Does the set of all those sets that do not contain themselves, contain itself?
Does the set of all those sets that do not contain themselves, contain itself?
10 years ago by MadMonk
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Does the set of all those sets that do not contain themselves, contain itself?
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This is known as the Russel's Paradox
Can you explain that for a layperson?
Essentially the paradox is exactly as OP said-- first you a define a set R such that it includes all sets that do not include themselves. (lets call them X sets). If R is not a member of itself, then by definition it would be an X set. However, if it is an X set, then R does include it, and boom, paradox!
Several systems have come to work around this paradox, generally by reducing the strength of statements (in Zermelo's Axiomatic system you simply cannot have a set like R). Did that make sense, or did I just make it worse?
You just made my head hurt. Please don't do that again!