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From: Kaz Kylheku <643-408-1753@kylheku.com>
Newsgroups: comp.lang.c
Subject: Re: More complex numbers than reals?
Date: Tue, 9 Jul 2024 02:25:40 -0000 (UTC)
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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.

-- 
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