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1d
comment Convolution $f * g$
You can't. The best you can do is write the answer in terms of the Fourier transform, however that is just a different way to write the integral (and isn't actually a real simplification).
1d
revised If $a > 0$,$b>0$, and $\frac{1}{a} + \frac{1}{b}$ is an integer, prove that $a=b$. And show that $a = 1$ or $2$
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1d
comment Showing a non-isomorphism of groups
@IdiotfromPrinceton Having a bijection is necessary, but a bijection might not preserve the algebraic structure.
2d
comment Definition of continuity up to the boundary
Hmm I would adjust your definition to have $\overline{\Omega}\cap B_{\delta}(x)$ instead. (You would like to approach $y$ from anywhere in $\Omega$, not just on the boundary. Also the reason you don't do it for unbounded $\Omega$ is that you might have to evaluate your function at infinity.. That can get into some very murky water very fast.
2d
comment Show if $A^TA = I$ and $\det A = 1$ , then $A$ is a rotational matrix
Your reasoning is slightly off. $a = \pm \cos\theta$ and $c = \pm\sin\theta$ or $a = \pm \sin\theta$ and $c = \pm\cos\theta$ for some $\theta$. (There is a way to just drop down to one condition, but you will still have the $\pm$.)
2d
comment Why do we teach Calculus in High School instead of, say, programming?
@SimpleArt Ahh I see. It's a common misconception and your question made it seem like you weren't sure, so I thought I'd clarify.
2d
comment Why do we teach Calculus in High School instead of, say, programming?
@SimpleArt Complex analysis isn't about the study of complex numbers, it's about calculus with functions of complex variables.
2d
comment Generalization of Liouville's theorem
This has to be one of the absolute best questions asked on this site. I've never even considered such a thing but it's so natural.
2d
comment Why do we teach Calculus in High School instead of, say, programming?
@SimpleArt I would not say calculus is easier, just easier to grasp. I think discrete math and linear algebra are simpler in terms of actual content, but the fact that they aren't as graphical is a huge detriment for most students. The vast majority of people are visual learners and need graphical aids. Calculus is far and away superior to the previous two in this respect.
2d
comment Why do we teach Calculus in High School instead of, say, programming?
@SimpleArt For math people that is the case, but the problem is you absolutely cannot teach to the top of the class in the K-12 years. If you do, you'll leave absolutely everyone else behind.
2d
comment Why do we teach Calculus in High School instead of, say, programming?
@SimpleArt Most kids are not ready for anything more advanced than calculus. If you replaced calculus with anything, it would be either discrete math or statistics. Many students would hate discrete math for being too "mathy". Even elementary number theory wouldn't work because it gets very challenging very fast. In Canada, they teach EXTREMELY basic linear algebra, but the reality is that again, it is a bit too abstract for many students. Calculus is at least extremely graphical and intuitive.
2d
comment Why do we teach Calculus in High School instead of, say, programming?
At least two or three major branches of mathematics are founded upon calculus and its generalizations. I think you seriously misunderstand the role of calculus in mathematics. Also "programming" does not require an understanding of any of those subjects. Doing programming FOR those subjects requires an understanding of those subjects. There are very few branches of math that do not invoke calculus or calculus-like ideas. Take your elitism elsewhere ("physics, lol").
2d
revised limit of $f(x) = \lim \limits_{x \to 0} (\frac{\sin x}{x})^{1/x}$
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2d
comment limit of $f(x) = \lim \limits_{x \to 0} (\frac{\sin x}{x})^{1/x}$
@W-t-P Which can be remedied by noting that $\ln\left(\frac{\sin x}{x}\right) = \ln\left(\frac{\sin(-x)}{(-x)}\right).$
Feb
5
comment Why the Sum of all possible outcomes does not equal to one, in this case?
You are correct that it is glossy/glossy only. You made an error in just counting the possible outcomes. The outcomes are not independent. If you select one glossy paint can, the probability of selecting another is lessened. The probability of one is $3/5$ and the probability of a second is $2/4$ so you get an overall probability of $6/20$ which gives a total probability of $1$.
Feb
5
comment Why the Sum of all possible outcomes does not equal to one, in this case?
You should write down the entire problem. I do not even have access to a preview of the text, many others may not as well.
Feb
5
comment Show that $\lim_{z\to z_0} cf(z)=ac$ (where $c$ is a complex number)
Do you know how to prove these results in the case of real-valued functions (via $\varepsilon$-$\delta$ arguments)? It's almost the exact same proof.
Feb
5
revised Is the ideal generated by the polynomial $x^2-2$ maximal in the ring $\mathbb{C}[x]$?
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Feb
5
revised Are there complex numbers whose sines are zero?
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Feb
4
comment Is there a name for an infinite product series?
@Lucian I would encourage you not to post stuff like that because it causes WAY too many misconceptions and arguments.