Re: Is {{}} a valid construct?

On Feb 6, 8:03 am, "Neo" <neo55..._at_hotmail.com> wrote:
> > A necessary precondition for getting unconfused is figuring out the difference
> > between the empty set and the set containing the empty set.
>
> Actually it is realizing that 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.

> But using your logic, for U = { {}, apple, orange} which of
> the following is the correct answer?
>
> NOT {} = apple, orange
> -or-
> NOT {} = {}, apple, orange
>
> One solution gives 2 elements and the other 3. Which count do you
> prefer?

Some posts back you used a technique of arbitrary symbol substitution to make a point. In the place you used it, it was invalid, because that
example depended on one of the symbols you replaced being a natural number. But in this case, the same technique is perfectly valid.

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

You will I suppose feel drawn to arguing about whether es exists or not. However, when you said "U = {es, a, o}" you explicitly said it did exist. So if you want to raise that issue, you have to take back what you said U was. In which case you can't ask the question of what is "NOT {es}".

Marshall Received on Tue Feb 06 2007 - 18:20:23 CET