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Re: Approximate Zero Times A Symbol

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. 

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}]


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.

I should have patented it :)

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