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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
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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?
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