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 Feb7 answered Expected value of the product of functions of two independent random variables Feb5 comment $\lim_{n\to\infty} \sqrt[n]n = 1$ @dkuper when I took that class we introduced the exponential function later, so we couldn't use that argument. It is indeed even simpler though. Feb5 revised $\lim_{n\to\infty} \sqrt[n]n = 1$ added 215 characters in body Feb5 awarded Yearling Feb5 answered Give me a example of a function Lebesgue Integrable over [a,b] that is not bounded in any subinterval of [a,b] Feb4 answered $\lim_{n\to\infty} \sqrt[n]n = 1$ Feb4 comment Is it acceptable to solve hypothetical statements in Linear Algebra using actual numbers? To this I'd add that trying to find counterexamples to true statements can be a good first step towards understanding how to prove them. May20 comment Finite difference method stability The extra term doesn't go to zero, because the solution of the PDE doesn't necessarily go to zero as $n\to\infty$ if there's a forcing term. However, if you have some numerical solution $U$ with a right-hand side $f^i$ and another solution $V$ with the right-hand $f^i+\delta f^i$, then $\|V^n-U^n\| \le \|B^n\|\|U^0-V^0\|+k\sum_{i=1}^n\|B^{n-i}\|\|\delta f^i\|$. Knowing that the discretization is consistent, you can use this fact to show it's convergent as $n\to\infty$ and $k\to 0$, provided $kn \to$ some finite number $T$. May17 revised Finite difference method stability adding more info a propos of an additional comment by OP May17 awarded Constituent May17 awarded Caucus May17 answered Finite difference method stability May17 comment Finite difference method stability Perhaps this is better migrated to the computational science stack exchange? May17 awarded Critic May15 comment Is restriction of compact operator always compact? Bingo! Also: that sequence isn't bounded in the graph norm, so you can't use it to say that the operator isn't closed. @julien: Thanks for pointing that out -- the upshot is that the set of compact operators is closed in the strong operator topology, right? May13 answered Is restriction of compact operator always compact? May8 answered Need help in question for conditional expectation May2 comment Functions differentiable on {$z \in \mathbb{C}: 0 < |z| < 1$} The square root function has a branch cut; it's not differentiable in the disk, you have to remove a line along some axis, usually the negative real line. Apr18 comment For any graph G, How do I find the algorithm that returns the permutation of vertices with minimum bandwidth? (a) I'm exaggerating yes, but it's still O(n!) right? (b) I stand corrected! I didn't know about interval graphs but the maximal clique ordering property would make it much easier to order them nicely. The "stupid example" I'm thinking of is the matrix discretizing a differential operator in 1D. Apr18 answered For any graph G, How do I find the algorithm that returns the permutation of vertices with minimum bandwidth?