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visits member for 4 years
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9h
comment How many undecidable statements are there in ZFC?
@ThomasAndrews: Please post this as an answer!
13h
comment Symmetric Borel sets in the plane
I'm not seeing how this completes the proof. This shows that the $\sigma$-algebra generated by the symmetric rectangles contains the symmetric open sets. To finish, we would need to show that the $\sigma$-algebra generated by the symmetric open sets contains all the symmetric Borel sets, and that seems like it may be the hard part. I think I can see how to do it via transfinite induction, but there ought to be something more slick.
Aug
18
comment Show that $S = \{f \in L^1(\mathbb{R}) \mid \int_{\mathbb{R}}f dm = 0\}$ is closed in $L^1(\mathbb{R})$.
We don't even really need the language of functional analysis: this is just the "triangle inequality" $\left| \int (f_n -f) \right| \le \int |f_n - f|$.
Aug
17
answered Where did the negative answer come from?
Aug
17
comment Is there an interval notation for complex numbers?
This is correct in a sense, but likely to be misleading unless explained. Whether $\mathbb{C}$ "is" $\mathbb{R}^2$ depends on your personal view of the foundations, and readers who prefer to define $\mathbb{C}$ in a different way may be confused.
Aug
17
comment countable group, uncountably many distinct subgroup?
@Bryan: Indeed, thank you.
Aug
17
comment countable group, uncountably many distinct subgroup?
@Bryan: Hmm, is it obvious that these subgroups are non-isomorphic?
Aug
17
awarded  Nice Answer
Aug
17
comment If $(X \times Y, \overline{\Sigma \times \tau}, \mu \times \nu)$ is $\sigma$-finite, does that imply $(X, \Sigma, \mu)$ is $\sigma$-finite?
Hint: What if $\nu$ is the zero measure?
Aug
17
revised Is it true that, $x\rho(x/t)\in H^{s}$ for $\rho\in \mathcal{D}(\mathbb R)$ and $s>3/2$?
edited title
Aug
17
answered Is it true that, $x\rho(x/t)\in H^{s}$ for $\rho\in \mathcal{D}(\mathbb R)$ and $s>3/2$?
Aug
17
comment holomorphic map on a rectangle — hint requested
As stated this is not true. Did you mean to assume that f maps Q into Q?
Aug
16
answered What exactly is a product measure?
Aug
16
reviewed Leave Open $a_1 = 2, a_{n+1} = 2a^2_n+1, a_n = ?$
Aug
16
reviewed Leave Open Sum and Product of two transcendental numbers cannot be simultaneously algebraic
Aug
16
reviewed Close Probability of ace in each hand
Aug
16
answered Does $S^\bot+T^\bot = (S\cap T)^\bot$ hold in infinite-dimensional spaces?
Aug
15
revised Zero correlation does not imply independence
missing word
Aug
15
comment Why isn't the volume of a sphere $ π^2r^3?$
@taratm: Your formula is assuming those disks are "flat": their top and bottom surfaces are parallel. If you try to arrange such disks to approximate a sphere, you will find either large gaps or large overlap. This introduces an error that does not tend to zero in the limit. Wedge shaped disks would avoid this, but of course they have a different volume (which may be hard to compute without already knowing the volume of a sphere).
Aug
15
revised How is Cartesian coordinate system related to his philosophy
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