From Ted.Harding at manchester.ac.uk  Wed Feb 13 16:57:07 2008
From: Ted.Harding at manchester.ac.uk ( (Ted Harding))
Date: Wed, 13 Feb 2008 15:57:07 -0000 (GMT)
Subject: [Rd] 0.45<0.45 = TRUE (PR#10744)
In-Reply-To: <47B2E550.2020604@lancaster.ac.uk>
Message-ID: <XFMail.080213155707.Ted.Harding@manchester.ac.uk>

On 13-Feb-08 12:40:48, Barry Rowlingson wrote:
> hadley wickham wrote:
> 
>> It's more than that as though, as floating point addition is
>> no longer guaranteed to be commutative or associative, and
>> multiplication does not distribute over addition. Many concepts
>> that are clear cut in pure math become fuzzy in floating point
>> math - equality, singularity of matrices etc etc.
> 
>   I've just noticed that R doesn't calculate e^pi - pi as equal to 20:
> 
>   > exp(pi)-pi == 20
>   [1] FALSE
> 
>   See: http://www.xkcd.com/217/
> 
> Barry

Barry,
These things fluctuate. Once upon a time (sometime in 1915 will do)
you could get $[US]4.81 for ?1.00 sterling.

One of the rare brief periods when the folks on opposite side
of the Atlantic saw i^i (to within .Machine$double.eps, which
at the time was about 0.001, if you were lucky and didn't
make a slip of the pen).

R still gets it approximately right:

  1/(1i^1i)
  [1] 4.810477+0i

$i^i = ?1

Best wishes,
Ted.

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Date: 13-Feb-08                                       Time: 15:57:02
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[Rd] 0.45<0.45 = TRUE (PR#10744)
 (Ted Harding