Dominic Michaelis
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 Feb 23 awarded Enlightened Feb 23 awarded Nice Answer Feb 14 awarded Yearling Dec 3 awarded Nice Answer Oct 29 awarded Popular Question Oct 18 comment $\sum_{n=0}^{\infty} \sin (nx) = \cot(x/2)$? I think it should be $$\sum_{k=1}^\infty 2\sin(k x) = \cot(\frac{x}{2})$$ Oct 18 comment Does the series $\sum{(\frac{1}{n^2} - \frac{1}{n})}$ converge or diverge? @SyedMuhammadAsad yeah that is correct Oct 13 answered suppose $A$ is a set where $x \in A \iff x + T \in A$ and $\mu$ denotes the lesbesque measure. prove that $\mu(A\cap[0,T]) = \mu(A\cap[a,a+T])$ Oct 13 comment suppose $A$ is a set where $x \in A \iff x + T \in A$ and $\mu$ denotes the lesbesque measure. prove that $\mu(A\cap[0,T]) = \mu(A\cap[a,a+T])$ Why should the set $A$ be measurable? Oct 9 comment If a $p$ is prime number, for some $p$ ,fraction $1/p$ ,is decimal is $p-1$ period repetition, can anyone prove it? you mean like for $p=2$ or like $p=3$ or $p=5$ ? in these cases they don't have a period repeatation or of the wrong length. What exactly is your question? Oct 9 comment Compute the integral over these paths @beak why? what is different there`? Oct 9 comment Compute the integral over these paths @baek yeah and split it up in the four paths you already gave us. The integral you get is always of the form $\int \frac{1}{t+c} \, \mathrm{d}t$ if you factor out some constants and this shouldn't be that hard Oct 9 comment Compute the integral over these paths @DanielFischer I assumed that it is one path $C:[0,4]\to \mathbb{C}$ so it is just the boundary of a square where one singularity is in the interior of the closed curve Oct 9 comment Compute the integral over these paths @beak well then just ignore that part. Later in the lecture you will see that the line integral (for holomorphic functions) is not only well defined on the set of all curves but even on the quotient where you say that two curves are equivalent if they are homotopic. Just use the definition of line integral Oct 9 comment Question on infinite T4 topological space Before I start thinking, is $T_4$ for you stronger than $T_2$ or incomparable? Oct 9 answered Compute the integral over these paths Oct 6 revised Limit of $\frac{\frac{1}{e}(1+x)^{1/x}-1+\frac{x}{2}}{x^2}$ when $x\to0$ added 559 characters in body Oct 6 comment Inner Product for Functions Well you should point out, that the nontrivial part is to proof that $\langle f,f\rangle=0$ iff $f=0$ Oct 6 revised Limit of $\frac{\frac{1}{e}(1+x)^{1/x}-1+\frac{x}{2}}{x^2}$ when $x\to0$ added 21 characters in body Oct 6 revised Limit of $\frac{\frac{1}{e}(1+x)^{1/x}-1+\frac{x}{2}}{x^2}$ when $x\to0$ added 335 characters in body