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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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Esther Clellerbit - Sun, 20 Nov 2016 13:48:25 EST ID:Z1cD9cwV No.15278 Ignore Report Quick Reply
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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Fanny Blackfuck - Wed, 30 Nov 2016 20:31:05 EST ID:FFd5rNZG No.15280 Ignore Report Quick Reply
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
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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Cornelius Buzzspear - Thu, 05 Jan 2017 16:43:05 EST ID:Ua6hy53G No.15308 Ignore Report Quick Reply
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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
>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
Are you certain of this
Barnaby Chindlestadging - Tue, 10 Jan 2017 16:28:23 EST ID:2HEwuEDh No.15319 Ignore Report Quick Reply
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

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
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

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.
Caroline Burringfoot - Thu, 23 Mar 2017 03:22:14 EST ID:zYLZ69Gw No.15432 Ignore Report Quick Reply
no, fuck sets
Thomas Derringbock - Thu, 23 Mar 2017 10:27:39 EST ID:2BTsxPZ9 No.15433 Ignore Report Quick Reply
What do you advocate instead of sets? Topoi or some new-fangled nonsense?
Nigel Nublingstock - Fri, 24 Mar 2017 01:19:20 EST ID:vrOFV9fT No.15434 Ignore Report Quick Reply
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fuck you
Hugh Guffingfield - Wed, 09 May 2018 12:39:40 EST ID:NVr7Ludj No.15649 Ignore Report Quick Reply
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You know what blocked me in college? Discovering water-tight proofs. I honor and love solid proofs but sometimes you be sittin with a coffee and whiskey in your lap makin pen mark on the paper and all you're operating by is your intuition. Don't let yourself be in the canyon lookin up from the bottom of proof atomics. We can occupy ourselves forever with hairsplitting and defining what we already know. Let's use a crutch like we've always used. Call it axiomatic if you're more comfortable with it. The point is, you're on the struts that have made the building... you don't need to look up from the bottom of the hole to see the top of the building. Be creative. Be a true mathematician. Don't get stifled by proof theory. Get some muthafuckin coffee, get some whiskey, and worship the primes and break bank encryption. [email protected]*EstarStar
Ernest Drivingstutch - Sat, 12 May 2018 05:26:04 EST ID:Ng8/H/+7 No.15653 Ignore Report Quick Reply
Sidney Pickbanks - Sat, 19 May 2018 00:59:50 EST ID:drSlH/C1 No.15655 Ignore Report Quick Reply

The vast majority of mathematicians don't understand how inference rules and logic actually work from an axiomatic level.

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