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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 14:01:13 -0700
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On 7/9/2024 12:17 PM, Chris M. Thomasson wrote:
> 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?

The fact that n-ary data can be stored in 1-ary data seems to suggest 
that the reals are just as dense as the complex numbers? Fair enough?



> Or is that the wrong 
> way to think about it? Thanks.


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