Re: Zenkin's paper on Cantor (reply of Dr. Zenkin)

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 11/24/04 

Date: Wed, 24 Nov 2004 08:59:54 +0100

examachine@gmail.com (Eray Ozkural exa) writes:

> "Jesse F. Hughes" <jesse@phiwumbda.org> wrote in message news:<87zn187lzj.fsf@phiwumbda.org>...
>> So what is the obvious meaning of "size of a set"?
>
> I did not say that "size of a set" has an obvious meaning, I said that
> it is obvious that cardinality must explain "size of a set", or it
> does not explain anything.

Cardinality is well-motivated to capture the size of a set. When a
child counts a collection of pencils, he is creating a bijection
between an initial segment of N and the set of pencils. For finite
sets, assigning a size clearly involves a bijection.

I've seen no reason why this isn't the essence of counting.

>
> Since there is the observed antinomy of the infinitely big,
> unfortunately "size of a set" is far from being an obvious concept.

What antinomy is that? 

-- 
Jesse F. Hughes
"Wiles made somewhere around half a million dollars U.S. that I heard
about, and I know he didn't take major endorsements."  
  --JSH on the rewards of proving Fermat's last theorem.

Relevant Pages

  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... child counts a collection of pencils, ... between an initial segment of N and the set of pencils. ... assigning a size clearly involves a bijection. ... > Since there is the observed antinomy of the infinitely big, ...
    (comp.theory)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... > child counts a collection of pencils, ... > between an initial segment of N and the set of pencils. ... assigning a size clearly involves a bijection. ...
    (comp.theory)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... > child counts a collection of pencils, ... > between an initial segment of N and the set of pencils. ... assigning a size clearly involves a bijection. ...
    (sci.math)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... >> between an initial segment of N and the set of pencils. ... assigning a size clearly involves a bijection. ... This is nonsense, of course. ... It is nonsense on the literal reading because counting does not ...
    (sci.math)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... >> between an initial segment of N and the set of pencils. ... assigning a size clearly involves a bijection. ... This is nonsense, of course. ... It is nonsense on the literal reading because counting does not ...
    (comp.theory)