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  • 0 posts edited
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  • 31 votes cast
Jun
19
accepted If, $\lim x_n$ exists and finite then there is a function $f$ that is continuous
Jun
19
asked If, $\lim x_n$ exists and finite then there is a function $f$ that is continuous
Jun
6
accepted Difficult limits every grad should be able to do
Jun
5
asked Difficult limits every grad should be able to do
May
27
accepted $\lim_{n\to \infty} n^{1/n^2}$
May
27
comment $\lim_{n\to \infty} n^{1/n^2}$
Ahh, this is much better. Thanks!
May
27
asked $\lim_{n\to \infty} n^{1/n^2}$
May
26
comment Bounded sequence of positive numbers
Do you mean $r $ instead of $K $?
May
26
accepted Bounded sequence of positive numbers
May
26
asked Bounded sequence of positive numbers
May
19
accepted Residue Theorem and Homologous to zero
Apr
14
accepted Improper Integral with trigonometric functions
Apr
14
comment Improper Integral with trigonometric functions
Well this integral diverges so my integral will diverge by the comparison test. Correct?
Apr
14
asked Improper Integral with trigonometric functions
Apr
1
awarded  Notable Question
Mar
17
comment Residue Theorem and Homologous to zero
In your definition of being homologous to zero, if there is a point outside of $G $ that isn't so that the winding number is zero, then wouldn't that mean the the curve does not meet the hypothesis of the RT?
Mar
17
comment Residue Theorem and Homologous to zero
This is the heart of my question I think. If $C_2$ is NOT homologous to 0, then it does not satisfy the hypothesis because in order to use the Residue Theorem, we need a curve that is homologous to 0. I apologize if I'm being stupid here...
Mar
17
comment Residue Theorem and Homologous to zero
So this was my question; we don't consider such curves as $C_2$ for the residue theorem because it does not satisfy the hypothesis. Correct?
Mar
17
comment Residue Theorem and Homologous to zero
Well in this picture the answer is no, you can't deform $C_2$ to a single point and still stay in $K$.
Mar
17
comment Residue Theorem and Homologous to zero
So in this picture, $C_2$ is not homologous to 0? Then for the Residue Theorem we couldn't use a curve such as $C_2$ but can only consider curves that are either $C_1$ or curves that wrap around $H$ in such a way so that the winding number is 0, correct?