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Watch my set please by Basil Fussletut - Fri, 18 Nov 2016 11:24:03 EST ID:FFd5rNZG No.15275 Ignore Report Quick Reply
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Hey /math/, can you guys watch my set for me? I'll be right back.
>>
Esther Poddleweck - Fri, 18 Nov 2016 16:23:44 EST ID:PayHQ+YN No.15276 Ignore Report Quick Reply
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>>15275
Shit...
>>
Archie Fuckingcocke - Sat, 19 Nov 2016 11:35:22 EST ID:FbvrfMz9 No.15277 Ignore Report Quick Reply
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>>15276
We'll just put this there and it's like nothing even happened.
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Esther Clellerbit - Sun, 20 Nov 2016 13:48:25 EST ID:Z1cD9cwV No.15278 Ignore Report Quick Reply
>>15277
Good call, that was a close one
>>
Hedda Herrybed - Sun, 27 Nov 2016 14:22:26 EST ID:d7aT3WKf No.15279 Ignore Report Quick Reply
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DICKS EVERYWHERE
>>
Fanny Blackfuck - Wed, 30 Nov 2016 20:31:05 EST ID:FFd5rNZG No.15280 Ignore Report Quick Reply
>>15279
What is that thing?
>>
Esther Blatherfoot - Sun, 04 Dec 2016 00:52:41 EST ID:tgwdoW8d No.15287 Ignore Report Quick Reply
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Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves.
>>
Fucking Pickwell - Sun, 04 Dec 2016 12:28:55 EST ID:d7aT3WKf No.15288 Ignore Report Quick Reply
>>15280
It's a number muncher (!)
>>
Betsy Fuckinggold - Wed, 21 Dec 2016 19:31:04 EST ID:GmQCz3Ds No.15299 Ignore Report Quick Reply
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>>15287
>>
Cornelius Buzzspear - Thu, 05 Jan 2017 16:43:05 EST ID:Ua6hy53G No.15308 Ignore Report Quick Reply
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>>15287
I knew i already heard this somewhere
>>
Jenny Tootbury - Sun, 08 Jan 2017 13:13:49 EST ID:a1cMDxo8 No.15315 Ignore Report Quick Reply
>>15308
>does a set of all sets contain itself

That's not a paradox. How... paradoxical.
>>
Phineas Hinnerwill - Mon, 09 Jan 2017 22:47:18 EST ID:TdtLbn0v No.15318 Ignore Report Quick Reply
>>15315
Are you certain of this
>>
Barnaby Chindlestadging - Tue, 10 Jan 2017 16:28:23 EST ID:2HEwuEDh No.15319 Ignore Report Quick Reply
>>15318
Yes, a set of all sets would contain itself. The set of all sets which do not contain themselves is paradoxical and we call this Russell's Paradox. The set of all sets cannot exist in naive set theory due to Cantor's Theorem, which says that you can't have a surjection from a set onto its power set. Since the set of all sets is its own power set and the identity map from that set to itself is a surjection, we have a genuine contradiction. Cue: type theory or wrangling with the category of all categories instead.
>>
Polly Crazzlestodge - Thu, 12 Jan 2017 13:12:19 EST ID:zauFrAWR No.15321 Ignore Report Quick Reply
>>15319

You don't absolutely have to use category theory or type theory to talk about that kind of collection. There are extensions of ZFC in which you can discuss proper classes like the collection of all objects that don't contain themselves, like Neumann-Bernays-Godel set theory. In New Foundations set theory there is powerful comprehension so the collection of all sets is indeed a set. It dodges Russel's paradox by specifying what kind of predicates are allowed to define sets.
>>
Ebenezer Genkinnadge - Thu, 12 Jan 2017 14:29:49 EST ID:jD/Lrc1O No.15322 Ignore Report Quick Reply
>>15321
Both of those systems you mention seem to be exploiting the idea of different "levels" of sets, which sounds like a type-theoretic way of dealing with the problem to me.
>>
Augustus Bambleson - Thu, 12 Jan 2017 19:13:32 EST ID:zauFrAWR No.15323 Ignore Report Quick Reply
>>15322

Yeah, there are different "types" of objects, but often times it's not apparent what a given object is. From this perspective you could make an argument that every set theory is a type theory, with just one type in consideration, which seems to obfuscate what distinguishes what is considered type theory as opposed to something else. In type theory you know exactly what sort of element you are dealing with, while this might not be the case in set theory.


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