Re: More complex numbers than reals?

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

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.

You are repeating yourself.  What do you mean by "more"?  Can you think
if a general rule -- a test maybe -- that could be applied to any two
set to find one which has more elements?

So, wrt the complex. Well... Every complex number has a x, or real
component. However, not every real has a y, or imaginary component...
>
Fair enough? Or still crap? ;^o

So you are using WM's definition based on subsets?  That's a shame.  WM
is not a reasonable person to agree with!

One consequence is that you can't say if the set of even numbers has
more or fewer elements than {1,3,5} because {1,3,5} is not a subset of
the even numbers, and the set of even numbers is not a subset of
{1,3,5}.  They just can't be compared using your (and WM's) notion of
"more".

--
Ben.