Sets Puzzles and Paradoxes.

Ok, so in math there are sets
E.g.

The set of all prime numbers:

1,2,3, 5, etc...

The set of all Even Numbers
2,4,6,8,10 etc...

In the set of all even numbers, the number "2" is considered a member of the set of all even numbers, or a member of that set.

Some sets are self swallowing however. For instance:

The set of all things, except Joan of Arc. (I know random example)

Within the set of all things except Joan of Arc, the set "Of all things except Joan of Arc" itself is included as a member of that set, since the set as its own entity is not Joan of Arc, so it can be included in the set of all things except Joan of Arc.. It continually swallows itself.

Now the "set of all things, except Joan of Arc." would be considered a self swallowing set.

A "run of the mill set" would be considered a set that is just a plain old set, not self swallowing, such as the first examples I gave you. The set of all prime numbers and the set of all even numbers.

But what becomes of this set:

The set of all run of the mill sets

I'll let yall try to figure it out..

First, sets are not ordered.

Second, the "run of the mill" set would be an infinite set where each member of the "ROTM" set is itself a non-swallowing set.

Third, If you really want to confuse yourself, look into the power set of the empty set.