Michael Hardy

Minneapolis

After doing nearly all the coursework for a Ph.D. in math, I then did all the coursework for a Ph.D. in statistics and completed that degree.
3h
revised Let $(A_n)$ be a decreasing sequence of sets such that $A_n\to A=\cap_n A_n$, is the following true when measure is infinite?
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3h
comment $(x_n,y_n) \in \{(x,y)\mid y=kx\}, n=1,2,3,4\Leftrightarrow$ $\frac{z_1-z_3}{z_2-z_3} \div \frac{z_1-z_4}{z_2-z_4} \in \mathbb{R}, z_n = x_n+iy_n$
$\uparrow$ I didn't finish a sentence: I meant $a/b\in\mathbb R \Longleftarrow{}$ $a$ and $b$ are both real or $a$ and $b$ are both imaginary. ${}\qquad{}$
3h
answered $(x_n,y_n) \in \{(x,y)\mid y=kx\}, n=1,2,3,4\Leftrightarrow$ $\frac{z_1-z_3}{z_2-z_3} \div \frac{z_1-z_4}{z_2-z_4} \in \mathbb{R}, z_n = x_n+iy_n$
3h
comment $(x_n,y_n) \in \{(x,y)\mid y=kx\}, n=1,2,3,4\Leftrightarrow$ $\frac{z_1-z_3}{z_2-z_3} \div \frac{z_1-z_4}{z_2-z_4} \in \mathbb{R}, z_n = x_n+iy_n$
The question started by saying the quotient of two complex numbers is real if and only if they are either both real or both imaginary. That is false. "if" is correct; "only if" is not. ${}\qquad{}$
3h
comment $(x_n,y_n) \in \{(x,y)\mid y=kx\}, n=1,2,3,4\Leftrightarrow$ $\frac{z_1-z_3}{z_2-z_3} \div \frac{z_1-z_4}{z_2-z_4} \in \mathbb{R}, z_n = x_n+iy_n$
It is not correct that $a/b\in\mathbb R \Longleftrightarrow{}$ $a$ and $b$ are either both real or both imaginary. It is true that $a/b\in\mathbb R \Longleftarrow{}$ $a$ and $b$. However, suppose $a = 2+6i$ and $b=1+3i$. Then $a/b$ is real even though neither $a$ nor $b$ is real and neither $a$ nor $b$ is imaginary. ${}\qquad{}$
3h
revised $(x_n,y_n) \in \{(x,y)\mid y=kx\}, n=1,2,3,4\Leftrightarrow$ $\frac{z_1-z_3}{z_2-z_3} \div \frac{z_1-z_4}{z_2-z_4} \in \mathbb{R}, z_n = x_n+iy_n$
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3h
revised Is $SO(n)$ a topological space?
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3h
revised Is $SO(n)$ a topological space?
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3h
comment Principal $n$th Root
@DavidHouse : What is the "long W sub K" formula? ${}\qquad{}$
3h
revised Is $p_n \sim \frac{5}{4}n\log(n) + \frac{1}{2}n + \frac{(p_1+\ldots+p_{n-1})}{n-1}$ a good approximation for the $n^\text{th}$ prime?
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3h
comment Principal $n$th Root
Insteat of "principal $n$th root of $(-9)^{1/2}$, might you have meant "principal square root of $-9$"? ${}\qquad{}$
3h
revised Principal $n$th Root
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4h
revised Calculate the flux through a closed surface
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4h
revised Calculate the flux through a surface S from a field described by vectors
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4h
comment Calculate the flux through a surface S from a field described by vectors
Are you sure you didn't read $\vec{F}\cdot d\vec{s}$ (a dot-product of vectors) and mis-copy it as $\vec{F}\,\vec{ds}$? And should it not just be a single integral along the boundary, i.e. $\displaystyle\int\limits_{\partial S}$ rather than $\displaystyle\iint\limits_S$? ${}\qquad{}$
4h
revised Jensen inequality conceptual doubt
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4h
revised $\int\frac{1+x^2}{x^4+3x^3+3x^2-3x+1}dx$
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4h
revised Determinant structure of symplectic matrix
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4h
comment $ \lim_\limits{x \to \infty} x(\sqrt{x^2+1}-x) $ = $ \frac{1}{2}$?
If it's not clear what was done here, see Claude Leibovici's comment under the question. ${}\qquad{}$
4h
revised $ \lim_\limits{x \to \infty} x(\sqrt{x^2+1}-x) $ = $ \frac{1}{2}$?
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