Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!

-- Nth Complexity --
-- Have A Nice Day! --
http://www.insurgent.org/~kook-faq/s...query=Uncle+Al
"The teaching of science and mathematics must be purged of its
authoritarian and elitist characteristics, and the content of these
subjects enriched by incorporating the insights of the feminist,
queer, multiculturalist and ecological critiques." -- A.D.S.





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Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!

The IEEE Floating-Point Arithmetic Standard (IEEE 754) defines zero
representions as positive zero and negative zero. Just about every CPU on
the planet uses this standard. If zero is not positive or negative, then
what do you figure it is?

Nth Complexity wrote:

Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!

Idiot.

-- Nth Complexity --
-- Have A Nice Day! --
http://www.insurgent.org/~kook-faq/s...query=Uncle+Al
"The teaching of science and mathematics must be purged of its
authoritarian and elitist characteristics, and the content of these
subjects enriched by incorporating the insights of the feminist,
queer, multiculturalist and ecological critiques." -- A.D.S.

****ing imbecile.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

On Fri, 09 Sep 2005 23:05:41 +0000, Nth Complexity wrote:

Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!

-- Nth Complexity --
-- Have A Nice Day! --
http://www.insurgent.org/~kook-faq/s...query=Uncle+Al
"The teaching of science and mathematics must be purged of its
authoritarian and elitist characteristics, and the content of these
subjects enriched by incorporating the insights of the feminist,
queer, multiculturalist and ecological critiques." -- A.D.S.

Kooks can't nominate. Sorry those are the rules old boy.



--
mhm 27x12
smeeter #28
Usenet Valhalla Circle #19 & #21
Bartlo's hate lits #1:
CEO Alcatroll Labs Inc.

The Way of the Kook:
http://www.insurgent.org/~jhd/kookway.htm

in
Alexa "Crackpot" Cameron explains electromagnetism, and how
the sun has an 'iron core':
"The sun and the earth are 'magnets', each with an iron
based core, and both have an electrical force between them."

in Message-ID:
Mark "Woody" Ferguson shows his mastery of the English language:
"With patients and practice you could be nominated next time around..."

in Message-MID:
Mark "The illiterate" Ferguson astonishes everybody saying:
"Oh, for ****s sake, Gary no matter how angery he thinks he makes there
are lines I will not cross unless I believe what I say is the true, I
know more then you."

in Message-ID:
Alexa "Tequila Titsz" Cameron explains world religions:
"The jews roots are islamic."

in Message-ID:
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in Message-ID:
Alexa "Word Salad" Cameron shows her knowledge of science:
"Einstein never found the double superimposed doubl 'equilateral' triangle."

in Message-ID:
Alexa "Kook of the year 2004" Cameron uses words she doesn't understand again:
"Why is the Pentagon killing American citizens with non-lethal technology?"

in Message-ID:
Alexa "Imnotalexadammit" Cameron has problems with that extra finger
on her hand:
"Why do the Jews use the Star of David as symbolic of the Pentagon, or
Pentagram?"

reminder: Message-ID: in
The quote naziwhore Don Ocean stole.

In article ],
(Nth Complexity) wrote:

Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!

Depends. According to Bourbaki both, but by the common English standard,
neither.

Nth Complexity wrote:
Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!

I'm not certain Dirk is wrong. Most websites (like Wolframs) imply that
0 is neither positive or negative, but I don't think it's possible to
prove this (at least I can't, perhaps someone else can comment).

If you consider commutative rings (e.g. integers) or ordered fields
(e.g. reals) there is the additive identity axiom:

There exists y such that for all x, x + y = x

This is entirely insufficient to imply a single unique additive
identity y, although this seems to be the universal interpretation. 'y'
is usually called zero and given symbol 0.

Considering the integers Z, you can split Z into two sets P and N such
that:
1. For all x in Z, P contains x iff N contains -x; AND
2. P is closed under addition and multiplication.

Trivially, P is the set of positive integers and R is the set of
negative integers.

Where does 0 lie in here?

Well if it lies in BOTH P and Q there are no contradictions at all. But
this implies that 0 occurs twice in the integers (otherwise it couldn't
be placed in any of P or Q). Again, this is not strictly prohibited by
additive identity axiom. You could say there are two additive
identities 0+ and 0-, positive and negative respectively. A cursory
analysis their arithmetic reveals no axiomatic contradictions.

Based on this, I would need to say that 0 by itself does not exist.
Rather you have positive 0+ and negative 0-.

Is there an error here?


REMARK: The widely used terminology related to all this is:
"Positive integers" = 1,2,3, ...
"nonnegative integers" = 0, 1, 2, 3, ...
"negative integers" = -1, -2, -3, ...
"nonpositive integers" = 0, -1, -2, -3, ....





-- Nth Complexity --
-- Have A Nice Day! --
http://www.insurgent.org/~kook-faq/s...query=Uncle+Al
"The teaching of science and mathematics must be purged of its
authoritarian and elitist characteristics, and the content of these
subjects enriched by incorporating the insights of the feminist,
queer, multiculturalist and ecological critiques." -- A.D.S.





--
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This is a spam protected message. Please answer with reference header.
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"Schoenfeld" writes:

Nth Complexity wrote:
Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!

I'm not certain Dirk is wrong. Most websites (like Wolframs) imply that
0 is neither positive or negative, but I don't think it's possible to
prove this (at least I can't, perhaps someone else can comment).

You don't prove definitions.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum

Schoenfeld wrote:
Nth Complexity wrote:
Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!


