Re: More complex numbers than reals?

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:
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Le 09/07/2024 à 14:37, Ben Bacarisse a écrit :
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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.

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Good mathematicians could.
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  So, what do you mean by "more" when applied to
sets like C and R?

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Proper subsets have less elements than their supersets.

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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}.
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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.
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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.

 

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Fair enough? Or still crap? ;^o