Re: ONE
- From: Martin Wanvik <martinw@xxxxxxxxxxxx>
- Date: Tue, 10 Jan 2006 04:01:32 EST
> 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.
> 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.
> 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.
> 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.
> Zuhair
>
.
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