On 9/13/05 8:17 AM, "Guillaume Melquiond" <guillaume.melquiond@ens-lyon.fr> 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. -- Daryle Walker Mac, Internet, and Video Game Junkie darylew AT hotmail DOT com