Re: how to explain this weird effect? Integrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg46544] Re: how to explain this weird effect? Integrate*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Mon, 23 Feb 2004 02:15:37 -0500 (EST)*References*: <20040218182324.673$gV@newsreader.com> <c11se0$nkq$1@smc.vnet.net> <c14738$4bt$1@smc.vnet.net> <c16mc3$5q1$1@smc.vnet.net> <c1am0c$3oe$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

drbob at bigfoot.com (Bobby R. Treat) wrote concerning the bug which causes Limit[Floor[Cos[x]], x -> 0] to give 1, rather than 0: > The problem with Floor[Cos[x]] may be related to this situation: > > Floor[1 - 10.^(-17)] > 1 Thanks. Yes, it might be related to that. But it _shouldn't_ be related since everything in Limit[Floor[Cos[x]], x -> 0] is _exact_. BTW, I doesn't trouble me -- well, at least, not much -- that Floor[1 - 10.^(-17)] yields 1 . I've often mentioned (although perhaps not in this newsgroup) that using discontinuous functions such as Floor in floating-point arithmetic is _inherently_ perilous. One needs to learn to expect things like Floor[1 - 10.^(-17)] possibly being 1 . OTOH, note that Mathematica correctly gives 0 for Floor[1 - 10^(-17)] . Since everything there was exact, I would have been greatly troubled if Mathematica hadn't gotten that right. David