His proof is to show that a subgroup of index $i$ in $A_5$ embeds into $S_i$... Then, show that when $H=\langle(123), (12345) \rangle$, you actually have $H=A_5$.
Let $X$ be a compact topological space, and let $\{C_{i}\}_{i\in\mathbb{Z}_{+}}$ be a collection of nonempty closed sets in $X$ satisfying $C_{i+1}\subset C_{i}$ for each $i\in\mathbb{Z}_{+}$. Prove that $\bigcap_{i=1}^{\infty}C_{i}\neq\emptyset$.
Do I really need to use the fact that the sets $C_{i}$ are closed?
I want to argue by contradiction, but it seems a little too easy.
@KannappanSampath Yes, sure. I will be there for a few months, my availability is not a big constraint. We can agree on any evening and we could meet. Perhaps next week (allowing myself a little time to settle down).
Wikipedia: "The problem of their multiplicity [eigenvalues of the DFT matrix] was solved by McClellan and Parks (1972), although it was later shown to have been equivalent to a problem solved by Gauss. Naturally.
@KannappanSampath Well well. I'm quite sure he'll just twist her neck once he disappears out of sight (around the next corner). That's what people are like.
But she might have died anyway...
@Ilya : )
And I'll explore some maths now : ) See you later.
@KannappanSampath not until I finish what needs to be finished
@Ilya That's right, I remember you made a comment about being across the Pacific. I asked where you were, but I never saw a reply. It doesn't mean you didn't reply. :-)
@KannappanSampath I've long settled on the belief that most people vote things for giggles, not necessarily because they read and understood the answer...
I rarely upvote going by someone's name. For instance, I know that a post certainly deserves more credit; then I upvote that post if it comes from an user I know. Or if someone whose compliments matter says, that is a nice answer , then...
@AmithKK: Let's make the number you seek into a variable, say x. Now what is the statement "in x years the age of the son will be half the age of the man" in an equation?
A man completed a trip of 136km's in 8 hours.Some parts f the trip was covered at 15km/hr and the remaining at 18km/hr.Find the part of the trip that was covered at 18km/h
@JM (On a serious note:) I guess that the OP is confused because she/he thinks that the two definitions are different "forms" of the same object, while in fact they are altogether different. The terminology does not help the matter either (normalised form vs. unnormalised form).
@Srivatsan Reminds me of the time I was ragging at this guy for not saying at once that he was using degrees instead of radians in his trigonometric functions...
@JM I mean... first and second course in probability is a triviality. You are looking at simple stuff. No measure theory. Nothing difficult to bang your head...
(Optionally, one does cover Markov chains, and some instructors choose to cover Poisson processes and Brownian motion. I agree these are non-trivial in some sense.)
We are being taught Markov and poisson and hinted that Brownian exists.
@Srivatsan Another thing you might like: I asked several math related TeX questions of TeX. SX. You might like some of them too.
@ymar Your question is very clear. I have not ruled out all of those examples as yet. I am a lazy fellow trying to figure out more and more about Jordan blocks and less and less about those fields. : (
