# What do I need to create a coherent new set of numbers?

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### Answers (1)

Pavl M.
on 14 Oct 2024 at 17:30

Edited: Pavl M.
on 14 Oct 2024 at 17:34

According to phylosophy, the novel set of numbers should be closed under:

- Distinction property (i.m. how to distinguish between one or another number). And more advance of this property is comparison property (comparator operator). If you make it closed also under comparison, then the set of numbers is just some transformation of the set of Regnal Numbers.

%New_number for new dimension evaluation class:

classdef new_n

properties

x

y

z

end

methods

function obj = new_n(x1,y1,z1)

obj.x = x1;

obj.y = y1;

obj.z = z1;

end

function r = X_(obj)

r = obj.x;

end

function r = Y_(obj)

r = obj.y;

end

function r = Z_(obj)

r = obj.z;

end

function r = ThirdDimension(obj)

r = obj.z;

end

function r = R(obj)

r = sqrt(obj.x^2 + obj.y^2 + obj.z^2);;

end

function ang = angle(obj)

u = [obj.x obj.y obj.z];

v = [1 0 0]; % or v = [0 1 0];

ang = atan2(norm(cross(u,v)), dot(u,v));

end

end

end

%new_symbol = 0^0*k_s; % Matlab so far only has i,j symbols for Complex Numbers (max)

%new_number = [x y z];

%new_number = Re(new_number) + i*Im(new_number) + new_symbol*ThirdDimension(new_number);

%where Re and Im are the regular Real and Imaginary parts of Complex Number

%and ThirdDimension is the your new dimension.

%Graphically it will be 3rd axis Z. So 3D plot instead for 2D for z = Real + j*Imaginary;

%It will be polar plot in 3D, just the radius will be R radius of sphere

%R = sqrt(Re(new_number)^2 + Im(new_number)^2 + ThirdDimension(new_number)^2);

%The angle will be

%u = [Re(new_number) Im(new_number) ThirdDimension(new_number)];

%v = [1 0 0]; % or v = [0 1 0];

%phase = atan2(norm(cross(u,v)), dot(u,v));

%To be continued: 3D polar representation of new number:

%new_number = R*exp(phase*3DUnitVector)

%You may try graphically

%disp('For many works dedicated to only you, pay me salary in natural number to my real account number for work in on the specific subdomain of hyperreal analysis domain or other custom.')

%Developed from needing help code by

%https://independent.academia.edu/PMazniker

%+380990535261

%https://diag.net/u/u6r3ondjie0w0l8138bafm095b

%https://github.com/goodengineer

%https://orcid.org/0000-0001-8184-8166

%https://join.skype.com/invite/oXnJhbgys7oW

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%https://www.youtube.com/channel/UCC__7jMOAHak0MVkUFtmO-w

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