Re: set of a set etc.

On Wed, 20 Jul 2005, Jasper wrote:
>
> Can you describe the difference without metaphor? (especially boxes and
> bags).

If a is a set, then {a} is the set with exactly one member, viz a.

> What is the difference between "my cat" and "the collection of
> my cat", (except that the latter sounds funny).
>
For example let a be R the set of real numbers.
Then 0, 1, pi, -1, etc are members of R, ie 0 in R, 1 in R, etc.

{ R } is another set whose only member is R, the set of reals.
Thus R in { R } and nothing else.

Let Q be the set of rationals.
Then { Q,R } is the set who's members are sets of numbers,
viz the rationals and the reals.
Q in { Q,R }, R in { Q,R } and nothing else is in { Q,R }.

Thus is much different than the union of Q and R, ie Q \/ R
which because Q subset R, Q \/ R = R

.

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