Re: Is {{}} a valid construct?

On Feb 6, 9:58 pm, "Marshall" <marshall.spi..._at_gmail.com> wrote:
> 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

A merry dance this is indeed. Received on Wed Feb 07 2007 - 00:08:41 CET