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11h
comment Are closed simple curves with this property necessarily circles?
In $\mathbb R^2$, a centrally symmetric region is the same thing as a region symmetric under rotation by $180^\circ$, isn't it?
12h
comment Find all numbers divisible by 25, that begin with 6.
@RobertSoupe: Base $10$ is not just a "very reasonable guess", it's the default assumption. (And if it's pedantry that you want, the post has to be in base $10$, doesn't it? The only question is what does $10$ mean.)
17h
answered $x^n + y^n = z^n$, $n>1$ To show that $x,y,z$ is greater than $n$
17h
comment Find all numbers divisible by 25, that begin with 6.
@GeoffRobinson: Of course it's base $10$! I notice that you didn't query whether $25$ was in base $10$. That's because base $10$ is understood, unless otherwise specified.
19h
comment Let $X\subset \mathbb{R}$ be Borel measurable. Can it be that $\aleph_0 <|X|<2^{\aleph_0}$?
@Asaf: Perhaps this is just a language problem, and the OP meant "It might be helpful to know whether...".
20h
reviewed Close What is the mathematical distinction between closed and open sets?
20h
reviewed Leave Open Generate a random neutrally stable matrix
20h
reviewed Leave Open Open mathematical questions for which we really, really have no idea what the answer is
22h
revised Find the remainder when $(x+1)^n$ is divided by $(x-1)^3$
added 8 characters in body
1d
comment Find the smallest number divisible by $204$ the digits of which sum to $204$
Best lower bound: $99999899999999999999988$ (with thanks to Robert Israel).
1d
revised Little confusion about connectedness
added 1 character in body
1d
comment Find all real numbers $c$ satisfying the following condition: For all $n \in \mathbb{N}$, we have $n^c \in \mathbb{N}$.
This was Problem A6 in the 1971 Putnam exam. You can find a solution here.
2d
comment Find all real numbers $c$ satisfying the following condition: For all $n \in \mathbb{N}$, we have $n^c \in \mathbb{N}$.
There is a mathoverflow question on this topic.
2d
comment A CD players plays songs until a certain artist is selected.
The song that it picks from the chosen CD is totally irrelevant. So you can remove all mention of songs from the problem description.
2d
comment Continuous function does not map closed set to closed set
@user28111: Wouldn't simply $g(x)=\arctan(x)$ do the trick?
2d
comment Product of two sets with density zero has density zero?
I think your premise is sound. I don't see why the squarefree integers pose a problem: most of them contain factors from both $A_p$ and $B_p$, so are not in either $A$ or $B$.
2d
answered $\sin(x^2)$ in terms of $\sin(x)$ and $\cos(x)$
2d
comment Can we write “fractional root” symbol in math?
I would say it's asking for trouble. $x^{a/b} = \sqrt[b/a]{x}$, and people will forget to invert that fraction.
May
21
comment Product of two sets with density zero has density zero?
A small mistake: my $A \times B$ is not the whole of $\mathbb N$; it consists of all numbers not divisible by $3$. So it has asymptotic density $\frac23$.
May
21
comment Product of two sets with density zero has density zero?
(Contd.) See Problem 14.12 at this link: "to justify that most even numbers have a prime factor $p \equiv 2$ mod $3$..." (Of course, all even numbers have such a factor, namely $p=2$; I assume the author means "an odd prime factor $p \equiv 2$ mod $3$.") That would seem to take care of $A$, but what about $B$?