Re: in fact zero _is_ neither positive nor negative. THIS STATEMENT IS NOT TRUE



On Mar 29, 3:52 pm, "galathaea" <galath...@xxxxxxxxx> wrote:
On Mar 29, 11:12 am, "Timothy Golden BandTechnology.com"



<tttppp...@xxxxxxxxx> wrote:
On Mar 29, 1:58 pm, "galathaea" <galath...@xxxxxxxxx> wrote:

On Mar 29, 8:28 am, "Timothy Golden BandTechnology.com"

<tttppp...@xxxxxxxxx> wrote:
On Mar 29, 9:27 am, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:

On 28 Mar 2007 04:25:59 -0700, "Timothy Golden BandTechnology.com"

<tttppp...@xxxxxxxxx> wrote:
On Mar 28, 7:35 am, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On 27 Mar 2007 06:30:10 -0700, "Timothy Golden BandTechnology.com"

<tttppp...@xxxxxxxxx> wrote:
On Mar 21, 8:51 am, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On 20 Mar 2007 07:04:10 -0700, "Timothy Golden BandTechnology.com"

<tttppp...@xxxxxxxxx> wrote:
On Mar 20, 9:15 am, Bob Kolker <nowh...@xxxxxxxxxxx> wrote:
Timothy Golden BandTechnology.com wrote:
If I were a linguist and I said something like
antinegative energy
I would be criticized for using a double negative.
In mathematics we readily admit that the term "nonnegative real
number" admits the number zero and so should not be replaced with
"positive number".

0 can be thought of as neither negative or positive.

Bob Kolker

And it can be thought of as both negative and positive.

Yes. It can also be thought of as a rutabaga.

But in fact zero _is_ neither positive nor negative.

Actually there is no fact here at all.
The value
+0
is the same as the value
-0
and that is the same as
0
whether or not you use a default positive sign.
So in fact zero can be negative and can be positive and it just
doesn't matter. The usage of such an argument is meaningless as a
means of decision. The claimed distinction carries no value.

_What_ "claimed distinction"?

You're very confused. Yes, 0 = +0 = -0. That has no relevance
to the fact that 0 is neither positive nor negative.

The "claimed distinction" is your statement above. This distinction
has no consequence.

Again, _what_ "distinction"? I've looked at my atatement again,
and I don't see where I made any "disctinction".

Your statement:
"in fact zero _is_ neither positive nor negative."
distinguishes zero from the negative and positive numbers. This
distinction carries no value. There is no harmful consequence if zero
is allowed to be either positive or negative. The distinction of these
words is merely convention.

Would you respond to the Bourbaki claim made by others here? My own
conclusion is apparently in agreement with Bourbaki. Thus far I have
not found a reference for the reals but there is one for the counting
numbers, which most then build the reals from. I'd rather find a
direct reference. Regardless of whether this Bourbaki reference exists
I do not need it to prove my point.

Also I ask that you explain what the meaning of a convention is. For
instance if one were to replace the statement:
"Positive numbers are greater than zero"
with the statement:
"Positive numbers are magnitudes with a plus sign in front of them"
are there any harmful consequences? There are not harmful consequences
and so this distinction is merely convention. My restatement seems a
bit crude but the basics are there and this is already understood to
be what we've been discussing.

And lastly I have provided another argument about signed infinity that
I wish you would address.
Since I have responded to your questions I hope you will respond to
the issues which I repeatedly bring up as that is the good behavior
you yourself believe in.

This feels a bit like a game of chess where at the end the pieces are
nearly even and each opponent waits for the other to make a mistake.
Your moves are exposed here for all to see. Your credibility as a
regular poster to these groups hinges upon your honesty. Beyond that I
encourage you to keep an open mind and I will try to do the same.

timothy

i really enjoy your novel approach to sign
and agree that magnitude is much more fundamental

as you have mentioned
this was also mentioned at times by poincare
and corresponds to the basic foundations of our sciences

counting
measuring
distance
area
volume

this even has probabilistic support

however
i think if you want to appeal to these cases
you may have to recognise a special role for zero

we do not count to zero
we acknowledge the absence of things to count

in pattern recognition theory and neurolinguistic development research
this is a distinctly different activity than counting

we do not measure zero distance between two points

when the distance falls to zero
there is no longer a distinction between two points to measure

signed zeroes are useful abstractions
and i can understand why conceptually in your system they are more
"natural"
but i think if you make this argument
you lose the argument on magnitudes

the real numbers are also very useful abstractions

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar

Thanks for sharing your thoughts. I have considered this idea of
denying a zero distance and found some interesting consequences. They
are in the usenet somewhere. If we suppose a smallest distance a non-
lattice continuum is set up with a sort of planck length, though I
found the Fermi to be approximately the shortest length by guessing
that the shortest wavelength of emag radiation has already been
observed.

