4 ms·
The reason those things are strange is that uncountable sets have absolutely no bearing on computable objects (== enduring in math and science) but everyone mis
by reagency 11y ago
The reason those things are strange is that uncountable sets have absolutely no bearing on computable objects (== enduring in math and science) but everyone mistakenly applies their countable intuition to uncountable set theory.
- black_knight 11y agoIf one uses classical logic there are even many countable, even finite sets which are beyond computable distinction. The set of computable functions on say natural numbers is a countable set, but even distinguishing when two such are equal cannot be effectively done. The solution is either to distinguish between countable and enumerable and decidable, or to use intuitionistic logic.