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] straight-edge 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