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9h
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?
15h
comment How can I prove that G is abelian?
@IvanS.Guerra I only claim that $N$ is contained in $Z(G)$. For any $a\in N$, the inner automorphism $x\mapsto axa^{-1}$ has order dividing $|N|$ and order dividing $|\operatorname{Inn}(G)|$, hence dividing $(n,m)=1$. We conclude that $x\mapsto axa^{-1}$ is the identity, i.e.,, $a\in N$ commutes with all $x\in G$.
16h
comment Is this limit indeterminate or $e^2$ or what?
The fact that "naive" computation of the limit leads to an indeterminate form does not prevent the limit from possibly existing. For example, $\lim_{x\to 0}\frac{\sin x}{x}$ is also indeterminate of form $\frac 00$, but the limit exists.
16h
comment Linear Algebra. Is this question realte to combination and factorials?
For example with $n=3$, $$A=\begin{pmatrix}2\choose 1&3\choose 1&4\choose1\\3\choose2&4\choose 2&5\choose 2\\4\choose3&5\choose 3&6\choose 3\end{pmatrix}=\begin{pmatrix}2&3&4\\3&6&10\\4&10&20\end{pmatrix} $$
1d
comment Regarding the iteration of sum of prime factors
@user1952009 Don't you rather mean the twin prime conjecture?
1d
comment Can sum of rationals be irrational?
A series is not a sum.
2d
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 $m$.
2d
comment Is this identity about floor function true?
@MPW Me too, but the counterexamples kept failing :)
2d
comment Is this identity about floor function true?
@fleablood 1.9 is not a positive integer tho
2d
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 $g\circ f=\operatorname{id}_X$."
2d
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?
2d
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 $\Bbb Q(\alpha_1,\ldots,\alpha_{n-1})$.
2d
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.
Feb
8
comment is there a closed form expression for the following matrix infinite series
Note that $ASA^T-S=B$
Feb
8
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
Feb
8
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 ...
Feb
8
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.
Feb
8
comment How to show that any path $\gamma:[a, b]\rightarrow\mathbb C$ is rectifiable and that $L(\gamma)=\int_{a}^{b}|\gamma'(t)|dt$.
Hint: Any idea how to relate $\gamma(t_{i+1})-\gamma(t_i)$ with some $(t_{i+1}-t_i)\gamma'(\tau_i)$?
Feb
8
comment Property of Nowhere Dense Sets
@BrianM.Scott Ah, I somehow read closure instead of accumulation points
Feb
8
comment Property of Nowhere Dense Sets
Regarding counterexamples: With $X=\Bbb C$, how is $\Bbb R$ (being the boundary of the upper half plane) the closure of a discrete set?