STUFF!! and perhaps some meaningful stuff on set theory.

There was a time when I considered someone’s starting a post by telling that “it has been a long time since i posted..” and explaining why they were forced into doing this henious crime as immature.  Today, I’ll indulge into it: It has been a long time since i posted and I am posting because i found something really interesting at -

http://prasantgopal.com/blog/?p=486

Please go through that and then come back.. doing that will possibly make the rest of the post ‘ some meaningful stuff on set theory and STUFF otherwise.

Talking about the paradox:

I think everything was dismissed too soon. We have got a paradox here. This implies something must have been wrong/inconsistent somewhere before . I am considereing the paradox as a contradiction. And the fact that abnormal set is a set at the first place as the hypothesis. An abnormal set has itself in it, how can we accept that to be a set so straightaway. Afterall, a set is a collection of well defined objects.

A question which should be asked is “If a set has itself in it, then is it a set?” or “Is the set as an element of itself a well defined object?”.

So, an abnormal set might not be a set! Now, consider the paradox to be contradiction. Then, the hypothesis that Abnormal set is a set,  becomes wrong. That is to say abnormal set is not a set! So, this paradax was actually the proof of “Abnormal set not being a set”.

A Corollary would be, for a set to be a set it must not contain itself.

Maybe such kind of “not set” sets could be called pseudo-sets in future.

Btw, i can give a formal proof for the theorem, “A set cannot contain itself.” would be.

Hypothesis: let a set contain itself and still be called a set. (i.e. Abnormal sets are sets)

Then…..

All the paradox matererial comes here.

Since we get a contradiction (the paradox), the hypothesis is false.

Therefore, a set can’t contain itself.

Ps1: I have a gut feeling that this will create history….

Ps2: I know the same thoughts have been harped again and again……. and again..

Ps3: OBH calling…