-------- Forwarded Message -------- From: Victor Bandur <[EMAIL PROTECTED]> Reply-To: [EMAIL PROTECTED] To: Brandon Moore <[EMAIL PROTECTED]> Subject: Re: [Haskell-cafe] smallest double eps Date: Sat, 30 Sep 2006 20:17:05 -0400
Hi all, 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. Victor 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. > > Brandon > _______________________________________________ > Haskell-Cafe mailing list > [email protected] > http://www.haskell.org/mailman/listinfo/haskell-cafe _______________________________________________ Haskell-Cafe mailing list [email protected] http://www.haskell.org/mailman/listinfo/haskell-cafe
