Re: ONE


Martin Wanvik wrote:
> > I do not agree on that, because the symbole used to
> > seperate elements
> > in a set is the comma and not | .
> >
> > the comma should be defined.
>
> The notation used is not important. Sure, what I suggested is not the standard notation, but how is that relevant if it is used consistently?
>
> > a,b means a and b and a is different from b.
> >
> > Now S={a} here S is not equivalent to a. S is a
> > singleton set with a
> > as its only member, a is the member of S and it is
> > not identical with S.
> >
> > In a similar manner I can say S1={ a,b } here a,b is
> > the CONTENT of
> > the set S1 and a,b is not identical with S1.
>
> I don't think there are any meaningful way to separate the "content" of a set from the set itself, since the set basically /is/ the content, i.e one considers a collection of objects as a single entity.


Fair enough , then answer the following question is S in S={a}
identical to a. Now a is the content of set S,
In a previous post you said that a is different from set S.

Similarily speaking is emptyness which is the content of { } is the
same as { }.

If so then the set { { } } would equal { } , but this is against one
of the axioms of ZFC.

So I gave two example were the content of a set is seperate from the
set.

So why 1,2 ( which is the content of the set { 1,2 } ) is not
seperate from the set {1,2 }.

Can you explain why?

>
> > now let me take another set S2={c}
> >
> > Now Let S3= S1 U S2 = { a,b,c }
> >
> > Now if I form the set S1' = { a, b } but here a,b is
> > an element of S1'
> > and not like S1 were a,b are two elements of S1.
>
> You say a,b != {a,b} (!= means "not equal to"). In what way? I'd like a definition of a,b as a set, so that one can compare the elements of a,b to those of {a,b} and conclude that they really are different.

You cannot define a,b as a set , I will give you an analogy can you
define a in { a } as a set.
>
> > Now define S3' = S2 U S1' = { a, b, c}
> >
> > see that only listing S3' and S3 do not differentiate
> > between these two
> > sets.
>
> Correction: The /notation/ does not distinguish between the two sets, to the casual reader (i.e one not reading your explanations) the sets S3 and S3' are the same. But, clearly, they can be distinguished /as sets/, since you've /defined/ them to be different. After all, they don't contain the same elements, do they? This just means that the notation is brain-damaged, nothing else. Any notation that can't distinguish between different things is of limited use, to say the least.

No my dear, I offered the notation that should distinqish between them
, that is listing all possible orders of a set.

This is the only notation that can express a set in a right manner.

So a set which is composed of n elements should be expressed by n!
orders , in order for the set to be satisfactorily
displayed.
>
> > Now if we take the ordering of both sets S3' and S3
> > we can see the
> > difference between these two sets.
> >
> > S3 have six orders.
> >
> > S3' has four order because the orders { a,c,b } and {
> > b,c,a} are not
> > orders of S3' .
> >
> > because a,b = b,a work as one element .
>
> > I don't know if you are seeing what I mean.
>
> I think I do, but I still maintain that this is mainly a problem with your notation.

No you are wrong.

The real problem is that mathematicians think that the concepts of set
and set membership are prior to the concept
of number and especially the concept of one, while I think that the
concept of one is prior to the concepts of set and set member ship. To
my primitive and trivial understanding concepts like " is "
, " not " , "quality", "quantity", "part", "whole", "similar",
"repetition" ,"Exist" all of these are prior to the concept of "one"
and "many" , and thus prior to the concepts of set , set membership
and the concept of number.

Number is the concept which arise when we desribe "Many" in terms of
One.
Set is the concept which arise when we consider " Many" as one whole.
Set membership is One belonging to a set.

Zuhair

>
> > Zuhair
> >

.

Relevant Pages

  • Re: ONE
    ... Sure, what I suggested is not the standard notation, but how is that relevant if it is used consistently? ... So I gave two example were the content of a set is seperate from the ... Set membership is One belonging to a set. ... Zuhair ...
    (sci.math)
  • Re: ONE
    ... This just means that the notation ... > The real problem is that mathematicians think that ... > and set membership are prior to the concept ...
    (sci.math)
  • Re: ONE
    ... This just means that the notation ... >> The real problem is that mathematicians think that ... >> and set membership are prior to the concept ...
    (sci.math)
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