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From: "Marin David Condic" <marin.condic.auntie.spam@pacemicro.com>
Newsgroups: comp.lang.ada
Subject: Re: Large numbers (or is Ada the choice for me?)
Date: Fri, 9 Mar 2001 18:28:43 -0500
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"Robert A Duff" <bobduff@world.std.com> wrote in message
news:wcck85yeeat.fsf@world.std.com...
> "Marin David Condic" <marin.condic.auntie.spam@pacemicro.com> writes:
>
> > This is a hopeless mission. Consider the instant you're row reduction
> > results in 1/3 - can you put that into a computer *without* an
approximation
> > and still do math on it?
>
> Yes.  What's the problem?  A rational arithmetic package can do exact
> arithmetic on 1/3 or any other rational number you can name.
>
Well, let me check a few assumptions. 1) We can never run out of numbers.
(Go ahead. Use all you want. We'll make more! :-) 2) We *can* and *will*
eventually run out of memory. Hence, even if you did all the math with some
sort of fractional representation rather than a decimal representation, it
would be possible to construct numbers that exceed the capacity of the
machine. Hence, I think it stands to reason that you would be off on a
fool's errand to insist on no approximations or limitations whatsoever.
There has to be some sort of practical upper limit imposed by the available
memory if nothing else.

As I said elsewhere, I rather hastily picked a bad example - but I think the
point still stands that one will have to live with some sort of
approximation on the representation - even if in practice, it may be so
small as to not matter. (Until you intersect Chaos Theory, at least! :-)

MDC