Re: More complex numbers than reals?

On 7/9/2024 3:29 PM, FromTheRafters wrote:

Chris M. Thomasson formulated the question :

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 :
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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.
>

  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}.
>

>
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.

 Seems is a funny word. Does there not 'seem' to be 'more' naturals than primes? Intuition fails, these sets are of the same cardinality.

[...]
I do think that the number of primes is infinite in the sense that they are all in the naturals. Every prime is a natural, but not every natural is a prime? Strange thoughts? Is there a countable number of infinite primes, just like there is a countable number of infinite naturals? Fair enough? countable as in if this natural number passes inspection, its a prime?