{ }

Hi,

I am only beginning to read about set theory .

However I am becoming to understand that the concept of "set" was
intuitive at the beginning
that lateron became axiomatic .

Intuitively speaking a set of a and b means a is different from b
and a and b regarded as one whole.

So from that definition a set of entities is the heap of those entities
, more clearly it IS those entities regarded as One whole.

Now I can understand for example that a,b is different from { a, b }
, because a,b are
two different entities that are seperate , but { a,b } is a and b
regarded as one whole.

Now according to that intuitive understanding of what is a set. I find
it too difficult to

see why { a } do not equal a when a is a single entity.

Also I find it very difficult to see why { } is not equal to
nothingness.

If a set is a list of entities , then if there is no entities then
there is no set.

To say that there is no entities leads to that there is a set that has
no entities as its

members do not seem intuitively consistent as I should say.

So what is the intuitive grounds for believing in the second axiom of
axiomatic set theory.

namely there is a set which has no members.

Zuhair

.

Relevant Pages

  • Re: monomorphisms, epimorphisms, and isomorphisms
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    (comp.lang.functional)
  • Re: Axiomatic set theory is still contradictory
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    (sci.logic)
  • Re: Cardinality of N and P(N)
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  • Re: Cantor Confusion
    ... have different members at different times or anything like that. ... mathematicians could adhere to that point of view. ... Because no one who works with Z set theory claimed that for any ... That in Z set theories there is no set S that has the property that all ...
    (sci.math)
  • Re: Axiom of Pairing
    ... That all objects are indistinguishable is not a theorem of set theory. ... Without this conferring, objects are ... So I'll use 'Jgroup' for your notion. ... I also thought that sets neither have nor do not have members. ...
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