On 16 Nov 2004 09:08:02 -0800, David Bandel wrote: > "G.A." <smNOecklSPAMers@hotmTHANKSail.com> wrote in message news:<firstname.lastname@example.org>... >> "Robert Israel" <email@example.com> wrote in message >> <a href="news://firstname.lastname@example.org...">news://email@example.com...</a> >> > In article <LsqdncyEcPWZTQTcRVnyhA@casema.nl>, >> > Thinus Pollard <firstname.lastname@example.org> wrote: >> > >> > >Given the above, what's the difference between irrational and >> > >transcendal numbers? I read, only a few days ago, e is transcendal, pi >> > >is transcendal, but it's unknown if pi + e is. Are these two concepts >> > >related? >> > >> > The word is "transcendental", not "transcendal". A number x is >> > transcendental if there is no polynomial of degree at least 1 >> > with rational coefficients that has x as a root. All transcendental >> > numbers are irrational, but not all irrational numbers are >> > transcendental. >> > >> >> Also, 100% of real numbers are transcendental.
> that's incorrect. 2 is a real number and it's not transcendental.
That does not contradict what he said. Think measure theory.
> it was mentioned earlier in this post that the cardinality of > irationals is 1 lower than the cardinality of reals... i wouldn't be > surprised if the same were true for transcendentals vs. irationals
The cardinality of the transcendentals is the same as the cardinality of the irrationals, which is the same as the cardinality of the reals.