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/sci/ - Science & Math

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4298906 No.4298906 [Reply] [Original]

Let K = set of sets all of them doesn't conatain themselves. Does K contain itself?

>> No.4298914

>>4298906
>implying there is a set that contains all sets that dont contain themselves
You just disproved its existence right there.

>> No.4298935

http://en.wikipedia.org/wiki/Russell's_paradox

>> No.4298936

category theory >>>>>>>>>>>>>>>>> set theory

>> No.4298948

>>4298936
Please tell me you don't think category theory is somehow a successor of set theory.

>> No.4298952

>>4298948
Accidental sage was accidental.

My sincerest apologies.

>> No.4298970

>>4298914
you can have all kinds of sets
if you follow the set rules

old set theory breaks given this problem
the new rules state that sets can not contain themselves

and no one know weather the new rules don't allow for another paradox

maybe we just try to apply abstract ideas on something that has no uniform rules
and we're forever bound to wonder into the chaotic math world

>> No.4299083

>>4298970
No you cant, how >>4298906 proves.
There is, however, a set of all sets that contain all sets that dont contain themselves, and it is empty.
>What is the largest set that contains sets which dont contain themselves?