are int, float, long, double, side-effects of computer engineering?

[Albert van der Horst]

In article <5aaded58-af09-41dc-9afd-56d7b7ced239 at d7g2000pbl.googlegroups.com>,
Xah Lee  <xahlee at gmail.com> wrote:
<SNIP>
>
>what i meant to point out is that Mathematica deals with numbers at a
>high-level human way. That is, one doesn't think in terms of float,
>long, int, double. These words are never mentioned. Instead, you have
>concepts of machine precision, accuracy. The lang automatically handle
>the translation to hardware, and invoking exact value or infinite
>precision as required or requested.

With e.g. a vanderMonde matrix you can easily make Mathematica fail.
If you don't understand what a condition number is, you can't use
Mathematica. And yes condition numbers are fully in the realm
of concepts of machine precisions and accuracy.

Infinite precision takes infinite time. Approaching infinite precious
may take exponentional time.

>
> Xah

Groetjes Albert

--
-- 
Albert van der Horst, UTRECHT,THE NETHERLANDS
Economic growth -- being exponential -- ultimately falters.
albert at spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst