NOMINATION: Dirk Van de moortel for VVFWS
"Kadaitcha Man" wrote in message ]...
Dirk Van de moortel wrote:
"Schoenfeld" wrote in message oups.com...
Dirk Van de moortel wrote:
"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.
Is there any definition other than the one given by the additive
identity axiom for rings or fields? The remainder of this posts assumes
no.
AXIOM: Additive Identity
There exists y such that for all x, x + y = x
Does that axiom imply that there exists only 1 additive identity? Based
on my understanding of the existential quantifier, it does not.
Indeed, it does not.
So we suppose there are (at least) two such identities, let's not call them
George and Freddy, but Y1 and Y2.
Then we have, thanks to your axiom:
for all x: x + Y1 = x [1]
for all x: x + Y2 = x [2]
so we also have when we apply [1] to our number Y2:
You are assuming x = Y2.
You are an idiot.
Dirk Vdm
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