What are some of the most inconsistent uses of notations and words in maths?
For instance, a function $f$:
$f^{-1}(x)$ can be an inverse and a preimage and sometimes even $\frac{1}{f(x)}$. $f^2(x)$ can be $(f\circ f)(x)$ and $(f(x))^2$. $f^{(2)}(x)$ on the other hand, is the second derivativ...
I don't know about "abused", but the inconsistency that bothers me the most is sin^2 x versus sin^{-1} x.
First since I studied quantum mechanics I want sin^2 x to mean sin( sin (x) ), but even allowing that it is going to mean (sin x)^2 why the $#(& does sin^{-1} x stand in for arcsin instead of 1/(sin x)?
@dmckee Well, actually, that is consistent notation, since the preimage of a function $f$ is usually denoted $f^{-1}$, and $\mathrm{arcsin}$ is nothing else that the preimage of the sine restricted to a representant of the preimage in $[0,2\pi) - \{\pi\}$ or $(-\pi,\pi)$.
That some of these group/ring/field theorists like to denote the inverse of $x$ by $x^{-1}$ is an unfortunate accident :P
@New_new_newbie it never really hurts to flag if you're not sure, but personally I consider it an answer, just not a good one. After all, the question is "What's the difference between frequency domain and time domain spectra?" and it's hard to argue that "There are no differences" doesn't answer that question.
On another note: if the person who flagged a bunch of comments using the custom message "Just noise" happens to check in here, we have standard flag reasons including "obsolete" and "too chatty" that work for most of those kinds of comments. It's not a big deal, but it's nice to use the standard reasons when you can.
@ACuriousMind @KyleKanos @dmckee Richard Feynman in his autobiography, Surely You're Joking, Mr. Feynman mentions he also disagreed with the notation, and that it seemed inconsistent to him. In high school, he had his own notation, which was rather bizarre. If I remember correctly, he used some sort of uppercase sigma, elongated.
@JamalS I have seen some books use $\sin\,x$ for the sine function, which I think can be vague if you have multiple components (i.e., does $\sin\,xt$ mean $\sin(xt)$ or does it mean $\sin(x)\cdot t$?)
But creating your own new notation? Seems a bit extreme
Which, I suppose is classic Feynman
The actual quote, is: While I was doing all this trigonometry, I didn't like the symbols for sine, cosine, tangent, and so on. To me, "sin f" looked like s times i times n times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath.
please exercise better discretion in word choice. You may not mean in offensively, but terms with a strong history of abuse and offense should be avoided on SE, including chat
@Danu Haha...yes, it's on my continually expanding list of things to watch. When it comes to series, I always lag a few years behind pop culture, dunno why, exactly
Once you run out of close votes for the day you have to skip a lot of the other review items. It seems like a somewhat broken system to present items for review when not all of the possible responses are available.
http://stackoverflow.com/review-beta/low-quality-posts/ shows low quality questions and answers.
When out of close votes I'm not sure what to do with the questions. I can still handle the answers fine as there are no limits on the actions to I can take.
But for questions one of the actions (clo...
At least on Physics.SE "Skip" is a poor option for some of the queues. Almost no one looks at the "First Posts" queue and that's one of the main ways we get new homework questions into the close votes queue. I still try to edit / comment / downvote but I really don't like saying "I'm Done" when I know the question should be closed but I can't do anything to get it into the queue.
It would be nice if when you ran out of close votes you could instead flag for closure.
@KyleKanos So is @New_new_newbie lately but we still don't have anywhere near a critical mass of people doing the immediate cleanup work needed. When we have crap on the front page it just attracts more crap.
@Danu It wouldn't surprise me if most of the people in this chat are much more active reviewers than the average user on the site. Many of our quality issues on the site stem from our very low review participation and our very high influx of new users.
I thought Physics.SE was unique in this low review participation but I just looked at Math.SE and I think it's even worse there. They get a lot more questions than we do and it looks like many of their users stop reviewing when they get the gold badge for reviews.
All of their active reviewers are have run out of close votes for the day and there are quite a few questions still in the close queue for the day.
@Danu Perhaps. I'm not active in any other SEs so I have nothing to compare to. I don't think we have serious quality issues or anything like that. I just don't like that I have to either stop contributing or can't contribute at the level I think is needed simply because of close votes.
I don't know, I don't like the approach my algebra prof takes to geometry (he always talks about the stuff he did last semester and how it is related to what we do now, but I took that course the year before, and we were far more into general nonsense than he is)
String theory is surprisingly mundane, just quantizing this and calculating that (probably because the lecturer assumes basically no previous knowledge)
And well, the other stuff is similar - I just keep hearing what I already (partially) know, or I find it not all that interesting
And I really miss my lecturers from the last semester. Well, it can't always be that brilliant, I guess
At least I'm not the one working 60 hours a week :P
@ACuriousMind :) good, I just play random these days, 2v2s with friends...just solely for the fun of it, so don't worry we'll mostly be trolling and having fun with ladder games^^
@ACuriousMind have you played since the patch they added the mothership core?
@ACuriousMind shifted all the opening builds of toss, now they all double gas at 15, and start pressuring with well timed 2-stalker+core, basically every game, it is a very nice opener.
@Danu rough calculation? i've never had luck bringing scotch into the picture, although i had an advisor who swore by the "beer" method for getting a paper written
