Sanchez

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I really appreciate it when you take time to answer my questions. Thanks!

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4h	revised	A simple geometry problem with points edited tags
4h	comment	A simple geometry problem with points Hint: Reflect $N$ across the $x$-axis, and call it $N'$. Note that $PN = PN'$. Which $P$ should you take to minimize $MP + PN'$?
14h	comment	Convergence of $\sum \frac{a_n}{(a_1+\ldots+a_n)^2}$ @Norbert, in this case $b_{n+1} - b_n = a_{n+1}$, so RHS in timofei's comment is $\frac{1}{b_n} - \frac{1}{b_{n+1}}$.
1d	comment	Vanishing of Dirichlet Series This maybe an overkill, but given absolute convergence of Dirichlet series on $U$, we know that the Dirichlet series converges absolutely on some right half plane of $\mathbb{C}$. (Dirichlet series has a notion of abscicca of convergence, similar to radius of convergence for power series). Then one can use Perron to show that all the partial sum of $a_n$ is 0.
May 20	comment	Definition of Exact functors Yes. Break your latter sequence into a few short exact sequences involving kernels and cokernels.
May 17	awarded	Constituent
May 15	comment	If $f :\mathbb{R}\to\mathbb{R}$ is measurable, then $E = \{x: f(x) \geq 3\}$ is measurable @9959, I see that the definition you quoted is from wikipedia. Pick up any textbook on measure theory and read the definition of a measurable function there. You can probably prove this on your own then.
May 15	comment	If $f :\mathbb{R}\to\mathbb{R}$ is measurable, then $E = \{x: f(x) \geq 3\}$ is measurable @9959, so can you recognize what $[3,\infty)$ is? Also, in the definition you quoted, you didn't explain what a measurable function is. You only specified the measure spaces you are using.
May 11	comment	How does this step in the proof of the structure theorem for f.g. modules over a Dedekind domain work? I think so. (space fillers)
May 11	comment	How does this step in the proof of the structure theorem for f.g. modules over a Dedekind domain work? I think you can replace $Q$ by $Q' = \{a \in P: Frac(D) \otimes a \subset Frac(D) \otimes Q\}$ if necessary, which guarantees $P/Q'$ is torsion free.
May 9	answered	Planes, quadric surfaces and then …?
May 8	awarded	Informed
May 7	comment	$x_n\to x$ weakly for some $x$ in $X$ with $\\|x\\| = 1$, then show that $\\|x_n- x\\|^2 \to 0$. Ah, of course. Thanks!
May 7	comment	$x_n\to x$ weakly for some $x$ in $X$ with $\\|x\\| = 1$, then show that $\\|x_n- x\\|^2 \to 0$. I'm probably overlooking something, but how would $\lim \\|x_n\\| = 1$ imply $\\|x_n - x \\| \to 0$?
May 7	revised	*Intersection of open affines can be covered by open sets distinguished in bothaffines* added 194 characters in body
May 7	answered	*Intersection of open affines can be covered by open sets distinguished in bothaffines*
May 7	awarded	Caucus
May 4	comment	Planes, quadric surfaces and then …? Cubic hypersurface.
May 2	comment	Zeta function zeros and analytic continuation A simple example of analytic continuation is the geometric series. Consider $1+z+z^2+ \cdots$. This converges only within the unit disc. However, if you put it in another form: $\frac{1}{1-z}$ in the unti disc, then this makes sense whenever $z$ is not 1, i.e. you extended the domain to the whole plan except a point.
May 1	comment	Solve $x^3+x \equiv 1 \pmod p$ Is there any example for "explicit descriptions" in the last paragraph? I'm curious to see examples for nonabelian extensions.