On 12/17/2012 3:52 PM, Stavros Macrakis wrote:
> I'd say that floats represent /imprecise or approximate /numbers, so
> 3.0 might mean exactly 3 or some other number in the interval 3-eps ..
> 3+eps.
>
This is a commonly held view among "amateur" computing types, including
any number of programming language fans, and for
that matter, physicists like Stephen Wolfram, but it doesn't work that
well.
I suspect that "professional"
numerical analysts would, by and large, say that floats represent
exactly some particular number. That is,
3.0 represents exactly the quantity 3. If you want to represent a
numeric interval you can do so with two numbers, each of
which represents exactly some particular number. e.g. [2.5, 3.5].
If you start by saying 3.0 represents 3+-eps, then what does 2.5
endpoint mean? 2.5+-eps? If it represents EXACTLY 2.5, then
you need a whole new number system of floats that mean what they say and
not some fuzzball.
RJF
> -s
>
> On Mon, Dec 17, 2012 at 6:36 PM, Barton Willis <willisb at unk.edu
> <mailto:willisb at unk.edu>> wrote:
>
> Maxima says that real floats are noninteger. There are arguments
> for and against this, I think. Of course for binary64 numbers 3.0 = 3
> is 100% true. I have been goofing around with the nonintegerp
> function--ahh it would be a great deal easier to keep the policy that
> floats are noninteger, by the way :)
>
> (%i3) map(lambda([s],featurep(s,'noninteger)),[x,%pi, 2/3,
> sqrt(42), 3.0, 6.0b0, [], [5]]);
> (%o3) [false,true,true,true,true,true,false,false]
>
> --Barton (who blames all recent mistakes on a bad cold).
>
>
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