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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: More complex numbers than reals?
Date: Tue, 9 Jul 2024 12:17:05 -0700
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On 7/9/2024 12:11 PM, Chris M. Thomasson wrote:
> On 7/9/2024 10:30 AM, Ben Bacarisse wrote:
>> WM <wolfgang.mueckenheim@tha.de> writes:
>>
>>> Le 09/07/2024 à 14:37, Ben Bacarisse a écrit :
>>>
>>>> A mathematician, to whom this is a whole new topic, would start by
>>>> asking you what you mean by "more".  Without that, they could not
>>>> possibly answer you.
>>>
>>> Good mathematicians could.
>>>
>>>>   So, what do you mean by "more" when applied to
>>>> sets like C and R?
>>>
>>> Proper subsets have less elements than their supersets.
>>
>> Let's see if Chris is using that definition.  I think he's cleverer than
>> you so he will probably want to be able to say that {1,2,3} has "more"
>> elements than {4,5}.
>>
> 
> I was just thinking that there seems to be "more" reals than natural 
> numbers. Every natural number is a real, but not all reals are natural 
> numbers.
> 
> So, wrt the complex. Well... Every complex number has a x, or real 
> component. However, not every real has a y, or imaginary component...

To refine it... NO Real has a y, or imaginary component. The complex 
numbers do. So, can be thought of as being more dense? Or space filling 
a 2d plane? Reals are 1d. Is 2d "denser" than 1d? Or is that the wrong 
way to think about it? Thanks.


> 
> Fair enough? Or still crap? ;^o