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Fynjy-87 — Magic
#mlp #pony #cyborg #mlpmylittlepony #mlpfriendshipismagic #twilight_sparkle #twilightsparkle
Published: 2017-02-23 22:34:26 +0000 UTC; Views: 732; Favourites: 31; Downloads: 10
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Comments: 10
Robo Twilight and a mechanical Element of Magic. Did I get that right?
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Hey Robo-Twi, what's one divided by zero?
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Robo-Twilight, "But that's...analyzing..." [DING!] "The answer cannot be defined, because the expression has no meaning. If you cannot multiply 1 by 0, you cannot divide 1 by 0. It is a mathematical impossibility that cannot exist in conventional arithmetic."
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"Okay, but does a set of all sets contain itself?"
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Robo-Twi, "Accessing archives... This is what's been called 'Raven's Paradox', formulated by famous Griffysh Isles philosopher and mathematician Bright Raven (Birthname Red Raven)*. According to naive set theory, any definable collection is a set. 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 - in essence, a paradox.
There are several proposed solutions to this paradox: the first possible solution is by replacing arbitrary set comprehension with weaker existence axioms, such as an axiom of separation; this has formed the basis of the axiomic set theory known as ZFC. In ZFC, given a set A, it is possible to define a set B that consists of exactly the sets in A that are not members of themselves. B cannot be in A by the same reasoning in Russell's Paradox. This variation of Russell's paradox shows that no set contains everything.
Other possible solutions includes..."
*Basically Bertrand Russell as a pony/griffon
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"Okay, that's it--THIS SENTENCE IS FALSE!"
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Robo-Twi, "Analyzing... This statement makes no sense! ERROR! ERROR! Does not compute! DOES NO* "£$*%$) - !!"
[Robotic head explodes]
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(Brushes off a bit of scrap metal) "Guess she didn't download the last update."
[Puts on sunglasses and walks away from the explosion]
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