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location Dubuque, IA
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visits member for 3 years, 11 months
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As of August 2011 I am an assistant professor of mathematics at Loras College in Dubuque, Iowa, USA.


5h
comment Proving that the center of a factor group is trivial
See math.stackexchange.com/q/780802
5h
comment Proving that the center of a factor group is trivial
The last sentence isn't worded quite right. You may have proved that $Z(G)$ is a normal subgroup of $G$. In doing so, you have proved that $aZ(G)a^{-1}=Z(G)$ for all $a\in G$.
5h
comment Integrable function $f$ and simple function $\phi$ such that $ \int{|f-\phi|} \> d\mu < \epsilon.$
But the $\phi_n$s and $\psi_n$s, they're the same thing? Are the $\phi_n$s supposed to be $\psi_n$s?
5h
comment There is no polynomial $q$ such that $\int_0^1 p(x)q(x)\,dx=p(0)$ for each polynomial $p$.
I like how this only relies on there being infinitely many such $\alpha$ (rather than all but finitely many for example).
6h
answered There is no polynomial $q$ such that $\int_0^1 p(x)q(x)\,dx=p(0)$ for each polynomial $p$.
6h
revised There is no polynomial $q$ such that $\int_0^1 p(x)q(x)\,dx=p(0)$ for each polynomial $p$.
more informative title
13h
comment What does conditional probability $P(A|B)$ mean when $P(B)=0$?
It's the unfortunate typesetting of the numerals used on this website that caused Ahmed's confusion. $0123456789$ without dollar signs becomes 0123456789. The zero, 0, looks more like a lowercase o than the mathmode numeral $0$.
13h
revised What does conditional probability $P(A|B)$ mean when $P(B)=0$?
edited title
14h
revised How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$?
deleted 2 characters in body; edited title
15h
comment Cardinality of the set of complex numbers
$|\mathbb R|=|\mathbb R^2|=|\mathbb C|$ with or without the continuum hypothesis. The proofs in the linked questions do not use the continuum hypthesis.
15h
revised Algebraic proof of $\tan x>x$
added 46 characters in body
15h
comment Where is the most clear and concise exposition of the spectral theorem for self-adjoint operators on Hilbert space?
I find this unclear, because I don't know which expositions you've already read and found unsatisfying.
15h
revised Why do we still do symbolic math?
typo removal
16h
answered Holomorphic functions on a complex compact manifold are only constants
16h
answered When do evaluation and the integral sign “commute”?
17h
comment vector spaces whose algebra of endomorphisms is generated by its idempotents
Another closely related question to which I don't know the answer: Is there a field K and a K-vector space whose algebra of endomorphisms is not generated as a K-vector space by its idempotents?
17h
comment Fibonacci Numbers in Nature
An interesting rant: lhup.edu/~dsimanek/pseudo/fibonacc.htm
1d
comment Sequence of orthogonal vectors in a Hilbert space
It appears that you have shown that if you assume both (a) and (c) then you get (b). You cannot take $y=\sum_n x_n$ unless you know $\sum_n x_n$ exists.
1d
revised If $f$ is $+\infty$ on a set of positive measure and the integral exists in $[-\infty,+\infty]$, must the integral be $+\infty$?
deleted 2 characters in body; edited title
1d
answered If $f$ is $+\infty$ on a set of positive measure and the integral exists in $[-\infty,+\infty]$, must the integral be $+\infty$?