Re: { }


leo1476@xxxxxxxxxxx wrote:
> >>"Also I find it very difficult to see why { } is not equal to
> >>nothingness."
>
> Do you mean "...equal to nothingness"? Well the empty set is a subset
> of every set because it logically follows from this argument:
>
> [NOTATION: " !< " means not a subset of; so A !< B, means A not a
> subset of B.]
>
> Suppose { } !< of all sets A; then there exists a set B such that { } !
> < B. So by definition of not being a subset os some set, there is an
> element x in { } such that x is not in B. But by definition { } has no
> elements; so this contradicts { } !< B, so our original hypothesis must
> be false. So { } < every set A.

Good try! but I think the terminology confuses me.

To my primitive intuitions one cannot say that { } is a set. Because {
} leterally
means_ Nothingness regarded as one whole.

Now what is the difference between nothingness regarded as one whole
and nothingness?
To me zero * 1 = zero.

So back to your reply, you say suppose { } !< of all sets A. To me this
is makes no sense.

because { } is not a set so that you can apply the operator !< to it.

{ } needs to be a set , so that it can be regarded as a subset of any
other set A.

But { } is not a set , simply because it has no members.

To me if you give nothingness a symbole like Q for example, then { Q }
= { } = Q

Q cannot be a set, neither it can be a member of any set A.

Why Q cannot be a member?

Answer:-

To what my primitive intuitions understand a member refers to entity
that is either within
the set or outside the set, it cannot be within and outside the set at
the same time.

so if Q exist inside all sets A, then given any particular set A , Q
will exist inside it and at the same time inside its complementary set
A' , ie it exists both inside A and outside it at the same time.
therefore Q cannot be a member of any set A.

While a single entity a , can be a member of a set, but {a}=a because
1*1=1

A single entity regarded as One whole = { a } is exactly the same as a
single entity a.

regarding it as one whole will not change its state of oneness it only
asserts it.

Still confused. In reality I see no intuitive base to accept such a
statement as

" there is a set which has no members " , this statement is
counter-intuitive.

More it seems even inconsistent to me.

Zuhair

.