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7h
comment Does the convergence of a series $\sum_{n=1}^{\infty} x_n$ imply the convergence of the alternating series $\sum_{n=1}^{\infty} (-1)^{n} x_n $?
Try $x_n=(-1)^n\frac 1n$
7h
answered How to determine if this musical exercise is valid: will the pattern complete?
7h
answered How can we define that function?
7h
comment How to show a function is not Riemann integrable
@Quality Just evaluate at $x_n=\frac1{\sqrt{(2n+\frac12)\pi}}$
7h
comment Chinese New Year Equation 2016
@hypergeometric Among all choices of "$b$ minus integer", this gave the best bound (i.e., $Ab-B$ with $B/A$ minimal).
7h
comment Chinese New Year Equation 2016
How do you get from $(4b+94)(64-4b)\equiv 0\pmod{16}$ to $b=18n$? After all, already $b\equiv 0\pmod 2$ implies $(4b+94)(64-4b)\equiv 0\pmod{16}$ ...
8h
revised Chinese New Year Equation 2016
edited body
14h
answered Chinese New Year Equation 2016
14h
comment A problem of decimals..
By the way, $0.5\overline0$ has the same length of non periodic part as $0.4\overline 9$.
14h
comment Runtime of an algorithm: check if two strings overlap
A method of practical speed-up (but unfortunately not of theoretical value, this is still $O(\min(n,m)^2$): It may be possible to iteratively compute "hashes" of suffixes/prefixes and make an explcit characterwise comparison only when hashes match
15h
answered Numerical approximation of $\sin(11/8)$
16h
comment Numerical approximation of $\sin(11/8)$
it is not. You need to go to $x^6$ on the left. And you need pretty good approximations of $\pi$
16h
answered Does a closed set not discrete have a limit point?
16h
comment Is $\sigma(2^r)$ a palindrome (in base $10$) for some $r > 2$, where $\sigma$ is the sum-of-divisors function?
Heuristically, Benford's law applies so that we can say that the leading digit is $1$ quite often ...
18h
comment Solve $KA-BK=0$, for a $1 \times n$ dimension row vector $K$, where $A$ is known $n \times n$ matrix and $b$ is known scalar
That's a homogenuous linear system ...
1d
comment Is it true if $R = mZ/mdZ$ is isomorphic to $Z/dZ$, then it must have a unit element?
To avoid confusion it should be noted that $A\to B$ refers to the direction $\Bbb Z/d\Bbb Z\to m\Bbb Z/md\Bbb Z$ here
1d
comment Splitting fields and intermediates
Yes, it surely is
2d
revised Confused with the power set of an integer
added 3 characters in body
2d
comment Confused with the power set of an integer
If $\Bbb P$ denotes power set, isn't it strange that these are multiplied and compared?
2d
answered Confused with the power set of an integer