Re: More complex numbers than reals?

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

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 :
>

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.

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.

Eh?  There are lots of finite sets of numbers that "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?

I think you need to take more care with words.  There are no "infinite
primes" just as there are no "infinite naturals".  All naturals (and
thus all primes) are finite.  There are an infinite number of them, but
none are infinite.

--
Ben.