3 ms·
This gives rise to Russell's Paradox: Does the set of "all sets that do not contain themselves" contain itself?
by axblount 3y ago
This gives rise to Russell's Paradox:
Does the set of "all sets that do not contain themselves" contain itself?
- tikhonj 3y agoYou can have set theories that allows sets to contain themselves without allowing Russell's Paradox. You can read about non-well-founded set theory[1] if you're curious. [1]: https://en.wikipedia.org/wiki/Non-well-founded_set_theory https://en.wikipedia.org/wiki/Non-well-founded_set_theory
- hackandthink 3y agoI like the diagram of "the set containing itself". It illustrates non-well-foundedness niceley.
- l33t7332273 3y agoWhich diagram are you referring to?
- hackandthink 3y agoThis one: https://abuseofnotation.github.io/category-theory-illustrated/01_set/set_contains_itself.svg https://abuseofnotation.github.io/category-theory-illustrate...
- seanhunter 3y agoResolving this paradox is discussed in TFA as being the founding rationale for the Zermelo–Fraenkel set theory in fact.
- righttoolforjob 3y agosimple: there is no such set.