 1+2+3+4+⋯ is strictly divergent or simply 1+2+3+4+⋯=+∞ applying an argument by contradiction .
Category: Functions and Analysis

[2] viXra:2310.0045 [pdf] submitted on 2023-10-10 21:46:42

Infinity Tensors, the Strange at Tractor, and the Riemann Hypothesis: An Accurate Rewording of The Riemann Hypothesis Yields Forma L Proof

Authors: Parker Emmerson
Comments: 13 Pages.

The Riemann Hypothesis can be reworded to indicate that the real part of one half always balanced at the infinity tensor by stating that the Riemann zeta function has no more than an infinity tensor’s worth of zeros on the critical line. For something to be true in proof, it often requires an outside perspective. In other words, there must be some exterior, alternate perspective or system on or applied to the hypothesis from which the proof can be derived. Two perspectives, essentially must agree. Here, a fractal web with infinitesimal 3D strange attractor is theorized as present at the solutions to the Riemann Zeta function and in combination with the infinity tensor yields an abstract, mathematical object from which the rewording of the Riemann Zeta function can be derived. From the rewording, the law that mathematical sequences can be expressed in more concise and manageable forms is applied and the proof is manifested. The mathematical law that any mathematical sequence can be expressed in simpler and more concise terms: ∀s∃su2032⊆s: ∀φ: s⊆φ ⇒ su2032⊆φ, is the final key to the proof when comparing the real and imaginary parts. Parker Emmerson is affiliated with now defunct, Marlboro College, as he attained his B.A. in Psychology and Philosophy with a focus on mathematics of perception in 2010.
Category: Functions and Analysis

[1] viXra:2310.0009 [pdf] submitted on 2023-10-02 05:29:02

Change of Variable in Integration

Authors: Jouni Puuronen
Comments: 19 Pages.

We find one proof for one form of the change of variable in integration result with Lebesgue integrals.
Category: Functions and Analysis