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Yes, 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 "
by martincmartin 17y ago
Yes, 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.