[Haskell-cafe] smallest double eps
bandurvp at mcmaster.ca
Sat Sep 30 20:22:25 EDT 2006
-------- Forwarded Message --------
From: Victor Bandur <bandurvp at mcmaster.ca>
Reply-To: bandurvp at mcmaster.ca
To: Brandon Moore <brandonm at yahoo-inc.com>
Subject: Re: [Haskell-cafe] smallest double eps
Date: Sat, 30 Sep 2006 20:17:05 -0400
I'm new to this mailing list, so my response may be a little out of
place, but I think either what's being asked is what is the smallest x
such that 1 + x /= 1 (machine epsilon,) or the largest such that 1+x /=
x. The bounds seem to be confused.
On Sat, 2006-30-09 at 16:10 -0700, Brandon Moore wrote:
> Bryan Burgers wrote:
> >> >>> Hang on, hang on, now I'm getting confused.
> >> >>> First you asked for the smallest (positive) x such that
> >> >>> 1+x /= x
> >> >>> which is around x=4.5e15.
> >> >>
> >> >> 1 + 0 /= 0
> >> >>
> >> >> 0 is smaller than 4.5e15
> >> >>
> >> >> So I don't understand this at all...
> >> >
> >> > But then 0 isn't positive.
> >> Why not?
> >> In any case every positive number nust satisfy the above inequation
> >> so what
> >> about 0.1, which is certainly smaller than 4500000000000000?
> People are confusing equality and inequality -
> the nontrivial thing here is to find the smallest positive x
> that satisfies the equation 1 + x == x.
> > In math, every positive number must satisfy the above inequation, that
> > is true. But as Chad said, the smallest number in Haskell (at least
> > according to my GHC, it could be different with different processors,
> > right?) that satisfies the equation is 2.2e-16.
> And you've changed the subject - the stuff above was talking about
> x + 1 /= x, you're demonstrating solutions to a different problem,
> finding the smallest
> x such that 1 + x == 1. That's the number often called epsilon.
> >> 1 + 2.2e-16 /= 1
> > True
> >> 1 + 2.2e-17 /= 1
> > False
> Let's stop confusing ourselves about this.
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