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List of unusual Wikipedia articles
- drinian 17y agoBir Tawil would be a nice place for a data haven, were it not landlocked.
- ugh 17y agoHey, I know, let’s open a data haven on the Moon: http://en.wikipedia.org/wiki/Terra_nullius http://en.wikipedia.org/wiki/Terra_nullius (Oh, the joys of Wikipedia :)
- brown9-2 17y agoThis reminds me of: Does the set that contain all sets contain itself?
- jango102 17y agoI think lists and articles are distinct entities on Wikipedia, so a list of articles wouldn't contain a list.
- chickamade 17y agoExcept that they are not. They are called "List Articles", cf. http://en.wikipedia.org/wiki/Wikipedia:Lists#List_articles http://en.wikipedia.org/wiki/Wikipedia:Lists#List_articles Back to the main topic, I think in naive set theory a set of all sets will contains itself. Russell Paradox is problematic when asking the negated statement, i.e. whether a list of all lists that do not contain themselves contains itself.
- chronomex 17y agoOne of my favorite Wikipedia categories: http://en.wikipedia.org/wiki/Category:Lists_of_lists http://en.wikipedia.org/wiki/Category:Lists_of_lists
- philh 17y agoIf that set is well-defined, it obviously contains itself. Under ZFC, no set can contain itself, so that set is not well-defined. http://en.wikipedia.org/wiki/Axiom_of_regularity http://en.wikipedia.org/wiki/Axiom_of_regularity But there may well be set theories where it is well-defined, hence does contain itself.
- gambling8nt 17y agoAs noted above, the collection of all sets cannot be a set in any set theory with specification, regardless of regularity: Call the collection of all sets S. We specify T by T=\{x| x \in S \wedge \neg x \in x\} T is then the subclass of S of sets that do not contain themselves. Thus with specifiction (provable from replacement, or as an axiom by itself), it is contradictory for S to be a set. If you reject the law of excluded middle, you can have a intuitionist set theory where S is neither a set nor not a set; alternatively, you can have a set theory without specification one constructed based on a type theory might meet this requirement.
- martincmartin 17y agoYes, and that's not a contradiction. The problem comes with the set of all sets that don't contain themselves. Does that set contain itself? Both "yes" and "no" lead to contradiction. That contradiction is the basis of Godel's Incompleteness Theorem, the Halting Problem and others.
- gambling8nt 17y agoThe collection of all sets is not a set under ZF set theory, regardless of choice. Such a collection, if it were a set, would imply the existence of a set of all sets that did not contain themselves from the axiom schema of specification.
- RevRal 17y agoWTF (A chandelier made of human bones): http://en.wikipedia.org/wiki/File:Sedlec-Ossuary.jpg http://en.wikipedia.org/wiki/File:Sedlec-Ossuary.jpg
- adatta02 17y agowell there goes the next 4 hours of my life. the math ones are pretty neat - http://en.wikipedia.org/wiki/Vampire_number http://en.wikipedia.org/wiki/Vampire_number
- riffraff 17y agoI am surprised by the lack of the Brother Metal page, but I'm not sure if it deserves being added or deleted :) http://en.wikipedia.org/wiki/Cesare_Bonizzi http://en.wikipedia.org/wiki/Cesare_Bonizzi