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

From: Eray Ozkural exa (examachine_at_gmail.com)
Date: 11/21/04 

Date: 21 Nov 2004 09:19:08 -0800

stephen@nomail.com wrote in message news:<cnp65n$ibp$1@msunews.cl.msu.edu>...
> In sci.math Eray Ozkural exa <examachine@gmail.com> wrote:
> : stephen@nomail.com wrote in message news:<cnmolo$1gp8$1@msunews.cl.msu.edu>...
>
> : It is obvious what cardinality means, and it is not a definite thing,
> : because THIS PARADOX EXISTS. If you do not understand WHY this is a
> : paradox this is your problem.
>
> : Do you accept that there is a paradox or not?
>
> : Yes or no?
>
> What paradox are you talking about? There is no paradox
> involved with defining cardinality in terms of bijections
> of which I am aware. I would not call it paradoxical
> that different definitions of cardinality could be considered
> that lead to different conclusions. All results in mathematics
> are based upon your assumptions. Change the assumptions
> and the results change.

That would be mathematical solipsism. You can't define things
completely freely in mathematics. Once you define "number" you have
very little space to move...

I think "cardinality" must be synonymous with "size of a set" or
otherwise, it would be meaningless. To agree with your terminology,
consider that I've replaced all occurences of "cardinality" with
"size" in this exchange. Could you please answer my previous question
in that fashion?

I'm saying that there are two approaches for measuring the size of
sets, and in general the bijection account does not seem to be
satisfactory to reason about the size of infinite sets. Do you accept
that there is a paradox of the infinitely big? In other words, do you
agree with the received view in philosophy of mathematics, or not?

Regards, 

--
Eray Ozkural

Relevant Pages

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  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... :>: It is obvious what cardinality means, and it is not a definite thing, ... :>: paradox this is your problem. ... : completely freely in mathematics. ... idea of size and infinity this seems intuitive. ...
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  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... :>: It is obvious what cardinality means, and it is not a definite thing, ... :>: paradox this is your problem. ... : completely freely in mathematics. ... idea of size and infinity this seems intuitive. ...
    (sci.math)
  • Re: Zenkins paper on Cantor (reply of Dr. Zenkin)
    ... It is obvious what cardinality means, and it is not a definite thing, ... paradox this is your problem. ... completely freely in mathematics. ... satisfactory to reason about the size of infinite sets. ...
    (sci.math)
  • Re: Why is the Russell Paradox necessary?
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