@robjohn that integral I showed you yesterday is finally a simple application of beta function integral. I'll show you my proof as soon as I put things on latex.
@robjohn All gets reduced to the simple fact that our integral equals $$\int_0^{\pi/2} \log(2\sin^2(x)) \log(2\cos^2(x)) \ dx$$ Then, expanding this, we're almost done.
I want to find a maximal set $A \subseteq \mathbb{N}$ such that $$\forall x,y \in A: x+y \notin A.$$ I'm currently thinking about $$\mathbb{P} \cup \{1\} \setminus \{2\}.$$ Is this set maximal? If so, is it the unique solution?
@IceBoy This site needs more users like you. Lots of users here are like as straight as a ramrod. I don't know that is the correct way to describe it in English
Hello. With the help of math.se user Leo for the first draft I concocted a question that's stored here: http://meta.math.stackexchange.com/a/4668/140933 I'd like to know if there's redundant info and if it's understandable to people with no roleplaying games knowledge. Thank you.
“We start off with high hopes, then we bottle it. We realise that we’re all going to die, without really finding out the big answers. We develop all those long-winded ideas which just interpret the reality of our lives in different ways, without really extending our body of worthwhile knowledge, about the big things, the real things. Basically, we live a short disappointing life; and then we die. We fill up our lives with shite, things like careers and relationships to delude ourselves that it isn’t all totally pointless.”
I've just remembered this great quote while reading some about Trainspotting 2.
@Khallil: I'm not underestimating myself. I'm just putting @Balarka closer to $\infty$
@Khallil: You've probably heard this question before but if you haven't: How can you distribute 9 pigs into 4 pens so that there are an odd number of pigs in each pen?
@Khallil: The best answer with 101 upvotes is "This question is silly. You can't fit nine pigs into a pen. Only ink goes in pens. You have to liquidize the pigs into pig ink, and then you can divide the pig ink equally into four portions."
What do I think of them? As you said, the traffic is quite low, but it seems like a good place to talk.
I know of another forum which I was a member of, where the traffic was quite high, but the majority of users just wanted help with exam questions and homework questions, @BalarkaSen. So I guess that's the trade-off.
I want to provide an optional course for pupils at my high school in mathematics. I only get 2 lessons (45 minutes each) per week and it should be something I can cover within half a year. The pupils just started learning some vector geometry and differentiation, no integration yet. Does anyone have some nice ideas?
@Alizter: I need to find something nice in those areas. Geometry is a very broad subject. It needs to blow their minds and still have some kind of application, in my opinion.
Yep, it's just been something that I've been thinking about for a while. I was in a similar position a short while ago. Classes begin in just over a week and I'll be getting there in just under a week. ^_^
POWER METHOD
Let $x_0$ be an initial approximation to the eigenvector.
For $k=1,2,3,\ldots$ do
Compute $x_k=Ax_{k-1}$,
Normalize $x_k=x_k/\|x_k\|_\infty$.
Then $\|x_k\|_\infty$ approaches the dominant eigenvalue and $x_k$ approaches the corresponding eigenvector of the matrix $A$.
My que...
POWER METHOD
Let $x_0$ be an initial approximation to the eigenvector.
For $k=1,2,3,\ldots$ do
Compute $x_k=Ax_{k-1}$,
Normalize $x_k=x_k/\|x_k\|_\infty$.
Then $\|x_k\|_\infty$ approaches the dominant eigenvalue and $x_k$ approaches the corresponding eigenvector of the matrix $A$.
My que...
