# Theta30

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bio website location Canada age 37 member for 2 years, 10 months seen 10 hours ago profile views 159

# 52 Comments

 1d comment How to integrate $\int{ dx \over \sqrt{1 + x^2}}$ Regarding what @Michael Hardy said, these standard substitutions are usually listed in mainstream Calculus textbooks, usually in a conclusive chapter about integrals. Dec16 comment If $a$ is a member of a finite group, and $e$ is the identity, how can I prove that $a^n=e$ for some $n$? N is not group. Dec15 comment What is $(-1)^{\frac{2}{3}}$? thank you, it makes sense Dec15 comment A possible theorem @Did why do you take him the pleasure to know (s)he discovered a new theorem :P Dec15 comment What is $(-1)^{\frac{2}{3}}$? about 8) we can see it as a function with the codomain C^3, no? Sep2 comment Find $f_{X|Y}(x|y)$ given $f_{Y|X}(y|x) = I_{x,x+1}(y)$ and $f_{X}(x) = I_{0,1}(x)$. To be honest, I calculated $f(y_0)$ and $f(x|y_0)$ through integrals, and then I noticed it is uniform. I think we might have the following result: if $X$ is uniform, then for any other random variable $Y$, $X|y_0$ is uniform. Sep2 comment Cumulative distribution function, integration problem in the continuous case we take integrals. So in this case we have integral over the whole domain. Can we call it "whole integral" ?! Sep2 comment Cumulative distribution function, integration problem Right. In general, if g(x)=0 outside of [a,b] and nonzero inside [a,b], then cdf of g is 0 when x=b. In the latter case, yes, it is indeed as you say, the "whole sum" (more properly for discrete case). Sep2 comment Proof of Toeplitz's theorem. I did not find any error, just a small thing, in the last inequality, you assume $t_{k,n}$ are positive, which is not given. But adding absolute values does not change the rest. Sep2 comment $x_1=0,\,x_{2n}=\frac{x_{2n-1}}{2},\,x_{2n+1}=x_{2n}+\frac{1}{2}$ Find $\lim \sup {x_n}$ and $\lim \inf {x_n}$ I don't see how this helps-it's basically the same thing as the original question Sep2 comment Find the limit of $\lim_{n \to \infty}\frac{(-1)^{n^2}}{3} + 2 - \frac{1}{(-e)^n}$ though in a more advanced level, the possible limits of subsequences can be called limit points Sep2 comment Find the limit of $\lim_{n \to \infty}\frac{(-1)^{n^2}}{3} + 2 - \frac{1}{(-e)^n}$ the limit, if exists, is always unique. So you cannot say limit1 and limit2. What you can have however are limits of subsequences. If two subsequences of the initial sequence converge to different limits, then the limit does not exist. Sep2 comment Find the limit of $\lim_{n \to \infty}\frac{(-1)^{n^2}}{3} + 2 - \frac{1}{(-e)^n}$ Can you please explain what you mean by $\infty \lor 0 \lor -1$ ? Sep2 comment Find the limit of $\lim_{n \to \infty}\frac{(-1)^{n^2}}{3} + 2 - \frac{1}{(-e)^n}$ Do you like lemons or limes? Sep2 comment trigonometry and integral properties You actually lack the question. What you show is an equality. I reckon the exercise is "Show/prove that ..." May28 comment Sigma algebra generated by a set @UnadulteratedImagination No, you can have any number of atoms. Mar17 comment Show: grad f (x + y) = grad f (x) + grad f (y) saying x,y are in $R^2$ already implies x,y (hence x+y) are in the domain of $f$ and $g$. Mar14 comment Determining the dimensions of the null space and column space of a matrix "use this to find rank A" can it get more simpler than that? Mar3 comment Closed under equality this is known as the identity of indiscernibles Mar2 comment Are all integers fractions? @Carl Mummert . In my comment to an answer I ended up with "It is equal because there is a mathematical convention that makes it equal.", which I think it is incorrect in light of your answer. So they are not equal as mathematical entities. Are we left to say they are equal as a language convention? That is when we say Z is a subset of Q or z=z/1 for z integer, we make a language convention (shortcut, compromise)? Thanks