/sci/ - Science & Math

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Anonymous Tue Mar 28 21:57:03 2017 No.8786807 [Reply] [Original]

Does the set of all sets that do not contain themselves, contain itself?

>>	Anonymous Tue Mar 28 22:03:20 2017 No.8786819 >>8786807 Are you using ZFC for these sets?

Anonymous Tue Mar 28 22:33:57 2017 No.8786873
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Suppose such a set A exists. Since A is a set, its complement C is a set. If C contains itself, then it can not be a set*, and then A is not a set, so C must be in A. Similarly, every set in C must be in A, but C is a complement of A, so C must be empty. Now A consists of all sets, and thus contains itself contradicting its own definition. Such a set, therefore, does not exist.

*follows from
>Foundation (Regularity): Each nonempty class is disjoint from one of its elements.

>>	Anonymous Tue Mar 28 23:34:50 2017 No.8786991 >>8786873 good bait >>8786807 If a barber cuts the hair of all the people in the town except those who cut their own hair, does he cut his own hair?

>>	Anonymous Wed Mar 29 07:46:03 2017 No.8787842 >>8786873 Any literature that captures that statement not using 400 pages?

>>	Anonymous Wed Mar 29 17:49:50 2017 No.8788945 File: 105 KB, 1280x738, SUCCtion.jpg [View same] [iqdb] [saucenao] [google] >>8787842 No idea, sorry. It was just a train of thought before going to sleep. Maybe the intro chapter of Dugundji's book on topology. That's where I learned my axioms from.

>>	Anonymous Wed Mar 29 17:58:00 2017 No.8788965 >>8786807 There exists such a class in NBG, but not a set.

Anonymous Wed Mar 29 21:30:54 2017 No.8789480

>>8788945
>just a train of thought before going to sleep

So in other words, what you basically did was just pull a proof out of your ass? Well I can do that too.

If C contains itself it doesn't. If C doesn't contain itself it does. Hence this whole problem is fucked and indicates that you can't just make up sets in set theory and expect them to always make sense.

>>	Anonymous Wed Mar 29 22:58:24 2017 No.8789672 File: 117 KB, 1920x1080, 1485933027292.jpg [View same] [iqdb] [saucenao] [google] >>8789480 I did. But it follows logically from the idea that a set can't have itself as its element. Don't you ever prove stuff on your own?

>>	Anonymous Wed Mar 29 23:15:50 2017 No.8789701 >>8789672 >don't you ever prove stuff on your own Hahahahahahahahahaha, no.

>>	Anonymous Wed Mar 29 23:29:44 2017 No.8789720 >>8789701 >>8789672 just kidding. I'm simply saying that it's obvious such a set doesn't exist

>>	Anonymous Wed Mar 29 23:31:44 2017 No.8789721 >>8786807 I thought every set is a subset of itself? So how can there be a set of sets that do not contain themselves

>>	Anonymous Thu Mar 30 01:01:29 2017 No.8789836 >>8789721 This is linguistics

>>	Anonymous Thu Mar 30 01:07:27 2017 No.8789844 >>8786807 There is no set that can match those requirements, set theory is incomplete.

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