@AsafKaragila Looks like it was burninated (as Jeff would put it). I'm pretty sure that this question was tagged this way and the revision history doesn't show any edit removing the tag.
@JonasTeuwen just surprised by a situation: usually two questions either very close but appear almost in the same time, or the latter one mentions the first one and adds something more )
@Jonas: how are you? how is the 1st day of the defended PhD student? and thanks for upvoting btw
@Srivatsan I don't know if this still exists in Lion, but I'd assume so. For a long time there's been shift-command-4 which gives you a cross-hair with which you can select the region you want to take a shot of.
On the other hand, the preview reveals that the closing parenthesis is more or less tangent to the right hand border of the display, so I'd probably just leave it.
@JM "where the ratio is rounded up for even n and rounded down for odd n. For n ≥ 1, this gives the nearest integer." - nonstandard notation and the OP somehow picked only the math leaving the explanation
Er, =/. Another blunder @JM. I rolled back to revision 3 without realising your edit
@JM I still don't get it: say that !n is an integer and you know that !n > n!/e and the error is smaller than an integer. So ceil should do the job, no?
@robjohn [adding to robjohn's comment] In fact, since 1/e = 1/0! - 1/1! + ... is an alternating series, the partial sums alternate above and below 1/e.
@JM I was exaggerating a bit, but yes, it does come up everywhere. =)
@tb I thinking of a compelling case for sec. The main thing I can think of is that sec^2 is the derivative of tan. But you could of course, remember it as 1/cos^2...
Well, as I said, secant is pretty intertwined with the Mercator projection. Otherwise, I don't know any other reason to consider sec except convenience...
@Srivatsan That's what I always do. In fact, I was thinking about asking a question on the main site: "why do people here like to use sec/csc?" (I decided against it for being subj/arg. They seem like they only produce an overflow of trig identities for nothing. If I remember correctly dropping the other functions was a decision taken by the pedagogues sometime back in the early 20th century in Switzerland.
@JM And, another question: why place sine ahead of cosine? For some reason, I like cosine better. // It's reciprocal is this other nice function called "sec" =)
@robjohn The SE modifications script does that (so you can just right click on the time stamp and and copy the link). Jack said some time ago that it is easy to make a bookmarklet out of the relevant part.
Speaking of which: I'd estimate that about half the time the arctangent is being used, it'd be more appropriate to recast in terms of the two-argument form...
@JM I also like cos for another reason. It's usually nicer to keep the denominator clean and push the mess to the numerator. So, I like to think of tan as sqrt(1-cos^2)/cos, rather than as sin/sqrt(1-sin^2).
@JM I did not like real-analysis as the only tag here: math.stackexchange.com/posts/35625/revisions So I retagged - and I did not notice that I included (integral) tag, which Henning delete just a few minutes before.
That's a good but separate question. I think at least half of the (differential) questions are just there because someone typed "differential calculus" into the tag field. Very few of them are about actual differentials.
But I would be very happy if at the bottom of the (differential) pile I find that it all started with a question that subsequently migrated to mechanical-engineering.SE.
"Please frame your answer not in a high-technical manner, but in the way a beginner can understand, but please answer me in a detailed manner. " - sorta kinda oxymoronic, no?
@JM Yes, exactly. The "please tell me exactly what the the author of this-and-this particular enigmatic remark intended" theme is bad enough in itself, but this...
No problem, and the argument afterwards is very easy to follow even if it looks scary... But the prize of the scariest formulas of the week go to the other answer here (the Dirichlet thing)
What does it take to think like a pure mathematician?
My queation is what is the major difference between the way a pure mathematician thinks and the rest of us and what brought about that difference? Thank you.
@ZhenLin As Jonas put it the infinity case is the key mnemonic: (power) summable sequences must tend to zero, so must be bounded, so the little l^p spaces grow with p. The finite measure case was mentioned by him.
@Skullpatrol Not really. Think of this as the break room of MSE. Your conversation starters put me in mind of someone who walks in from the street and starts asking everybody present whether they shouldn't rather be out on the floor stocking shelves.
