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5h
reviewed Approve suggested edit on Question about $i$
5h
reviewed Approve suggested edit on Pumping lemma to prove that a language is not context free
6h
comment Let $G$ be a group. Prove the equivalence relation: If $H$ is a subgroup of $G$, let $a \sim b$ iff $ab^{-1} \in H$
You might want to omit the mention of fibers since that is a fairly advanced idea.
6h
revised Find this limit without L'hopital Rule : $\lim_{x\rightarrow +\infty}\frac{x(1+\sin(x))}{x-\sqrt{(1+x^2)}}$.
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6h
revised How can I calculate $\lim_{x \to 0} \log(\cos(x))/\log(\cos(3x))$ without l'Hopital?
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6h
revised Evaluate $\lim_{x\rightarrow 0} \frac{\sin (6x)}{\sin(2x)}$ without L'Hopital
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6h
comment Let $G$ be a group. Prove the equivalence relation: If $H$ is a subgroup of $G$, let $a \sim b$ iff $ab^{-1} \in H$
Yes, that is the whole point. You want to show that if $a\sim b$, then $b\sim a$. If $a\sim b$, that means that $ab^{-1}\in H$, so yes you are assuming it.
6h
comment Let $G$ be a group. Prove the equivalence relation: If $H$ is a subgroup of $G$, let $a \sim b$ iff $ab^{-1} \in H$
If $H$ is closed under inverses, that means that if $h\in H$, $h^{-1}\in H$. You showed that $(ab^{-1})^{-1} = ba^{-1}$. What does this say about $ba^{-1}$ in relation to $H$? Is it in $H$ or not?
6h
answered Let $G$ be a group. Prove the equivalence relation: If $H$ is a subgroup of $G$, let $a \sim b$ iff $ab^{-1} \in H$
1d
comment Can the zero vector be an eigenvector for a matrix?
The zero vector by convention is not an eigenvector, much in the same way that $1$ is not a prime number. If we let zero be an eigenvector, we would have to repeatedly say "assume $v$ is a nonzero eigenvector such that..." since we aren't interested in the zero vector. The reason being that $v=0$ is always a solution to the system $Av = \lambda v$.
1d
revised Finding $\lim_{n \to \infty }\sqrt[n]{b^{2^{-n}}-1}$ without L'hopital
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1d
revised Limit evaluation: very tough question, cannot use L'hopitals rule
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1d
revised Trigonometric limit: $(1-\sqrt{\cos x})/x^2$ as $x\to 0$, without using L'Hopital
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1d
answered Does $\int_0^{\infty}\frac{x\hspace{1mm}dx}{x^3+1}$ converge?
1d
comment How to compute $(i^2-i^4+i^6-i^8+…+i^{38})^2$
$i^4 = i^8 = i^{12} = \ldots$ and $i^2 = i^6 = i^{10} = \ldots$..
2d
comment Bump Functions on Open Intervals
Perhaps the better thing to ask yourself is what compact sets look like on $(0,\infty)$. Are they the same as on $\Bbb R$ or do they differ somehow because of the relative topology? (Hint: both notions of compactness are the same so $(0,a]$ cannot be compact which means that compact sets have to stay away from $0$.)
2d
comment Fourier series on an arbitrary interval
That's correct. I'm not sure why it's not working for you.
2d
comment Fourier series on an arbitrary interval
But the series isn't zero. I guess I don't quite understand the issue. Can you please provide your code?
Oct
23
comment Winding number of $e^{ix}$?
You are correct.
Oct
23
answered Winding number of $e^{ix}$?