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| Neil B.... |
 Posted: Sat Mar 21, 2009 3:18 pm |
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"William Elliot" <marsh at (no spam) rdrop.remove.com> wrote in message
news:20090316063841.Y74851 at (no spam) agora.rdrop.com...
[quote:07d4e05037]On Mon, 16 Mar 2009, David C. Ullrich wrote:
On Sun, 15 Mar 2009, Neil B. wrote:
roots of integers have to be either whole or irrational.
Assume r in N, r^(1/n) in Q. Thus some a,b in N with r^(1/n) = a/b.
I really wish you'd either write in complete sentences or
stop complaining to others about their grammar.
I'm not giving proofs, only outlines or sketches of proofs
with details left to the reader. Details like the reasons.
I strive to be complete and detailed. Complex logic is
better expressed in pseudo-symbolic logic than English.
You have no complaint about my writing.
Anyway:
rb^n = a^n; b^n | a^n; b | a (by simple theorem)
Do you know a complete proof of this "simple theorem"?
No. As I've said before, only an outline or sketch.
Will you be able to fill in the details?
BTW, simple is not trivial. For example
dx^2 / dx = 2x is simple and not trivial.
The theorem depends upon the equally not trivial simple theorem
(a^n,b^n) = (a,b)^n
which depends upon
(r^n,s^n) = 1
where
r = a/(a,b), s = b/(a,b)
and
(ku,kv) = k(u,v)
which of course isn't scalar vector multiplication
but multiplication of a positive integer by a gcf.
some k in N with a = kb; r = k^n, QED.
William, I'm not sure what the comma does in some of your examples. I[/quote:07d4e05037]
know e.g. that (a*b)^n = a^n * b^n, but what distinction is shown by the
use of commas there and elsewhere?
BTW, speaking of commas this is funny:
http://www.sackwear.com/product_info.php?products_id=34 |
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| A N Niel... |
| Posted: Sat Mar 21, 2009 3:59 pm |
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In article <2eOdnYdip5Nb1ljUnZ2dnUVZ_sHinZ2d at (no spam) posted.widowmaker>, Neil
B. <neil_delver at (no spam) caloricmail.com> wrote:
[quote:75be65b72b]William, I'm not sure what the comma does in some of your examples. I
know e.g. that (a*b)^n = a^n * b^n, but what distinction is shown by the
use of commas there and elsewhere?
[/quote:75be65b72b]
(a,b) means: greatest common divisor of a and b |
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