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Topic: adding irrational numbers
Replies: 14   Last Post: Oct 10, 2012 3:13 PM

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hagman

Posts: 1,923
Registered: 1/29/05
Re: adding irrational numbers
Posted: Aug 12, 2012 12:30 PM
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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)

hagman



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