Re: Approximate Zero Times A Symbol

*To*: mathgroup at smc.vnet.net*Subject*: [mg127113] Re: Approximate Zero Times A Symbol*From*: Richard Fateman <fateman at cs.berkeley.edu>*Date*: Sun, 1 Jul 2012 02:06:48 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201206270811.EAA18698@smc.vnet.net> <19783652.3140.1340794328091.JavaMail.root@m06> <jsh3a9$sir$1@smc.vnet.net>

On 6/28/2012 1:06 AM, djmpark wrote: .... The symbol x has a meaning, as one of > the basic elements of the algebra, that the scalar 0.0 does not have. Using > 0.0 x -> 0.0 changes the mathematical meaning of the expression. > This is certainly a useful discussion point. If x is "inches" then 0.0 * x still has a dimension (inches). If x is a vector, there is possibly a distinction worth drawing between a zero vector and a scalar. Etc. On the other hand, 0.0 in Mathematica means something other than mathematical zero in various versions of Mathematica. Though who can tell about the future. Try this. h = 0.50000000000000000000000 Do[ h = 2*h - h}, {i, 1, 50}] h One might think that h, being 0. would have the property that h*x would be 0. Also that h+1 would be 1. But you would be wrong. In the version 8 Mathematica, numbers like that 0. are displayed in a pink box, but of course there is no requirement that you print the result, and if you utter If[h==0,yes,no] the answer is "yes". So for programs it might as well be 0 if it is equal to 0. Aside: The pink box is not quite the right size. Too small. My suggestion (and implementation) was to display numbers with no significant digits in red. http://forums.wolfram.com/mathgroup/archive/2010/Jan/msg00897.html I should have patented it :)