Re: Is {{}} a valid construct?

From: Neo <neo55592_at_hotmail.com>
Date: 2 Feb 2007 20:13:47 -0800
Message-ID: <1170476027.740601.240320_at_v33g2000cwv.googlegroups.com>


> > My explanation is that a set is only defined by its elements and does
> > not include the container (ie {} or bag). Thus if there aren't any
> > elements, there is no set, not even an empty set. Only then can two
> > separate empty bags be considered equivalent.
>
> Sets don't have "containers".

I agree with you here. The {} are not part of the set.

> The empty set is most certainly a set.

Since you say the empty set is most certainly a set, can you tell me how I can verify this to be true also? I want to verify it with reference to some part of reality. IMO, because a set should be defined strictly by its elements, when there are no elements, there is no set, not even an empty set; otherwise I worry it could lead to invalid expressions like {{}}, similar to computing with NULLs in RMDBs.

> > how would one create/select {{}} within a relational db or similar?
>
> What makes you think that a relational database provides a complete
> model for ZFC?

So I take it, {{}} is unverifiable in RMDBs. Then how can I verify that the following expression proposed to me, represents the string bob:

{ {     {}   {{b}} }
  {    {{}}  {{o}} }
  { {{}{{}}} {{b}} } }
Received on Sat Feb 03 2007 - 05:13:47 CET

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