PS: I've never posted personal details of anyone (other than their
name, if and only if they've used their name publically) on usetnet or
the web. I have never ever sought to defame someone on the web, and any
suggestion otherwise are outright lies.

In article .com "Schoenfeld" writes:
Robert Low wrote:
Schoenfeld wrote:
....
I realize that now. Unfortunately I was thinking
"for all x there exists y such that x + y = x" which doesn't guarantee
uniqueness at all.

Indeed, it doesn't even guarantee the existence of an
additive identity.
....
hint: you made the error not me.

Here are your words:
| Indeed, it doesn't even guarantee the existence of an
| additive identity.

Will you admit to your error?


Do you think that "for all x there exists y such that x + y = x"
guarantees the existence of an additive identity?

I'd neglected to take into account your
other track record of being indignant
and offensive whenever your elementary
mistakes are pointed out.

And your snide remarks aren't indignant or offensive? If you follow the
thread, you'll find I only retaliate and never instigate. Girls play
tit-for-tat, I simply retaliate exponentially. An eye for a head,
girlie - sure it'll leave the world decapitated but only if someone's
left to observe it.

Good luck in your future investigations.

Thanks, girlie.

And goodbye.

Good riddance.



--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

Dik T. Winter wrote:
In article .com "Schoenfeld" writes:
Robert Low wrote:
Schoenfeld wrote:
...
I realize that now. Unfortunately I was thinking
"for all x there exists y such that x + y = x" which doesn't guarantee
uniqueness at all.

Indeed, it doesn't even guarantee the existence of an
additive identity.
...
hint: you made the error not me.

Here are your words:
| Indeed, it doesn't even guarantee the existence of an
| additive identity.

Will you admit to your error?


Do you think that "for all x there exists y such that x + y = x"
guarantees the existence of an additive identity?

As dirk would say, "in mathematics learn to be precise".

Axiom: Additive Identity
for all x there exists y such that x + y = x

guarantees an additive identity.





I'd neglected to take into account your
other track record of being indignant
and offensive whenever your elementary
mistakes are pointed out.

And your snide remarks aren't indignant or offensive? If you follow the
thread, you'll find I only retaliate and never instigate. Girls play
tit-for-tat, I simply retaliate exponentially. An eye for a head,
girlie - sure it'll leave the world decapitated but only if someone's
left to observe it.

Good luck in your future investigations.

Thanks, girlie.

And goodbye.

Good riddance.



--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

In article .com "Schoenfeld" writes:

Dik T. Winter wrote:
In article .com "Schoenfeld" writes:
Robert Low wrote:
Schoenfeld wrote:
...
I realize that now. Unfortunately I was thinking
"for all x there exists y such that x + y = x" which doesn't guarantee
uniqueness at all.

Indeed, it doesn't even guarantee the existence of an
additive identity.
...
hint: you made the error not me.

Here are your words:
| Indeed, it doesn't even guarantee the existence of an
| additive identity.

Will you admit to your error?


Do you think that "for all x there exists y such that x + y = x"
guarantees the existence of an additive identity?

As dirk would say, "in mathematics learn to be precise".

Axiom: Additive Identity
for all x there exists y such that x + y = x
guarantees an additive identity.

Nope. The axiom is "there is an y such that for all x: x + y = x".
Something slightly different.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

Dik T. Winter wrote:
In article .com "Schoenfeld" writes:

Dik T. Winter wrote:
In article .com "Schoenfeld" writes:
Robert Low wrote:
Schoenfeld wrote:
...
I realize that now. Unfortunately I was thinking
"for all x there exists y such that x + y = x" which doesn't guarantee
uniqueness at all.

Indeed, it doesn't even guarantee the existence of an
additive identity.
...
hint: you made the error not me.

Here are your words:
| Indeed, it doesn't even guarantee the existence of an
| additive identity.

Will you admit to your error?


Do you think that "for all x there exists y such that x + y = x"
guarantees the existence of an additive identity?

As dirk would say, "in mathematics learn to be precise".

Axiom: Additive Identity
for all x there exists y such that x + y = x
guarantees an additive identity.

Nope. The axiom is "there is an y such that for all x: x + y = x".
Something slightly different.

Is that your way of dodging an error you made but tacticly did not
explicitly write?

The statement,
Axiom: Additive Identity
"for all x there exists y such that x + y = x"

defines an additive identity for all x.

Your error was assuming that no such y existed because no such number
exists, but to get numbers you need a ring and the axiom above is not
compatable with that of a ring.

At least you were smarter than the coward Robert Low, and did not
explicitly state the error you were thinking.

--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

In article . com,
Schoenfeld wrote:

The statement,
Axiom: Additive Identity
"for all x there exists y such that x + y = x"

defines an additive identity for all x.

It defines a thing like an additive identity for *each* x, but it
doesn't require that it's the same for each one, which is what is
meant by "additive identity".

-- Richard

Richard Tobin wrote:
In article . com,
Schoenfeld wrote:

The statement,
Axiom: Additive Identity
"for all x there exists y such that x + y = x"

defines an additive identity for all x.

It defines a thing like an additive identity for *each* x, but it
doesn't require that it's the same for each one, which is what is
meant by "additive identity".

That's exceedingly obvious (as was acknowledged by me over 12 times in
this thread). But strictly speaking, with that definition, the additive
identity DOES exist but it is obviously not a number.

note: rather than admitting his mistake, Robert Low simply ran away
like the coward he is.

-- Richard

note: rather than admitting his mistake, Robert Low simply ran away
like the coward he is.
********

Was it like the brave soldiers in "Monty Python and the Holy Grail"
when they faced danger?????

"RUN AWAY!!!! RUN WAY!!!!!"

note: rather than admitting his mistake, Robert Low simply ran away
like the coward he is.
********

Was it like the brave soldiers in "Monty Python and the Holy Grail"
when they faced danger?????

"RUN AWAY!!!! RUN AWAY!!!!!"

In article .com,
Schoenfeld wrote:

The statement,
Axiom: Additive Identity
"for all x there exists y such that x + y = x"

defines an additive identity for all x.

It defines a thing like an additive identity for *each* x, but it
doesn't require that it's the same for each one, which is what is
meant by "additive identity".

That's exceedingly obvious

So why did you make the false claim above?

But strictly speaking, with that definition, the additive
identity DOES exist but it is obviously not a number.

That doesn't sound like "strictly speaking" to me. On the contrary, it
sounds like you're making it u p as you go along.

note:

Sorry, not interested.

-- Richard