Am Samstag, 11. August 2012 15:33:22 UTC+2 schrieb calvin: > On Aug 11, 6:07 am, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote: > > > calvin <cri...@windstream.net> wrote: > > > >2) Are there any known examples of irrationals not > > > > made up in this way which have rational sums? > > > > > > Just subtract any irrational from any rational - the difference will > > > of course be irrational too. e.g. pi + (4-pi) = 4. > > > > Yes, and thanks to you and quasi, but that's > > not really saying much of anything about adding > > irrationals, when the irrational just cancels > > out. My example was contrived, too, I know.
Maybe this is more along the line you are looking for: Consider the polynomial f(X) = X^3 -42 X^2 + pi X -sqrt(2) I have no idea about the exact value of the three (complex) roots of this guy, but I do know 1) they are transcendental 2) their sum is rational, namely 42 3) their product is algebraic, namely sqrt(2)