4 ms·
This is super interesting. Was not aware of this. Is there a proof that this is not provable?
by DontchaKnowit 4y ago
This is super interesting. Was not aware of this. Is there a proof that this is not provable?
- thayne 4y agoYes, Paul Cohen proved that the continuum hypothesis (that there is no set with cardinality between that of natural numbers and real numbers) was independent of the ZFC formulation of set theory (the most standard set of axioms used in today's set theory) in 1963.
- schoen 4y agoMore about this on Wikipedia: https://en.wikipedia.org/wiki/Continuum_hypothesis#Independence_from_ZFC https://en.wikipedia.org/wiki/Continuum_hypothesis#Independe... Also: https://en.wikipedia.org/wiki/Axiom_of_choice#Independence https://en.wikipedia.org/wiki/Axiom_of_choice#Independence And thanks to Wikipedia for this elaborate list: https://en.wikipedia.org/wiki/List_of_statements_independent_of_ZFC https://en.wikipedia.org/wiki/List_of_statements_independent...