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Jun
15
revised Expansion coefficients of an orthonormal basis must satisfy $c_n n^{1/2}\to 0$ as $n\to \infty$ for $\sum|c_n|^2$ to converge.
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Jun
15
answered Expansion coefficients of an orthonormal basis must satisfy $c_n n^{1/2}\to 0$ as $n\to \infty$ for $\sum|c_n|^2$ to converge.
Jun
15
comment Expansion coefficients of an orthonormal basis must satisfy $c_n n^{1/2}\to 0$ as $n\to \infty$ for $\sum|c_n|^2$ to converge.
is this the Cesaro sum or something? I don't think spacing the non-zero values changes the values of $c_n$.
Jun
15
comment Expansion coefficients of an orthonormal basis must satisfy $c_n n^{1/2}\to 0$ as $n\to \infty$ for $\sum|c_n|^2$ to converge.
no doesn't $\sum |c_n|^2 = \sum \frac{1}{n} = \infty$ ?
Jun
14
revised Two sets $X,Y \subset [0,1]$ such that $X+Y=[0,2]$
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Jun
14
answered Two sets $X,Y \subset [0,1]$ such that $X+Y=[0,2]$
Jun
14
comment Two sets $X,Y \subset [0,1]$ such that $X+Y=[0,2]$
It was Problem 3, Part 1 at CIIM 2010 Rio de Janeiro
Jun
14
comment Limits and Series in Smooth Infinitesimal Analysis
@StefanPerko I looked into it further. With these type of "nilpotent" infinitesimals, $\epsilon$ is not really "small" it just vanishes to a certain order. More specifically, the Intermediate Value Theorem is false. Likewise, many of the series and limit definitions you have defined may not work in SIA.
Jun
14
revised Limits and Series in Smooth Infinitesimal Analysis
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Jun
12
comment Regarding the connected component of $|1/J| < 1$ containing $\infty$
@glebovg does this also come from Fricke-Klein?
Jun
12
answered Calculate limits without L'Hospital's Rule
Jun
12
revised Limits and Series in Smooth Infinitesimal Analysis
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Jun
12
revised Limits and Series in Smooth Infinitesimal Analysis
added 433 characters in body
Jun
12
answered What do you need to perform Karatsuba multiplication?
Jun
12
comment Integral relations in Fricke and Klein
@glebovg I enjoyed this exercise since Fricke Klein is such an important read. It is in German fortunately we were able to decipher this passage and it was basically just some advanced calculus.
Jun
12
revised Integral relations in Fricke and Klein
Clarification about the * formula
Jun
10
comment Integral relations in Fricke and Klein
@glebovg OK I included details about those two equations. Let me know if you need more.
Jun
10
revised Integral relations in Fricke and Klein
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Jun
10
revised Integral relations in Fricke and Klein
added 417 characters in body
Jun
10
comment Prove that $(div \ w)(p) = \lim \limits_{r\rightarrow 0} \frac{1}{V_n r^n}\int_{S_r(p)} \langle w,\nu \rangle dS$ using Gauss's theorem
@Samuel I fixed an error that I use $f$ instead of $\vec{w}$. Divergence can be written as a dot product $\mathrm{div} (w) = \nabla \cdot w$.