[IGNORE PREVIOUS POST - SYMBOLS GOT MIXED UP DUE TO CARELESS EDITING]


I'm not certain Dirk is wrong. Most websites (like Wolframs) imply that
0 is neither positive or negative, but I don't think it's possible to
prove this (at least I can't, perhaps someone else can comment).

If you consider commutative rings (e.g. integers) or ordered fields
(e.g. reals) there is the additive identity axiom:

There exists y such that for all x, x + y = x

This is entirely insufficient to imply a single unique additive
identity y, although this seems to be the universal interpretation. 'y'
is usually called zero and given symbol 0.

Considering the integers Z, you can split Z into two sets P and N such
that:
1. For all x in Z, P contains x iff N contains -x; AND
2. P is closed under addition and multiplication.

Trivially, P is the set of positive integers and N is the set of
negative integers.

Where does 0 lie in here?

Well if it lies in BOTH P and N there are no contradictions at all. But
this implies that 0 occurs twice in the integers (otherwise it couldn't
be placed in any of P or N). Again, this is not strictly prohibited by
additive identity axiom. You could say there are two additive
identities 0+ and 0-, positive and negative respectively. A cursory
analysis their arithmetic reveals no axiomatic contradictions.

Based on this, I would need to say that 0 by itself does not exist.
Rather you have positive 0+ and negative 0-.

Is there an error here?


REMARK: The widely used terminology related to all this is:
"Positive integers" = 1,2,3, ...
"nonnegative integers" = 0, 1, 2, 3, ...
"negative integers" = -1, -2, -3, ...
"nonpositive integers" = 0, -1, -2, -3, ....

David Kastrup wrote:
"Schoenfeld" writes:

Nth Complexity wrote:
Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!

I'm not certain Dirk is wrong. Most websites (like Wolframs) imply that
0 is neither positive or negative, but I don't think it's possible to
prove this (at least I can't, perhaps someone else can comment).

You don't prove definitions.

Please READ what I said properly. I referred to the definitions (i
re-posted my post correcting symbol misplacements). Address queries in
other thread branch.

--
David Kastrup, Kriemhildstr. 15, 44793 Bochum

"Schoenfeld" wrote in message ps.com...

Schoenfeld wrote:
Nth Complexity wrote:
Dirk Van de moortel wrote:
By the way, zero is usually taken to be both positive and
negative.

Hahahahahahahahahahahahahahahahahahahahahahahahaha hahahahahahahaha!
And you expect to teach OTHERS?!


[IGNORE PREVIOUS POST - SYMBOLS GOT MIXED UP DUE TO CARELESS EDITING]


I'm not certain Dirk is wrong. Most websites (like Wolframs) imply that
0 is neither positive or negative, but I don't think it's possible to
prove this (at least I can't, perhaps someone else can comment).

As others have said, it is a question of defining things. In the part
of the world in which I live, Bourbaki is the standard. So my
statement that "zero is usually taken to be both positive and
negative" is correct - again, in the part of the world in which I
happen to live.



If you consider commutative rings (e.g. integers) or ordered fields
(e.g. reals) there is the additive identity axiom:

There exists y such that for all x, x + y = x

This is entirely insufficient to imply a single unique additive
identity y, although this seems to be the universal interpretation. 'y'
is usually called zero and given symbol 0.

Considering the integers Z, you can split Z into two sets P and N such
that:
1. For all x in Z, P contains x iff N contains -x; AND
2. P is closed under addition and multiplication.

Trivially, P is the set of positive integers and N is the set of
negative integers.

Where does 0 lie in here?

If your phrase "split Z into two sets P and N" implictly means
that the union of P and N is Z and that the intersection of P and N
is the empty set, then indeed by design, 0 is not in P and not in N.
So unless you explicitly specify what you mean, you can choose,
and the conditions you gave are not sufficient to decide more than
something like
P contains 0 == N contains -0 == N contains 0
i.o.w. 0 is in both or in neither.


Well if it lies in BOTH P and N there are no contradictions at all. But
this implies that 0 occurs twice in the integers (otherwise it couldn't
be placed in any of P or N).

That depends on what you want the phrase "split Z into two sets"
to mean. As soon as you decide on that, you have your answer.


Again, this is not strictly prohibited by
additive identity axiom. You could say there are two additive
identities 0+ and 0-, positive and negative respectively. A cursory
analysis their arithmetic reveals no axiomatic contradictions.

Based on this, I would need to say that 0 by itself does not exist.
Rather you have positive 0+ and negative 0-.

Is there an error here?


REMARK: The widely used terminology related to all this is:
"Positive integers" = 1,2,3, ...
"nonnegative integers" = 0, 1, 2, 3, ...
"negative integers" = -1, -2, -3, ...
"nonpositive integers" = 0, -1, -2, -3, ....

In my part of the world:
"Positive integers" = { 0, 1, 2, 3, ... }
"Strictly positive integers" = "Nonnegative integers" = { 1, 2, 3, ... }
"Negative integers" = { 0, -1, -2, -3, ... }
"Strictly negative integers" = "Nonpositive integers" = { -1, -2, -3, ... }

Gee.... what a silly non-issue.
Frenchman: "Ceci est une chaise."
Englishman: "No, this is a chair."
Frenchman: "Non, c'est une chaise!"
Englishman: "No, idiot, it is a chair!"
Frenchman: "Mais non, imbecile, je vous dis que c'est une chaise!!"
Englishman: "Get lost, idiot, it is a chair!!"
....

Dirk Vdm