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On Mon, Dec 14, 2009 at 11:09:16AM -0800, Jeff Davis wrote:
[...]
> I think "countable" is a more accurate word than "discrete". Strings are
> discrete but not countable.
Oh, no -- strings (of finite, but arbitrary length) are not discrete --
you can always squeeze one more between two given strings. In this sense
there are quite similar to rational numbers. Can we call them
continuous? -- it depends, it seems that the terminology here isn't
consistent: sometimes the rationals are considered continuous (as per
the property above mentioned), sometimes the reals (which are a much
more monstrous construct!) are referred to as "the continuum".
As Robert points out, they are countable; you'd need infinite length
for them to be more than that (then they would behave a bit like the
reals, Cantor diagonal and all that ;-)
All that said, it's moot: in computers, we can't represent strings of
arbitrary length (PostgreSQL has an upper limit of about 1GB, right?).
The situation is even more restricted with floats (they are much
smaller; thus one could say that they're more "discrete" than strings,
even). Problem with floats is -- the granule is not the "same size" over
the whole range (nasty), and it's all implementation-dependent
(nastier). But given an implementation, the concept of "next" and
"previous" on floats is (if you give me some slack with NANs) mostly
well-defined. Same with strings (up-to) some fixed length.
Still, it seems non-discrete is a useful abstraction?
Regards
- -- tomás
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