Re: { }
- From: "David R Tribble" <david@xxxxxxxxxxx>
- Date: 19 Jan 2006 14:19:00 -0800
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".
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 = ?
Also, the following sets are disallowed by your set theory, even
though standard set theory treats them all as different proper sets:
{ }
{ {} }
{ {}, { {} } }
{ { {} } }
etc.
.
- References:
- Prev by Date: Ergodic theorem for groups?
- Next by Date: Re: new paper
- Previous by thread: Re: { }
- Next by thread: Re: { }
- Index(es):
Relevant Pages
|
