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 Aug 13 comment Intersection of a non-empty set of natural numbers (set-theoretic definition) gives an element of that set? Wait a second, E is not a set of ordinals, E is a set of natural numbers! Aug 13 comment Intersection of a non-empty set of natural numbers (set-theoretic definition) gives an element of that set? Yes, we've proved this already. Aug 13 asked Intersection of a non-empty set of natural numbers (set-theoretic definition) gives an element of that set? Aug 12 comment Prove: If $E$ is a nonempty subset of natural numbers , then there exists an element $k$ in $E$ such that $k\in$ m for any $m$ in $E$ and$m \ne k$ I got this far, but I couldn't figure out how to prove that the intersection of E is an element of E. Any hints on this? Jul 2 awarded Curious May 31 awarded Nice Question May 17 comment Is there a connection between uncountable sets and exponential growth? Thanks. Should I close this question? (It doesn't really make sense anymore) May 17 comment Is there a connection between uncountable sets and exponential growth? Interesting... a few clarifications: (1) how did you formalize the notion of a "limit" here, (2) is there a concrete example of an element that's in the Cantor set but not in $C_n$ for any $n$, and (3) can you please give some more context for the last expression? May 17 asked Is there a connection between uncountable sets and exponential growth? May 17 comment Baby Rudin 2.26 Infinite subsets with limit points implies compactness +1, I also had trouble with this part of the problem, and your answer was extremely helpful. My original strategy was to write each $U \in \mathscr{U}$ as a union of $B \in \mathscr{B}$, and then show that the collection of all possible unions of $B \in \mathscr{B}$ is countable. Oops--this collection is actually uncountable. May 4 comment 6 keys and a door( probabilities) What have you tried so far? Can you break the problem down into smaller parts? Can you think of a simpler version of the problem that you can try solving first? Apr 10 awarded Popular Question Mar 12 awarded Notable Question Dec 18 awarded Yearling Nov 15 awarded Notable Question Oct 17 awarded Nice Question Aug 12 awarded Good Question May 7 awarded Popular Question Jan 30 awarded Popular Question Dec 18 awarded Yearling