Re: Rounding errors

From: Michael Wojcik (mwojcik_at_newsguy.com)
Date: 08/26/04 

Date: 26 Aug 2004 16:22:30 GMT

In article <a--dnYIif_ZeSrDcRVn-qg@giganews.com>, "JerryMouse" <nospam@bisusa.com> writes:
> Robert Wagner wrote:
> >
> > That's because a fraction will not produce zero. Zero isn't a rational
> > number, it's a limit. As x approaches infinity, 1/x approaches zero.
> >
> > You can find documents on the Web saying zero is not a natural number
> > but is a rational number. My counter is that every rational number can
> > be expressed as a fraction of natural numbers. Show me a fraction that
> > produces zero.
>
> 0/1 ?

And it turns out that this fascinating result is not isolated. In
fact, there are infinitely many ratios of natural numbers that equal
zero! Who knew?

And, alas, not all rational numbers can be expressed as ratios of
natural numbers. Besides zero, there's an uncountably infinite
set of rationals which cannot be expressed as ratios of natural
numbers. Hint: They *can* be expressed as ratios of *integers*,
which is the proper definition.

(Of course, there are also ratios of integers - infinitely many -
which aren't rational. They might be hysteretic, depending on
whose take on the subject you prefer. But they all have the same
denominator, so they're easy to spot.) 

-- 
Michael Wojcik                  michael.wojcik@microfocus.com
As always, great patience and a clean work area are required for fulfillment
of this diversion, and it should not be attempted if either are compromised.
  -- Chris Ware

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