Jonas:

That you call it something or anything does not make it a mathematical
entity, you have to prove you need it.

***

That you name it and use it, IS exactly what makes
a "mathematical entity."  Some terms in any axiomatic
system are left undefined.  "Zero," "number" and
"successor" are undefined terms in the Peano axioms.

It would in fact be impossible to do mathematics without
undefined terms.  Do you know why?

On 10 Apr, 10:14, "T.H. Ray" <thray...@aol.com> wrote:

Jonas:

That you call it something or anything does not make it a mathematical
entity, you have to prove you need it.

***

That you name it and use it, IS exactly what makes
a "mathematical entity."  Some terms in any axiomatic
system are left undefined.  "Zero," "number" and
"successor" are undefined terms in the Peano axioms.

4+0=4 isn't exactly using because if it was "THE RESULT" would be
anything but 4. So no there is not a number 0 "USED" in the above
operation.

It would in fact be impossible to do mathematics without
undefined terms.  Do you know why?

It works just fine.



Tom- Dölj citerad text -

- Visa citerad text -

On 7 Apr, 18:36, Randy Poe <poespam-t...@yahoo.com
wrote:
On Apr 7, 12:24 pm, jonas.thornv...@hotmail.com
wrote:

On 7 Apr, 18:08, "G.E. Ivey"
george.i...@gallaudet.edu> wrote:

Do you understand the concept of "equivalence"?
 one way of defining the natural numbers is to set
"0" to be the empty set, {}, "1" to be the set whose
only member is the empty set, {{}}, "2" to be the set
whose only members are the empty set and {{}}- that
is, whose only members are 0 and 1- {0, 1}, etc.

   We can then define the "successor" of any
number, x, to be the set containing x and all of its
members and show that Peano's axioms for the natural
numbers hold.
We could define addition of two such things by
"x+ 0= x and, (if b is not 1, then b= s(c) for some
some c) x+b= s(x+c) when b is not 0".  We could
define multiplication of two such things by "x*0= 0,
and x*b= x+ x*c for b not 0".

   For that particular system, with those
operations, yes, the empty set IS the number 0.  But
there are many other ways to define "numbers" that do
not use sets as numbers.  The important point is that
they are all "equivalent"- they all give the same
results.  You can think of "number" in terms of any
one of them.

But i claim i can calculate anything without
using zero as a number,

OK. What's the value of sin(x) at x=pi?

If I remove all the money from my bank account,
how much is in the account?

Well then your out of money, you could say your
account is absent of
money but that hardly make 0 a number.

Please calculate these things without using
zero.

        - Randhy

On 7 Apr, 18:36, Randy Poe <poespam-t...@yahoo.com
wrote:
On Apr 7, 12:24 pm, jonas.thornv...@hotmail.com
wrote:

On 7 Apr, 18:08, "G.E. Ivey"
george.i...@gallaudet.edu> wrote:

Do you understand the concept of "equivalence"?
 one way of defining the natural numbers is to set
"0" to be the empty set, {}, "1" to be the set whose
only member is the empty set, {{}}, "2" to be the set
whose only members are the empty set and {{}}- that
is, whose only members are 0 and 1- {0, 1}, etc.

   We can then define the "successor" of any
number, x, to be the set containing x and all of its
members and show that Peano's axioms for the natural
numbers hold.
We could define addition of two such things by
"x+ 0= x and, (if b is not 1, then b= s(c) for some
some c) x+b= s(x+c) when b is not 0".  We could
define multiplication of two such things by "x*0= 0,
and x*b= x+ x*c for b not 0".

   For that particular system, with those
operations, yes, the empty set IS the number 0.  But
there are many other ways to define "numbers" that do
not use sets as numbers.  The important point is that
they are all "equivalent"- they all give the same
results.  You can think of "number" in terms of any
one of them.

But i claim i can calculate anything without
using zero as a number,

OK. What's the value of sin(x) at x=pi?

If I remove all the money from my bank account,
how much is in the account?

Well then your out of money, you could say your
account is absent of
money but that hardly make 0 a number.

  Now it is starting to make sense.  The reason for asking this question, and the reason you not responded to the repeated question "what do you mean by 'a number'" is that you have no idea what a number is!





Please calculate these things without using
zero.

        - Randhy- Dölj citerad text -

- Visa citerad text -- Dölj citerad text -

- Visa citerad text -

On 7 Apr, 18:36, Randy Poe <poespam-t...@yahoo.com
wrote:
On Apr 7, 12:24 pm, jonas.thornv...@hotmail.com
wrote:

On 7 Apr, 18:08, "G.E. Ivey"
george.i...@gallaudet.edu> wrote:

Do you understand the concept of "equivalence"?
 one way of defining the natural numbers is to set
"0" to be the empty set, {}, "1" to be the set whose
only member is the empty set, {{}}, "2" to be the set
whose only members are the empty set and {{}}- that
is, whose only members are 0 and 1- {0, 1}, etc.

   We can then define the "successor" of any
number, x, to be the set containing x and all of its
members and show that Peano's axioms for the natural
numbers hold.
We could define addition of two such things by
"x+ 0= x and, (if b is not 1, then b= s(c) for some
some c) x+b= s(x+c) when b is not 0".  We could
define multiplication of two such things by "x*0= 0,
and x*b= x+ x*c for b not 0".

   For that particular system, with those
operations, yes, the empty set IS the number 0.  But
there are many other ways to define "numbers" that do
not use sets as numbers.  The important point is that
they are all "equivalent"- they all give the same
results.  You can think of "number" in terms of any
one of them.

But i claim i can calculate anything without
using zero as a number,

OK. What's the value of sin(x) at x=pi?

If I remove all the money from my bank account,
how much is in the account?

Well then your out of money, you could say your
account is absent of
money but that hardly make 0 a number.

  Now it is starting to make sense.  The reason for asking this question, and the reason you not responded to the repeated question "what do you mean by 'a number'" is that you have no idea what a number is!

Please calculate these things without using
zero.

        - Randhy- Dölj citerad text -

- Visa citerad text -- Dölj citerad text -

- Visa citerad text -

On 2008-04-10, in sci.math, Herman Rubin wrote:

One should be familiar with sufficiently many of the
representations that one can be said to understand
the integers.

Why? How do the set theoretic representations enter into our
understanding of the integers?

lwalke3'lausd.net wrote:
It appears that the OP has one of two concerns:
1. Is zero really a number?
2. Is the empty set really a set?
IMHO, no. The original question is:
Is the empty set a number?

On 9 Apr, 00:05, lwal...@lausd.net wrote:
So what numbers are in J? I doubt that the OP accepts the
existence of negative numbers, since then one would have
to wonder what -1+1 is.
Well that would be dent to no accept negative numbers of course i do.

Here is some expamples in "DECIMAL" base using positional value
representation and as you can guess 0 is missing representation in
this system.

-2000500009=-{[A,2][5,5][1,9]}

9000020005={[A,9][5,2][1.6]}

0,50000000009={[-1,5][-B,9]}

-1.90005=-{[1,1][-1,9][-5,5]}

In article
2cc61053-b0c1-4222-841f-af5fd0c6fd43@d45g2000hsc.googlegroups.com>,
Mariano Surez-Alvarez <mariano.suarezalvarez@gmail.com> wrote:

On Apr 8, 12:39 pm, Aatu Koskensilta <aatu.koskensi...@xortec.fi
wrote:
On 2008-04-08, in sci.math, Mariano Surez-Alvarez wrote:

Of course not, because the fact that
one can pick a specific construction
proves in particular that one can pick
*a* construction, thereby proving
non-vacuity of the theory (relative to
the consistency of whatever context one
is using to do the construction, of
course...)

Also, the construction of such concrete
models allows one to build intuitions.

But I would say that for all other
purposes, the Dedekind construction of
the reals, say, is absolutely irrelevant
from a mathematical perspective.

This paragraph I do not understand. I think that the
Dedekind construction of the real numbers is entertained
exactly for its relevance to mathematics.

On 2008-04-08, in sci.math, Mariano Surez-Alvarez wrote:
That was precisely my point. There is no
point in choosing a particular representation,
because all representations are isomorphic
and nothing one wants to do will depend
on the representation chosen. Hence, it
really does not make any sense to ask
`what is a number'.

So you think those who ask "What is a number?" are asking "What
representation for numbers should we choose?"?

One should be familiar with sufficiently many of the
representations that one can be said to understand
the integers.

Numbers are a type of naming in relation to things.

An empty set can only make sense in relation to other sets with a definable property.

The empty set designated as '0' is 'even' in relation to the integer number line pointing to size i.e., -2,-1, 0, 1, 2, etc...

But I think what your question is whether an empty set can be considered a 'thing.'

Numbers are not things. None of the numbers are things. They are just abstract concepts to rigidly classify and name things in rigid order. When you name a group of rocks '3.' The rocks are not '3', but the rigid naming relying on the abstract concept of '3' is '3.'

Abstract concepts like numbers cannot exist alone. Despite being 'nouns', they must also act as 'predicates' in that they must hook onto something in relation to something else to make sense.

This is because they are abstract. While all predicates are abstract not all nouns are. So it is important to make the splice in nouns.

This 'hooking' can take place among other 'abstract objects' and/or evemtually relationshps to physical things. Otherwise, you end up with nasty metaphysical dangling participles like Plato.

I hope that I have adequately answered your question.

B.T.

What do you mean by "out of money"? How would
you describe that state?

Well i guess the field for your account would actually show
" " space or []

That's your view of the representation of this
state (my bank uses "$0.00"). But forget trying
to represent it in a computer. Tell me what the
properties of this state are.