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From: sobriquet <dohduhdah@yahoo.com>
Newsgroups: sci.math
Subject: Re: More complex numbers than reals?
Date: Tue, 9 Jul 2024 21:38:19 +0200
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Op 09/07/2024 om 07:24 schreef Chris M. Thomasson:
> 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?

How can you compare them if they are not even in the same dimension?
It seems that instead of comparing the real number line to the complex 
plane (or the Cartesian plane for that matter), you might as well 
compare a unit of length to a square unit of area.
Numerically they might be the same, but they are not identical, because
a line has no area, so a unit of length 1 has an area of 0 units squared.