FOM: Axiom of Extensionality

[Franklin Vera Pacheco]

On Fri, 17 May 2002, Dean Buckner wrote:

> 
> Either (you would think) the set is one and the same with its members, in
> which case the axiom reduces to {Alice, Bob, Carol} = {Alice, Bob, Carol},
> and hardly seems necessary.
> 

 With finite sets the matter can be view as a trivial one but, when we are 
working with infinite sets we have to define the sets no by an enumeration 
but a proposition that must hold the elements of the set and we can have 
no so trivial equalities as:

  {2k+2 : k belons to N } = { p + q : p and q are prime numbers } 

In these case we indeed need the axiom of extensionality.


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Franklin Vera Pacheco
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