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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: comp.lang.c
Subject: Re: More complex numbers than reals?
Date: Mon, 8 Jul 2024 22:20:27 -0700
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On 7/8/2024 7:25 PM, Kaz Kylheku wrote:
> On 2024-07-08, Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
>> Are there "more" complex numbers than reals? It seems so, every real has
>> its y, or imaginary, component set to zero. Therefore for each real
>> there is an infinity of infinite embedding's for it wrt any real with a
>> non-zero y axis? Fair enough, or really dumb? A little stupid? What do
>> you think?
> 
> The argument is not that simple. If we restrict to just integer complex
> numbers like 4 + 5i, then no; there aren't more of these than integers.
> Yet the same argument about axes and embeddings could be wrongly applied.
> 
> Integer complex numbers are countable: you can start at 0, and then go
> in a spiral fashion:  1, 1 + i, i, -1 + i -1, ...  thus they can be put
> into correspondendce with the natural numbers.
> 

This was meant for sci.math... ARHG!!!! Well, shit. Sorry... Hummm... 
its fun to think about complex as vectors wrt addition, subtraction, but 
multiplication is different, division, ect...

Actually, here is some of my c++ code that might be relevant here wrt 
precision of complex numbers.... float, double, ect...

https://groups.google.com/g/comp.lang.c++/c/05XwgswUnDg/m/Wku2Oym_BQAJ

https://groups.google.com/g/comp.lang.c++/c/05XwgswUnDg/m/s_RNcUHCBQAJ

More info where complex numbers and their precision is important:

https://paulbourke.org/fractals/multijulia/
(read all!)

:^)