Elliott
Reputation
1,944
Top tag
Next privilege 2,000 Rep.
 Aug12 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? Jul2 awarded Curious May31 awarded Nice Question May17 comment Is there a connection between uncountable sets and exponential growth? Thanks. Should I close this question? (It doesn't really make sense anymore) May17 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? May17 asked Is there a connection between uncountable sets and exponential growth? May17 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. May4 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? Apr10 awarded Popular Question Mar12 awarded Notable Question Dec18 awarded Yearling Nov15 awarded Notable Question Oct17 awarded Nice Question Aug12 awarded Good Question May7 awarded Popular Question Jan30 awarded Popular Question Dec18 awarded Yearling Nov21 awarded Popular Question Jun8 awarded Caucus Dec18 awarded Yearling