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17h
comment A monotonically increasing series for $\pi^6-961$ to prove $\pi^3>31$
It's "easy" to write $\pi^6-c=\sum_{k=0}^\infty\frac 1{P(k)}$ with $c\ge 961$. One just starts with Euler's series and collects enough early terms to make $c$ big enough, that is we can take $P(k)=\frac1{945}(k+m)^6$ for suitable $m$.
18h
comment Is this identity about floor function true?
@MPW Me too, but the counterexamples kept failing :)
18h
revised Is this identity about floor function true?
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18h
answered Is this identity about floor function true?
18h
comment Is this identity about floor function true?
@fleablood 1.9 is not a positive integer tho
18h
revised Calculating $| \langle \cup_{i=1}^n P_i \rangle |$ where $P_i$ are Sylow subgroups of G
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19h
answered Calculating $| \langle \cup_{i=1}^n P_i \rangle |$ where $P_i$ are Sylow subgroups of G
20h
comment Conditions for a homeomorphism
If you'd define "$f$ is continuous and its inverse ..." your audience would interrupt you and shout "What inverse? Do you mean $f$ is in fact bijective? Or injective and you mean left inverse? Or surjective and you mean right inverse? But those are not even unique in general! Help, I'm lost!". You might shorten to "$f$ is continuous and has a continuous two-sided inverse". Or, more leaning towards category theory: "$f$ is continuous and there exists continuous $g\colon Y\to X$ with $f\circ g=\operatorname{id}_Y$ and $g\circ f=\operatorname{id}_X$."
20h
comment Is the following inequality true? $\sup\limits_{2T\leq t\leq 4T}f(t)\leq \sup\limits_{2T\leq t\leq 3T}f(t).\sup\limits_{3T\leq t\leq 4T}f(t)$
Why is the a period (full stop?) on the right?
20h
comment Can an infinite sum of irrational numbers be rational?
We might make the summands "even more" independent: $\sqrt{p_n}$ could be replaced by any $\alpha_n$ provided $\alpha_n>0$ and $\sum \alpha_n=\infty$. We might for instance pick $\alpha_n\in[1,2]$ such that it is transcendental over $\Bbb Q(\alpha_1,\ldots,\alpha_{n-1})$.
21h
comment Can an infinite sum of irrational numbers be rational?
@Debanil The square root ensures that the summands are irrational. Picking distict primes ensures that there is no rational relation among the summnds.
21h
answered In group theory, do $ \langle\mathbb{Z}, +\rangle $ and $ \langle\mathbb{R}, +\rangle $ have the same order?
21h
answered The solution of ODE $k'(x) = r(k(x))$ is infinitely differentiable if $r$ is
22h
revised Give examples showing why $0\cdot \infty$, $\infty/\infty$, and $0/0$ are meaningless
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1d
answered Find PDF on $[0,6]$ such that $P([1,3]) = 0.5$
1d
comment is there a closed form expression for the following matrix infinite series
Note that $ASA^T-S=B$
1d
comment Is the sequence $s_n= \frac{\sin\frac\pi2}{1\cdot 2}+\frac{\sin\frac\pi{2^2}}{2\cdot 3} + \dots + \frac{\sin\frac\pi{2^n}}{n\cdot(n+1)}$ convergent?
@TaylorTed Cf. Premtim's more explicit elaboration
1d
comment Why is multiplication in frequency domain equals convolution in time domain?
In a certain way, this is the same correspondence as between multiplying polynomials and convoluting their coefficients ...
2d
comment Finding subgroups with a specific property.
What about $G=\Bbb Z/4\Bbb Z$ and $H=\langle 2+2\Bbb Z\rangle$ (so $n=2$)? Actually, ths $H$ is normal.
2d
revised Finding subgroups with a specific property.
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