hagman
Posts:
1,923
Registered:
1/29/05
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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:
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> > calvin <cri...@windstream.net> wrote:
>
> > >2) Are there any known examples of irrationals not
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> > > made up in this way which have rational sums?
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> >
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> > Just subtract any irrational from any rational - the difference will
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> > of course be irrational too. e.g. pi + (4-pi) = 4.
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> Yes, and thanks to you and quasi, but that's
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> not really saying much of anything about adding
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> irrationals, when the irrational just cancels
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> 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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