Re: On writing negative zero - with or without sign



James Giles writes:

....

In simulating continuous reals, there are no exact zeros.

You keep repeating the same claim, but you don't offer any proof
of that claim. Do you deny that a subset of continuous reals
can be represented exactly with a finite number of bits?

Do you deny that a discrete subset of the continuous reals is
discrete?

I see that you didn't answer my question.

A property of a subset isn't necessarily a property
of the whole set.

A member of a subset is a member of the whole set. Is zero a
member of that subset?

Reals aren't discrete even though quite a
few differntly defined subsets of the reals are discrete.

Is zero a member of a discrete subset?

That's relevant because exactitude in computing is only
possible on discrete sets.

We're not talking about exactitude in general. We're talking
about the existence of an exact zero.

When simulating continuous sets
yuo have no exactitude.

So whenever the topic becomes whether pi is exact or not, you
can raise that point. But the issue is zero, not pi.

In simulating continuous reals there
are no exact numbers, zeros or otherwise.

I disagree. Consider the subset of reals that can be exactly
represented. I zero a member of that subset?

Well, you're now getting abusive as well.

Classic unsubstantiated and erroneous claim.

I have no interest in further proving you wrong.

Classic erroneous presupposition that you've proved me wrong.

No doubt you'll claim I've done no such thing.

With good reason.

In fact, nothing you've said is even slightly interesting,

On the contrary, you've been interested enough in what I've said
to keep responding for several days, several times per day.

much less convincing that anything I've said is wrong.

If you want to go through life thinking that there's no way for
a processor to represent an exact zero, that's your choice, Giles.

.



Relevant Pages

  • Re: Math, The Friend of Relativity
    ... Don't be reassured by the ranting of Uncle Bonehead, ... As if we would believe something just because Einstein said so. ... zero, either, by the same argument Uncle Ben gave for real numbers. ... I've already proven h does NOT belong to the set of reals, ...
    (sci.physics.relativity)
  • Re: in fact zero _is_ neither positive nor negative. THIS STATEMENT IS NOT TRUE
    ... So in fact zero can be negative and can be positive and it just ... which most then build the reals from. ... and agree that magnitude is much more fundamental ... and if you want to use the bourbaki "positive" (positif ?) to include ...
    (sci.math)
  • Re: An Alternative to Standard Arithmetic
    ... You have raised some extremely interesting issues concerning zero ... Wallis number in my original post because I thought it would ... suffers that same problem of reliance upon the reals to communicate. ... of new fundamentals, and so erasing some of the accumulation is ...
    (sci.math)
  • Re: The common usage of "nonnegative real number" is ludicrous.
    ... not necessarily zero, and that is usually what is meant by ... a complicated construction. ... When I want to talk about magnitude I am talking about ... reals contain zero or not is just convention. ...
    (sci.math)
  • Re: On writing negative zero - with or without sign
    ... exact zero, contrary to your claim that there is no such thing. ... that using float for something *other* than simulating continuous reals ... "exactitude" in general, but rather a very specific issue, namely ...
    (comp.lang.fortran)