Fine by me, @Jasper. Moderators need to censor him for his insulting behavior toward me. Although he thinks I have harassed him, I've only corrected his math when he was wrong, and he cannot abide that.
If I leave in a fit of anger (and trust me, I'm furious now), I'm just rewarding him for his inappropriate behavior.
At any rate, I posted a correct answer for the OP.
LOL @Pedro: He now downvoted me. That's his mature reaction.
@TedShifrin Let's forget about this... so did you assign the problem to show $B(x,y)=\Gamma(x+y)/\Gamma(x)\Gamma(y)$ using polar coords? It is super nice. =D
No, it's way off from what is appropriate for these students/this class. I assigned the problem only for the grad student/Honors students, anyhow. Most of the class was lost today when I was doing high school algebra to compute basic stuff with expectation of a function of a random variable. Sigh. :(
Besides, @Kaj, if you had five prizes to try to get (randomly) from Burger King, wouldn't you be curious -- on average -- how many times you'd have to go eat there to get all five prizes? :D
Ah, he couldn't resist writing his own notes even for someone else's class :P
Yeah, we're going kind of slow @TedShifrin. It's a little frustrating when I can see roughly how to prove something once it's written on the board, and then we proceed to take up 15 minutes discussing it.
Consider the set of all irrational numbers in the interval [0, 1] with decimal expansions containing only 4's and 7's. Is this set closed? Perfect? Anywhere dense?
No, no, @Kaj .. As far as I know, he's teaching it. I just meant I don't know if he'll do the particular discussion (or assign the exercise) I have in mind relative to the Cantor set.
@TedShifrin, sent. I left out all the extra and just kept the one sentence that was giving problems. My preamble is probably embarrassingly error-full.
Can someone point me in the right direction? I need to prove that all functions with domain $\mathbb{R}$ can be written as a sum of an even function and an odd function, and that this summation is unique.
Hey guys, does anybody here know how to calculate a trend line for a scatter plot, given n points? I'm trying to find the equation so that I can do it programatically, but I've only been able to find resources that indicate drawing said trend line by hand, with guesses
@Ted Let $k$ be a CRing. Given a set of polynomials $P_\alpha$ in the coefficients of $n \times n$ matrices $M_n(k)$ write $G(k')$ to be the set cut out of $GL_n(k')$ by $P_\alpha$ for any associative unital $k$-algebra $k'$. He says $G(k)$ is an 'algebraic group' if $G(k')$ is a subgroup of $GL_n(k')$ for all $k'$.
Anyway, then he defines the Lie algebra of an algebraic group to be: $X \in \mathfrak g$ iff $1 + \varepsilon X \in G(k[\varepsilon])$, where $k[\varepsilon]$ is $k$ adjoined with an $\varepsilon^2=0$.
To prove that this is indeed a Lie algebra, he first has to show it's a vector space; in the process he says that $P_\alpha(1+\varepsilon X) = P_\alpha(1) + dP_\alpha(X) \varepsilon$. In context the only way one could possibly interpret $dP_\alpha$ is as the total derivative of $P_\alpha$. But I don't see how the claimed equation is actually true unless 1 is the all-1s matrix, and that doesn't make a bit of sense!
It only makes sense for it to be the identity for the analogy with the Lie groups situation.
"total derivative" is the wrong word... I mean $\partial/\partial x_1 + \dots + \partial/\partial x_n$
It was René going off on me, telling me he'd told me not to comment on him, and telling me to "go back to stalking little boys." Incompetent homophobe that he is.
Hey guys. I don't suppose any of you know of resources that would be helpful in understanding Linear Regression Modelling, maybe made for someone who's highest mathematics education was Year 12 some 6 years ago?
Yes, that's true, @PedroTamaroff, but I was suggesting a way to prove that. If a (suitably smooth) curve is contractible in some open subset $U \subset \Bbb C$, then the integral of a holomorphic function (in that open subset) along that curve is 0. $U = \Bbb C \setminus \{0\}$.
@PedroTamaroff The point of what I was saying is to show that the integral along your curve is equal to the one along $S^1$. But I guess you're taking this as fact.
Question: I am not getting the correct answer. How do I get the solution (and why does my solution not work?)
Find volume that lies inside both spheres:
\begin{align}
A: 4 &= (x+2)^2 + (y-1)^2 + (z+2)^2\\
B: 4 &= x^2 + y^2 + z^2\\
\end{align}
My solution gives the answer $V \approx 11$, where...
It was René going off on me, telling me he'd told me not to comment on him, and telling me to "go back to stalking little boys." Incompetent homophobe that he is.
i mean, i can understand some level of frustration. putting out a good answer does take some amount of effort, and if that doesn't get recognized it's annouying.
Not that anyone asked me, but I find the progression week-month-year to be irregularly spaced. The ratios between consecutive periods are 1:4 and 1:12.
Thanks, @Alex. He just cannot be so hateful, for starters, and to think I should be banned from correcting his perfect mathematics ... Sigh. Hell, people catch me in mistakes and I say, "Oops. So sorry. Thank you. I'll fix it." Wth ...
Oh yeah. Presumably related to why he couldn't keep a job. @Alex But he may hate me. It doesn't matter. He can't be around here and act abusively or god-like.
@BalarkaSen embarassing confession: I read that as "much heathier," like a Health bar, for the entire time he had that. I only figured it out after he changed it. I am an idiot.
I think he's unstable and depressed, @skull. But he can't go off on me in public when I say politely that there is some confusion .... In the field of my expertise! And slandering me on top of it?
@IceBoy Yeah. first time, maybe you got heated and stepped over the line- i get it. 1 week to cool, fair enough. Second time, you've showed the first time wasn't an accident, but we're not ready to say you don't deserve to be here at all. Third time, you're a menace with no intent to change.
Then there is $\delta >0$ and $c>0$ such that $|f(x+h)-f(x)|\geqslant c|h|$ for every $x\in K$ and $|h|<\delta$, provided $Df(x)$ is injective at points of the compact set $K$.
English Language & Usage: Multi-Layer…
English Language & Usage: Multi-Layer…
Question: I am not getting the correct answer. How do I get the solution (and why does my solution not work?)
Find volume that lies inside both spheres:
\begin{align}
A: 4 &= (x+2)^2 + (y-1)^2 + (z+2)^2\\
B: 4 &= x^2 + y^2 + z^2\\
\end{align}
My solution gives the answer $V \approx 11$, where...
