Number Theory

    

For All Hyperoperations, 2^4 = 4^2 is The Only Whole Number Pair Exception to their Anticommutativity

Authors: Anthony Veglia

All higher-order hyperoperations beyond multiplication are anticommutative, featuring a pair of distinct input values being the base and the power, such as x^y. Using real whole numbers, other than the infinite trivial examples where x = y, it has been proven that 2^4 = 4^2 is the only exception to the anticommutativity property of the hyperoperation exponentiation. This proof shows that for all higher-order hyperoperations, including tetration, pentation, and beyond, thatsingular exception, H3(2, 4) = H3(4, 2), remains the sole example of "anti"-anticommutativityusing real whole number inputs.

Comments: 7 Pages.

Download: PDF

Submission history

[v1] 2026-05-02 23:19:56

Unique-IP document downloads: 0 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus