Is the empty set a number?

On 7 Apr, 17:36, jonas.thornv...@hotmail.com wrote:

Is the empty set a number?

I am also wondering if the empty set isn't a missnaming?
For all i know {3}-{3}={} or it could be {3}-{3}=

All this leaves me with one question what is the set when there is no
values, and i must say it leaves me abit cofuseed, is there really an
empty set?

If so what is actually the set, i always thought the group initself
was the set.
And there is no member in the group, there is no group and no set, so
what is actually the empty set.

JT

On Apr 7, 11:46 am, jonas.thornv...@hotmail.com wrote:





On 7 Apr, 17:36, jonas.thornv...@hotmail.com wrote:

Is the empty set a number?

I am also wondering if the empty set isn't a missnaming?
For all i know {3}-{3}={} or it could be {3}-{3}
All this leaves me with one question what is the set when there is no
values, and i must say it leaves me abit cofuseed, is there really an
empty set?

If so what is actually the set, i always thought the group initself
was the set.
And there is no member in the group, there is no group and no set, so
what is actually the empty set.

JT

Why are you starting so many different threads
on the same topic? Do you actually want to
discuss this topic or do you just want to
start a lot of threads and not participate in
any of them?

             - Randy- Dölj citerad text -

- Visa citerad text -

On 7 Apr, 18:02, Randy Poe <poespam-t...@yahoo.com> wrote:



On Apr 7, 11:46 am, jonas.thornv...@hotmail.com wrote:

On 7 Apr, 17:36, jonas.thornv...@hotmail.com wrote:

Is the empty set a number?

I am also wondering if the empty set isn't a missnaming?
For all i know {3}-{3}={} or it could be {3}-{3}
All this leaves me with one question what is the set when there is no
values, and i must say it leaves me abit cofuseed, is there really an
empty set?

If so what is actually the set, i always thought the group initself
was the set.
And there is no member in the group, there is no group and no set, so
what is actually the empty set.

JT

Why are you starting so many different threads
on the same topic? Do you actually want to
discuss this topic or do you just want to
start a lot of threads and not participate in
any of them?

- Randy- Dölj citerad text -

- Visa citerad text -

Well i want you to prove that 0 is a number

Well i want you to prove that 0 is a number

And there is no member in the group, there is no group and no set, so
what is actually the empty set.

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.

On Apr 7, 1:08 pm, jonas.thornv...@hotmail.com wrote:





On 7 Apr, 18:02, Randy Poe <poespam-t...@yahoo.com> wrote:

On Apr 7, 11:46 am, jonas.thornv...@hotmail.com wrote:

On 7 Apr, 17:36, jonas.thornv...@hotmail.com wrote:

Is the empty set a number?

I am also wondering if the empty set isn't a missnaming?
For all i know {3}-{3}={} or it could be {3}-{3}
All this leaves me with one question what is the set when there is no
values, and i must say it leaves me abit cofuseed, is there really an
empty set?

If so what is actually the set, i always thought the group initself
was the set.
And there is no member in the group, there is no group and no set, so
what is actually the empty set.

JT

Why are you starting so many different threads
on the same topic? Do you actually want to
discuss this topic or do you just want to
start a lot of threads and not participate in
any of them?

             - Randy- Dölj citerad text -

- Visa citerad text -

Well i want you to prove that 0 is a number

In order to make sense of this question,
you have to be explicit about what exactly
do you mean by 'being a number'.

-- m- Dölj citerad text -

- Visa citerad text -

On Apr 7, 12:08 pm, jonas.thornv...@hotmail.com wrote:

Well i want you to prove that 0 is a number

OK. Let's start with your definition of "number"
and your definition of "0". What do you mean
by "0"? What do you mean by proving that
something is a number?

         - Randy

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,

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?

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.

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- Dölj citerad text -

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