Re: Is {{}} a valid construct?

> > ... there is no set when there are no elements.
>
> There is such a set if we say there is.
> Because sets are something that we made up!
> The axiom of the empty set is how we formalize that.
> You are of course free to come up with your
> own axiomatization of set theory.
> However I don't see you succeeding at that endevour when
> you can't master the simplest of axioms of existing set
> theory.

I am not questioning you right to make axioms; however according to wiki, It is a fundamental requirement of scientific method that all hypotheses and theories must be tested against observations of the natural world, rather than resting solely on a priori reasoning, intuition, or revelation.

> U = {es, a, o}
> NOT {es} = {a, o}

If es is equivalent to the "empty set", then the solution to NOT es is either {a, o} or {es, a, o}, one having 2 elements the other 3. If a construct (ie {} ) leads to ambiguity in set theory at this simple level, there is a problem. Received on Tue Feb 06 2007 - 20:54:57 CET