Re: Rational and irrational numbers
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Sun, 28 Aug 2005 18:19:49 +0000 (UTC)
In article <1125230698.132863.242410@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<deepkdeb@xxxxxxxxx> wrote:
>I would appreciate any comment upon the correctness of the following
>assertion:
>
>Consider (1) below
>xy = z (1) where x,y,z are real numbers such that z is an
>integer,both x and y are irrational.
>Assertion: Both x and y must satisfy (2) and (3); (a,b) = 1.
>x = sqrt(a)+ sqrt(b) (2) and y = sqrt(a) - sqrt(b) (3)
>where atleast one of a or b must be a non-square.
This is false. Pick your favorite integer z, pick your favorite
irrational, e.g., pi. Set x = pi, y = z/pi.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
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Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx
.
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