Re: More /.{I->-1} craziness. Schools
- To: mathgroup at smc.vnet.net
- Subject: [mg107055] Re: More /.{I->-1} craziness. Schools
- From: David Bailey <dave at removedbailey.co.uk>
- Date: Tue, 2 Feb 2010 03:23:51 -0500 (EST)
- References: <hjbvc0$2tp$1@smc.vnet.net> <hjeqh1$g3c$1@smc.vnet.net> <hjh877$r4r$1@smc.vnet.net> <201001261133.GAA00712@smc.vnet.net> <201001270644.BAA04729@smc.vnet.net> <op.u67uiib3tgfoz2@bobbys-imac.local> <hjrf98$n1e$1@smc.vnet.net>
Daniel Lichtblau wrote: > I had in mind the spoiler answer Richard Fateman provided in his first > post mentioning this particular tangent, err, example. > > http://forums.wolfram.com/mathgroup/archive/2010/Jan/msg00638.html > > At the bottom we find: > --- > I would especially avoid .nb objects, and most especially on topics of > numerical analysis, where the design flaws are, in my opinion, so > fundamental. Example (mathematica 7.0): > {x >= 1, x > 1, x > 0, x} > evaluates to > {True, False, False, 0.} > > can you construct x? > > RJF > > One possible answer, below.... > > x=0``-.5 > --- > > The point is that with Mathematica's version of significance arithmetic, > equality, I believe, is effectively treated as having a nontrivial an > intersection (of the implicit intervals defining two numbers). If > neither has any fuzz (i.e. both are exact), then Equal allows for no > fuzz, so this is only a subtlety if at least one of the values is > approximate. > > One implication is that a "zero" of sufficiently low (as in bad) > accuracy can be regarded as 1, or -1, or Pi, if those values happen to > fall within the accuracy (which I refer to as fuzz). > > The other inequalities follow from the preservation of trichotomy. For > explicitly real values we regard that as important. mathematica makes no > pretense that Equal is transitive and I do not see any way to do that > and also have useful approximate arithmetic. > > There has been some amount of communication off-line on this topic, > which is why some of us (well, me, at least) sometimes forget the > examples are not universally obvious to those who have not memorized the > enitre thread. > > Daniel > Maybe an notebook option to flag numbers of extremely low precision with a colour might be useful. I guess this might be useful more generally in numerical analysis. David Bailey http://www.dbaileyconsultancy.co.uk