Re: The s x construction

On Mar 28, 7:37 am, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On 27 Mar 2007 11:37:04 -0700, "Timothy Golden BandTechnology.com"



<tttppp...@xxxxxxxxx> wrote:
On Mar 27, 12:29 pm, Bart Goddard <goddar...@xxxxxxxxxxxx> wrote:
tttppp...@xxxxxxxxx wrote:
This is exactly the point. The choice of both or neither is
meaningless and so I snicker along with you here.

You can't snicker with me, because I'm snickering AT you.

Well I'd rather not argue that too seriously. I think we each have the
right to laugh.
But beyond that we should find a conflict in the argument and
particularly a mathematical one which you are attempting below here.
However the statement you make is not related to the statements I have
made. So where you ask if
0 > 0
or I suppose better yet
+ 0 > 0
I must respond no I do not believe these statements to be true.

And no, the point is _exactly_ that the little symbol in
front of a number tells you nothing about whether it is
positive or negative. E.g., tell me whether -a is positive
or negative. Or tell me whether -(3^e^pi - pi^e^3) is positive.

Is + 1 positive or negative? Does your logic work on that one?
The little symbol in front of the concrete instance does indeed tell
you what sign the number is.
And furthermore the non-concrete instance
- a
allows the construction of - 0. Just let a = 0.

The WHOLE point is that you don't look at or choose or anything
else the +/- sign in order to tell if a number is positive.
The only thing you look at is whether the number is >0.

So the question still remains, do you think 0>0?

It is here that the denial started
and I would hope that some of the people who deny this construction by
denying zero a sign can now see that they are mistaken to reject the
construction on that ground.

So you're confusing numbers with the symbols for the numbers?

Certainly this is not confusion. Mathematicians generally treat their
symbols to perfection and here I am exposing a problem in symbolic
usage in existing mathematics.

No, you're exposing a problem in your _understanding_ of
standard usage.

You're also exposing a problem in your understanding of
appropriate ways of conducting an argument. You never
answered his question: Does the fact that 1 = -(-1)
mean that 1 is negative?

Oops. I'll concede that. The answer is no, I don't think that
1
is negative or that
-(-1)
resolves to a negative value, though it is not uncommom to use the
terminology
'negative a'
where a could be
'negative one' .
All of this is sign mechanics. The sign '-' is generally accepted to
mean 'negative' and so this question is not a complete context. When
sign mechanics are resolved via
s x
we see that a string of signs sum and that this is a product
operation:
s1 s2 s3 s4 x = (s1 + s2 + s3 + s4) x
where for the reals the sum over s is modulo two with zero
representing '+'.

This is the complete answer and I look back at the original I actually
did address this. Still, I should be careful to answer each '?'
directly. I'll try to make a better habit of it. Thank you.




Certainly you should be in denial of
this, but upon applying effort to the situation we will hopefully
expose a conflict or even a resolution.

And you think everyone else is in denial? I'm still snickering
at you.

B.

--
The man without a .sig

I've said all along that
- 0 = + 0 = 0 .
There is no distinction and a rule to deny zero a sign is arbitrary
and without consequence. Where is the conflict? Is the above equation
accurate? If you see a conflict I hope you will let me know. These are
concrete instances of real numbers. The only reason that I quibble is
because some people seem to think that the
s x
construction is flawed by this argument about zero carrying a sign.
This is a trivial point and I am surprised that so many have
difficulty with this. There is a large discrepancy between convention
and consequence. Convention is an arbitrary choice which carries no
consequence other than consistency amongst communicating parties.
Strangely enough one of the most often used is 'nonnegative real
number' which is quite a mouthful for such a simple concept.

It is interesting to me that this comes up since I've been discussing
generalized sign for some time and this new stumbling point is
instructive to why it is so hard to communicate.

To quibble a bit further don't you accept that a numerical without
explicit sign is taken to be positive? This then is more contaminant
to the logic of the real numbers and here again we see magnitude being
dealt out as a subset of the reals. That is a mistake either way
right?

a = + a .
1 = + 1 .
0 = + 0 .

Nowhere have you actually found fault with my statements. Instead you
manufacture new ones that I find fault with. I think I understand the
tone of your snicker.

-Tim

************************

David C. Ullrich


.

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