Orchid Win7 v1 <voi### [at] dev null> wrote:
> Consider for a moment the set of all natural numbers, N. This is (by
> definition) a countable set. Yet the set of all possible subsets of N is
> *uncountable*. And that's just plain ordinary subsets; the decimal
> expansion of a number is not merely a subset of N but an *ordered
> sequence* of digits. Intuitively it sounds like there should be *more*
> of these. (But, as with many things in set theory, it turns out actually
> the cardinalities are the same.)
> Wikipedia explicitly mentions this:
>
http://en.wikipedia.org/wiki/Cardinality_of_the_continuum#Alternative_explanation_for
Perhaps the mapping you proposed between the points on a unit line and
the ones in a unit square is indeed valid.
Although proving that it indeed is would be better than by something else
than "can you show me a counter-example?" :)
--
- Warp
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