@Hippalectryon here you might find more info on chocolate that you don't know yet. There are serious studies behind them. perfecthealthdiet.com/2012/11/…
I'm wondering, I've shown that if $G$ is simple, of order 60, than it is isomorphic to $A_5$. As hinted, I have shown it by considering the sylow-2 subgroups, and 'easily' proven they must be either 5 or 15. One way or another, I've shown a subgroup of index 5, homomorphism to $S_5$ and completed. It made me wonder how many sylow-2 subgroup actually are.
So I checked in $A_5$, it's easy to see there are 5.
I wonder why in proving the isomorphism, I could've went along with 15 sylow-2 subgroups too - why does it work that the isomorphism exists even in a case which, apperently, doesn't exist?
@UserX For instance, look at that - ncbi.nlm.nih.gov/pubmed/21875885?dopt=AbstractPlus "The highest levels of chocolate consumption were associated with a 37% reduction in cardiovascular disease (relative risk 0.63 (95% confidence interval 0.44 to 0.90)) and a 29% reduction in stroke compared with the lowest levels."
I bet that's why people hate science. "Wrong! Muh sources". @skullpatrol nah. It was another article. But that other article had the original one as a source. So a=b=a
Can all the references construct a permutation group?
16 sources. Say $n$ of them with $n\leq 16$ do "symmetric reference". Then the group $G$ of the sources is isomorphic to $D_{n}$ which is isomorphic to $S_{n}$
That must be the most meaningless usage of group theory ever.
@UserX: I wrote an answer to that DE question (more or less what another guy posted after he removed his wrong answer). ... Oh, and I heard back from Mike Spivak. Did you tell me that your version of his book was an e-book or hardback?
@Mike: Did you stun your students with a great recitation? :P
oh, @Pedro ... You need to learn cross ratio and some projective geometry. I sent you that stuff ages ago :P
This question has three close votes, all for different reasons. We should get someone to close as a duplicate and someone to close as primarily opinion based.
I don't agree that that one's an obvious dupe... it doesn't make any mention of coefficients. A standard reading would be "why does the quadratic equation work for all polys with real coeffs?"
@Pedro: Here's a warm-up exercise for you (regarding your circle one). Find a conformal mapping fixing the standard unit circle (as a set, of course), fixing $1$, and sending the origin to infinity. Now can we do it sending the origin to $2i$? to $3i/2$?
I don't think those papers ever said they could do Stiefel-Whitney. I think they were talking about Chern mod 2, but maybe I didn't look carefully enough, @Mike.
@TedShifrin I already said that the automorphism $$\frac{z-\alpha}{1-\bar \alpha z}$$ preserves $|z|=1$ and fixes the two roots of $\alpha/\bar \alpha$.
I have been using it for ages, @Mike, but (a) it doesn't do chat, (b) I was a beta-tester and could no longer get their latest versions after I updated my OS (and Safari is still a total disaster).
I had to load a dummy page with the link on it somehow, @Mike. If you want, I can try to recapture how. I told robjohn in here over a year ago how I did it. Perhaps he saved what I said.
