Re: { }
- From: "zuhair" <zaljohar@xxxxxxxxx>
- Date: 19 Jan 2006 21:32:44 -0800
David R Tribble wrote:
> Zuhair wrote:
> >> 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.
> >
>
> David R Tribble wrote:
> >> You're confusing concepts. { } means a set with nothing in it, but
> >> the set itself is not nothing.
> >
>
> Zuhair wrote:
> > The problem is that traditional language about set theory doesn't
> > mention any defintion for a container at all. [...]
> >
> > A set is defined by its members only, and equivalence between sets
> > depends on their members only , there is no definition for a container
> > that contains them. [...]
> >
> > Now { } has no members , and since any set is defined by its members,
> > then It seems more consistent to say that { } means "no set" .
>
> It would be more consistent to say that { } means "no members".
> Then you have to decide whether "no members" is the same as
> "empty set" or as "no set".
>
>
> > Again I say : set is a list of distinct entities considered as One whole.
> >
> > So, When there are no entities, then there are no sets.
> > When there are no distinct entities then there are no sets.
> > Only many entities can form sets.
>
> You are defining "set" as "a collection of one or more members".
No I am defining set as "a collection of more than one distinct member
regarded as one whole"
more precisely speaking: set is_ Collection of distinct entities
considered as One whole,when this consideration alter the original
meaning of the gathering of these entities.
There is a difference between a,b considered as two wholes from when
they are considered as one whole.
While for "a" which is a single entity,it want make any difference to
consider it as one whole or not because a is already defined as one .
That's why I say that {a} =a if a is a single entity, while {a,b} is
not necessarily the same as a,b for example since a,b can be
looked as a collection of two wholes like for example {a},{b},
therefore when you say {a,b} this statement is significant in a sense
that you are asserting that the collection a,b is treated as one whole
and not as two wholes. But what would {a} asserts , it only tells us
that a ( which we already know it to be one) is one whole. is that a
significant change in the meaning of a, It is like that man who said
answering about what was that woman doing he said: She is a dancer And
she Dance. what an assertion.
{a}=a , a is a single entity.
{ }= nothing
{A} =A , were A= All things.
>
> So how do you give any meaning to the intersection of two sets
> having no members in common, e.g., what is the meaning of
> A = { 1, 2, 3 }
> B = { 4, 5, 6 }
> A intersect B = ?
A interesect B = nothing
It means that there is nothing in common between A and B , not a member
not a set.
This would be the meaning of A disjoint from B.
>
> Also, the following sets are disallowed by your set theory, even
> though standard set theory treats them all as different proper sets:
> { }
> { {} }
> { {}, { {} } }
> { { {} } }
> etc.
Of coarse all of these are the same they are nothingness only , they
are not different proper sets, they are not sets at all. ZFC treats
them as proper sets, but my intuitive explanation of sets is against
that of coarse.
Zuhair
.
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