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Let me worry about blank!


4h
comment If you have $\max(a,b)$ and $\min(a,b)$, how would one find expressions for these using addition, subtraction, and absolute value?
@NickFreeman: On the real axis, $(a+b)/2$ is the point which lies directly between $a$ and $b$; $|a-b|$ is the distance between $a$ and $b$. How can you combine these two values to get the max and min?
Oct
7
comment Every infinite subset of E in R having a limit point in E implies E is closed and bounded
Hint: Assume for a contradiction that $E$ is not closed. Then there exists an infinite sequence of points in $E$ such that... (fill in the blank here)? Now assume for a contradiction that $E$ is not bounded. Then there exists an infinite sequence of points in $E$ such that... (fill in the blank here)?
Sep
30
comment Why coefficients of Fourier series are countable, though the initial periodic function is described with an uncountable set of points
@Mike Earnest: Can you elaborate on which countably many choices you are making in your last sentence?
Sep
27
comment If $B$ is an uncountable set and $A$ is a countable set, then prove that $B$ is similar to $B-A$.
Hint: Use the same idea as in Hilbert's hotel. To make room for countably many new guests, take countably many rooms $1,2,3,\ldots$ and move the guests in those rooms to rooms $2,4,6,\ldots$.
Sep
24
awarded  Autobiographer
Sep
22
comment Is it true that $n^2+3n+13$ is prime for all $n\in\mathbb ℤ^+$?
Here's a polynomial prime-generating formula: $f(n)=17$.
Sep
22
comment In Whitehead & Russell's PM, what is the name of that symbol in series of segments?
Maybe $\varsigma$ (\varsigma), $\zeta$ (zeta) or digamma? en.wikipedia.org/wiki/Digamma
Sep
17
comment Traveling salesman problem: can a terrible strategy beat a good one?
@RobertIsrael: I think the way the question is formulated implies that nearest-neighbor need not be best. The alternative would make an interesting follow-up question. I would like to see your solution to the former.
Sep
16
revised How can I show $F$ is not monotonic in any subinterval?
deleted 163 characters in body
Sep
15
answered How can I show $F$ is not monotonic in any subinterval?
Sep
15
comment How can I show $F$ is not monotonic in any subinterval?
The hint says that if one term $3^{-k}g(x-r_k)$ goes through a "full period" (that is, assumes both the values $\pm 3^{-k}$) on a given interval, then the sum $\sum_{n=k+1}^\infty 3^{-n}g(x-r_n)$ is too small to ruin the non-monotonicity of $3^{-k}g(x-r_k)$ in that interval.
Sep
11
comment Can one measurably partition the interval $[0,1]=A\cup B$ with mass equally distributed between $A$ and $B$?
No. mathoverflow.net/questions/42119/…
Sep
9
reviewed Approve suggested edit on How to show that $\|a+b+c\|^2\leq 3\|a\|^2+3\|b\|^2+3\|c\|^2$
Aug
12
comment How to make 3D object smooth?
@JyrkiLahtonen: A better approach might be convolving a two-variable parametrization of the surface with a 2D bump function. The main difficulty with your suggestion is not calculating the integral (which can easily be done numerically), but finding the points where it exceeds your given threshold. For the 3D object in the OP however, it might be a pain to get a parametrization of the surface.
Jul
31
comment Prove that $\mathbb{R}^{n}-A$ with the standard topology is connected where $n \geq 2$ and $A \subset \mathbb{R}^{n}$ is countable.
@user166967: What does your proof by contradiction look like? The only one I can think of uses the fact that any given two points in $\mathbb R^2$ lie on a comon path, and thus I prove simultaneously that $\mathbb R^2$ is path-connected.
Jul
29
awarded  Yearling
Jul
21
revised Rearrangement of dinner guests
added 773 characters in body
Jul
21
revised Rearrangement of dinner guests
added 773 characters in body
Jul
21
revised Rearrangement of dinner guests
added 773 characters in body
Jul
20
answered Rearrangement of dinner guests