Re: { }

Zuhair wrote:
>> Also I find it very difficult to see why { } is not equal to nothingness.
>

leo1476 wrote:
>> Do you mean "...equal to nothingness"? Well the empty set is a subset
>> of every set because it logically follows from this argument:
>

Zuhair wrote:
> To my primitive intuitions one cannot say that { } is a set.
> Because {} leterally means_ Nothingness regarded as one whole.
> Now what is the difference between nothingness regarded as one whole
> and nothingness? To me zero * 1 = zero.

You're confusing concepts. { } means a set with nothing in it, but
the set itself is not nothing.

Consider a universe consisting of only fruits and boxes.
Fruits can be placed into boxes, and boxes can also be placed into
boxes (but obviously, nothing in that universe can be placed into
fruits). We also assume that there are different kinds of fruits,
and that a box containing fruits can only contain one kind of
each fruit.

Now if I have a box with three fruits (each one a different kind),
this is the same as a set with three members, {apple,banana,cherry}.
If I have a box with no fruits, this is the same as the empty set, {}.
It's still a box (still a set), but it has no fruits (no members).

In our universe, the concept of "nothing" is the same as saying
no box or fruit (no set or member) at all. Obviously, "nothing"
is not the same as an empty box (or empty set), because even
an empty box (empty set) is something. "Nothing" is no "thing"
at all.

.