Physically I concur that this signed zero thing is not of value. Yet
there is no contradiction by building things this way and here someone
is refuting the
s x
construction by setting x to zero and claiming there is no s for that
special case. It's a granular point that allows me to explore how
other people see the real number system. There are other gripes about
subtraction being different than addition and so forth that are also
quagmire type discussions. Some people are hung up on sign products
and don't seem willing to let go. Just a few moments of thought are
needed to see that the signed zero works just fine. Humans doing
math...

I'm not really clear on why you reject zero as a magnitude. I
understand the idea about if two points have zero distance then they
are the same point, but I don't see an inherent contradiction in
allowing a zero magnitude. I'm not trying to break the real numbers.
They are built in the polysign system as two-signed numbers, with
complex numbers following them with no additional rules. The
acceptance of generalized sign is problematic because of the way that
tradition has built the reals. People do not see the signs for what
they are.

i did not mean to imply
that i felt zero was not a magnitude

only that it is special in certain ways
that make it useful to differentiate from

I agree that zero is a special value.
I do think your discussion below about the inequality is also
purposeful.
I tend not to work with the inequaltiy very much but it is considered
fundamental to the notion of magnitude where the ability to order
instances is paramount. Is this your existential predicate in
continuous form? This is an interesting juncture since we sometimes
see many ways to perform ordering and even our numerical system allots
for multiple symbollic representations with the flexibility of radix,
which is also very close to the quality of sign under the polysign
construction.

The inequality deserves a sort of 'preconstruction' in the fundamental
of magnitude, or rather these two are nearly synonymous as in Dedekind
cuts so whatever the construction of continuous magnitude the discrete
instances whose existence we assume allow such a quality. The equality
of such things might lend itself to your earlier point logic 'if the
distance is zero then the two points are one point' (not a direct
quote). Is this concept broken since we have no geomtetry to work on
at the level of magnitude? The introduction of sign allows for
geometry and so the significance of sign to geometry is exposed.

This probably sounds too loose but I believe that this interpretation
is accurate under the polysign system. Like the many definitions of
the real numbers interpretations will vary but the underlying
principles do not break between interpretations.

Galathea your writing is really interesting and I enjoy reading most
of your stuff on usenet. I have a hard time following sometimes but
usually I can pick up something here or there even when lost. Thanks
for corresponding here. I do not enjoy the nitpicking conversations
that I get into here, but I am compelled to persist in them. This
medium has a value in this way not so much to push an idea as to prove
(or disprove) an idea. Human nature is so cleanly exposed here that it
makes me want to barf sometimes. You should see some of the stuff I
delete from my own posts. Censorship at the internal level I think
should be encouraged on this medium that is so free of it.

-Tim



in the real
the classical notion of positive does not include zero
allowing many useful formulations

the positive inequality is strict

positive x > 0

the "nonnegative" inequality is not

"nonnegative" x >= 0

counting a positive implies an existential predicate

those tiny little conveniences
get used in a number of places

obviously
in a polysign formalism
the term "nonnegative" is not the appropriate term to use
but i think you will find some use in making the distinction
just using a different naming scheme that makes more sense for your
numbers

in other words

i am not attacking +0, -0, *0, ...
i am just saying that there is a reason someone might differentiate

+ x

when x can be 0 or cannot be 0

and if you want to use the bourbaki "positive" (positif ?) to include
0
you may wish to come up with a clever name for the other case

..

it is interesting watching
what are essentially linguistic revolutions
and the back-reactions formed

mathematicians seem to regularly obey a natural partition
( the same goes for computer scientists
and other scientists that fashion themselves mathematically
rigorous )

- those who create new symbologies to explore creative relationships
- those who rigorously adhere to "standardised" symbologies and names

the latter group rarely makes more than incremental advances
and the former group tends to make more mistakes

as with much
this seems the neophobia / neophilia distinction in action

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar


.