Re: AW: [FWP] japhy had a silly idea...

["Daniel S. Wilkerson" <dsw@digital-integrity.com>]

"Pense, Joachim" wrote:

> Daniel S.Wilkerson wrote:
> >Bernie Cosell wrote:
> >
> >> > .. And since there is an obvious,
> >> > 1-to-1 mapping between the set of reals between 0 and 1 and the set of
> ...
> >Therefore, R1 and S have the same cardinality.  By the
> Schroeder-Cantor-Bernstein
> >theorem
> >(http://www.math.lsa.umich.edu/~mathsch/courses/Infinity/Cardinality/Lesson
> 4.shtml),
> >there is a 1-1 onto map between R1 and S.  (Perhaps I could be accused of
>
> The objective of the sub-discussion is not the existence of an 1-1 mapping
> between the two sets, but the presentation of an "obvious" one.
>
> Joachim

1 - That's what *you* think the subject is.  It wasn't at all clear that people
were clear that there existed such a mapping at all.

2 - Constructing such a mapping in a reasonably straightforward way is not
difficult, however it is a bit tedious.  Its your opinion whether such a thing
is obvious.

3 - The original discussion was about the cardinality of the set of infinte
sequences of characters from a finite alphabet.  Cantor's Diagonalization
Argument shows that this cardinality is strictly greater than countable.  This
is much more straightforward than any arguments about the Real numbers.

Daniel


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