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Apr
9
comment Infinite sets don't exist!?
You could mention, that Von Neumann proposed that all natural numbers can be bootstrapped out of the empty set by the operation you described.
Jan
16
comment When is $f(x) = \frac{ax}{e^{-b}-{(e^{c})}^x}$ monotonic?
By the way, is this a homework related question? If so, then please consider adding the appropriate tag - furthermore show what you have done so far and what you don't understand so we see that you at least tried something.
Jan
14
comment Parameterized curve describing trajectory of thrown object
I don't know whether this is correct, but we never did such complicated computations in class. I tried to solve this problem now by not factorizing so that I have $\sqrt{v_0^2\cos^2\beta+(v_0\sin\beta-gt)^2}$ and simplify that with other (much easier) approaches. Do you have some other suggestions?
Jan
14
comment Parameterized curve describing trajectory of thrown object
Actually I never saw this method, but I think that this yields $\int \|k'(u)\|\,\mathrm du=\frac{1}{2}g\left(u-\frac{v_0\sin(\beta)}{g}\right)^2+v_0\cos(\beta)u+\text{c‌​onstant}$. Did I understand this substitution right?
Jan
8
comment Proving that $\left(\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\cdots+\frac{1}{n!}\right)$ has a limit
Careful, you say that $x_n$ is a finite sum and saying that it equals an infinite sum. Furthermore you ambiguously use $n$. These are just small mistakes with the notation. How about saying $\lim_{n\to \infty} x_n = \lim_{n\to \infty} \frac{1}{0!}+\ldots+\frac{1}{n!}=\sum_{k=0}^{\infty}\frac{1}{k!}=e$?
Jan
7
comment If $\sum_{n=1}^\infty a_n$ is convergent, then $\sum_{n=1}^{\infty} a_n\sin(n)$
@GEdgar: I thought about that fact that $|\sin(n)|\leq 1$ like Andrew mentioned this could be an "easier" example to simplify $\sin$ if you understand.
Jan
7
comment If $\sum_{n=1}^\infty a_n$ is convergent, then $\sum_{n=1}^{\infty} a_n\sin(n)$
Have you tried to think about $(-1)^n\cdot\frac{1}{n}\to 0$? This could be some motivation.
Jan
7
comment Differentiation with respect to integral boundary
@macydanim: Holy shit... this looks awesome. I will write this down as a possible alternative solution.
Dec
22
comment Calculating a function limit
Exact duplicate of: math.stackexchange.com/q/263306/12864
Dec
21
comment Complicated limit calculation
What have you tried so far?
Dec
10
comment Antisymmetric and irreflexive relation which is not asymmetric
I see it now. Let's forget what I was talking about.
Dec
10
comment Antisymmetric and irreflexive relation which is not asymmetric
Isn't this example antisymmetric, not reflexive and not asymmetric? If not, why?
Dec
10
comment Antisymmetric and irreflexive relation which is not asymmetric
I just got a question right now. What aboout $M=\{1,2\}$ and $R=\{(1,1),(1,2)\}$?
Dec
10
comment Antisymmetric and irreflexive relation which is not asymmetric
Thank you for the second part - i was totally confused here.
Dec
8
comment Algorithm to check whether a graph has no cycles
Considering correctness, what do you suggest for a better approch with the cycle $C$?
Dec
8
comment Algorithm to check whether a graph has no cycles
Please have a look at my updated question. Is this the kind of proof for correctness you recommended me?
Dec
8
comment Algorithm to check whether a graph has no cycles
Furthermore to reduce redundancy as $\mu$ and $V'$ would hold visited nodes, an option would be to use $\mu$ for a topsort.
Dec
8
comment Algorithm to check whether a graph has no cycles
How about the following idea: Each time we visit a node we could set µ to 0 and add the visited node to a new set $V'$. At the end of the while loop we could check for emptiness of $V\setminus V'=\emptyset$. If this is true we can return false because there are no more components left; otherwise we pick an arbitrary $v'\in V\setminus V'$ and then repeat everything with $U=\{v'\}$. Do you think that would solve my problem with the components?
Dec
3
comment Derivatives and their domains
@Siminore: Do you have some other clues about the domains of (3)-(5)?
Dec
3
comment Derivatives and their domains
@Siminore: Yet one can argument that e.g. $\sqrt{\sqrt{-8}}$ leads to problems if we don't care about complex numbers (which are excluded in this excercise - I did forgot to mention this), or am I wrong here?