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Mar
25
comment Why are turns not used as the default angle measure?
So the question is: Do you want to use such a measure of angle that the mathematical sine is the same as the physical one? If yes, you can't but have 6.28 as the full turn. If no, you can do whatever you wish of course, but you're likely not simplifying things once you need any higher mathematics than pure Euclidean geometry involved.
Mar
25
comment Why are turns not used as the default angle measure?
@zahbaz Well, you can define the angle as you wish. My favourite definition of sine is that it's the solution to $y''+y=0$ for which $y(0)=0$ and $y'(0)=1$. Or that $\sin x = \frac{e^{ix}-e^{-ix}}{2i}$, where $e$ is such number that the derivative of $e^x$ at $0$ is $1$. Note that I as a mathematician cannot care less about SI and their units; sine does not take an angle as an argument, it takes a number.
Mar
24
comment Does there exists this kind of real sequence?
Well, you asked two questions in one, causing this mess. Next time, please do not do that.
Mar
24
comment Does there exists this kind of real sequence?
Ok, in that case you accepted an answer that does not answer the question.
Mar
24
comment Is there a connection between the “independent sets” in matroids and “independent sets” in graph theory?
I believe it's a coincidence of notions, but I wonder if any relation exists.
Mar
24
comment Does there exists this kind of real sequence?
What does it mean to be bounded by $\max\{a_1,a\}$ in case they are both negative?
Mar
24
comment Does there exists this kind of real sequence?
I really wonder who have downvoted both my and your answer without leaving a comment, and why he has done so.
Mar
24
comment Why are turns not used as the default angle measure?
@IlmariKaronen Thanks!
Mar
24
comment Why are turns not used as the default angle measure?
@Henry Yeah, and that one is missing the important thing: the original includes all 3 basic operations, together with the 5 constants: addition, multiplication, and power. You're missing one constant and one operation ;)
Mar
24
comment Sum of inverse of Fibonacci numbers
+1 This is one of the good ways how to estimate the error.
Mar
24
comment Solving a system of equations with 3 variables in under a minute
@egreg I don't buy this your point. To me, the question is formulated in such a way that the equation has some solution. The asker has $x$, $y$ and $z$ in his head and only shares that they satisfy the three equalities. This means that the problem has at least one solution, and then the method in Carl's answer works.
Jan
22
comment Subgroup of $\mathbb{Q}$ containing $\mathbb{Z}$
Do you take group w.r.t. to $+$ or $\times$?
Jan
22
comment How can you find $m$ in $mx^2+(m-3)x+1=0 $ so that there is only one solution
I don't think so and I give you +1; this approach is slightly different than in the other answers and shows a nice use of Vièta's formulas.
Jan
22
comment Calculating $\lim_{n\to\infty}\sqrt[n]{ \sqrt[n]{n} - 1 }$
No, the OP did not do that, but it's easy, because $n^{1/n}>1$ for all $n$.
Jan
10
comment When does one consider the laplacian as a dirac delta function?
The direct calculation does not work at zero (the origin), which is where you're losing your delta function. It's similar to saying that the derivative of $x\mapsto|x|$ is the signum of $x$; you lose one point.
Jan
10
comment How many sequences of rational numbers converging to 1 are there?
Isn't simply $\mathbb{N}^\mathbb{N}$ a continuum, whence also $\mathbb{Q}^\mathbb{N}$ is?
Dec
27
comment How can one determinate the variationt of $f(g(x))$
@user233658 Because $f$ is decreasing for arguments $<1$ and increasing for arguments $>1$.
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
mickep @Ian Oh I now realize the trick (sorry it's early in the morning here). That looks really nice, thanks!
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
@Ian Yes, I know. The problem is that this is for 1st year university students, and we tend to disallow using derivatives for limits at the beginning. And after one does what you do, it gets very complicated. Thanks for your help anyway!
Dec
16
comment Limit of $e^x/x^3$ at infinity without l'Hopital
@Ian If you ever write $y'$, you are quite obviously using derivatives.