Re: uncountability without cantor


roh5337 wrote:
> "dwwdkddb" <kimfierens@xxxxxxxxxxx> wrote in message
> news:486882.1128512998163.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxxxxx
> > Is it possible to demonstrate the uncountability of the real numbers
> > without Cantor's diagonalization argument, or, even better, without any
> > explicit reference to decimal (or binary, or whatever) expansions, using,
> > for example, Dedekind cuts instead. What would such a proof look like.
> > Thank you.
>
> A measure theoritic proof uses the fact that every countable subset of real
> numbers have Lebesgue measure zero.
> An analytic proof uses Cantor's nested interval theorem to show that R\S is
> nonempty where S is any countable subset of R.

These are equivalent ways of saying the same thing.

To the OP's question, I will say that there seems to be a unique
concept that gives rise to "uncountability".

Regards,

--
Eray

.

Relevant Pages