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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: More complex numbers than reals?
Date: Tue, 09 Jul 2024 06:00:50 -0400
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Chris M. Thomasson explained on 7/9/2024 :
> 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?

In a sense there are 'more' since the reals are all on the x axis line 
whereas the 2D R x R space is filled with complex numbers. R is 
contained in C. In another sense they are the same size set, Q being 
basically R by R in the same sense as Q being Z by Z).

Are there any other sizes of sets between countable Q and uncountable 
R? How about between uncountable R and uncountable C?