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From: Guillaume Melquiond (guillaume.melquiond_at_[hidden])
Date: 20050914 02:10:15
Le mercredi 14 septembre 2005 à 02:12 0400, Daryle Walker a écrit :
> On 9/13/05 8:17 AM, "Guillaume Melquiond" wrote:
>
> [SNIP]
> > [1] Rational numbers are constructible. Irrational numbers are
> > constructible. Pi, E, and other common mathematical constants are
> > constructible. Numbers derived from them are constructible. Omega (the
> > halting problem encoding) is not constructible.
>
> I couldn't find this mathematical definition of "constructible;" is it known
> by another term? (The only definition I know of is for those ancient Greek
> compass & [unmarked] straightedge puzzles. But all the associated numbers
> for those are a subset of algebraic numbers. By that definition, pi and e
> are not constructible, since they're transcendental.) I looked in the
> Wikipedia, BTW. But maybe you mistyped; rational and irrational numbers
> cover _every_ real number, so you didn't have to specify pi, e, common
> constants, or derived values.
Sorry, "algebraic" is missing in my sentence; I wanted to express a
progression in the complexity of the numbers. As for what I called
constructible reals, you can look at the "computable numbers" page in
the Wikipedia. I should have checked beforehand that the word I use in
French was the one used in English :)
Anyway, my point was: "by definition", computable numbers are the ones a
computer can handle in arbitrary precision (emphasis on arbitrary), and
they cover a wider range than just rational numbers.
Best regards,
Guillaume
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