Re: Is {{}} a valid construct?

On Feb 6, 11:54 am, "Neo" <neo55..._at_hotmail.com> wrote:
> > > ... 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.

Set theory is part of math. Find me a link on wikipedia that says that math theorems must be tested against observations in the natural world.

> > 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.

Your problem here is a result of your difficulty with the difference between {} and {{}}.

I said "NOT {es}"
You changed it to "NOT es"

es != {es}
{} != {{}}

Not {} != Not {{}}
Not {} = {{},apple, orange}
Not {{}} = {apple, orange}

No ambiguity if one can correctly distinguish between {} and {{}}.

Marshall Received on Tue Feb 06 2007 - 22:58:54 CET