@QED 0 having no reciprocal is the short and overly laconic answer to this entire question about division by 0, so what better way to end the endless "why, why, why... " than to prove 0a = 0? Professor
When we first got there, they said that the spine had probably been crushed (assuming it was hit by a car) so we should just euthanize it. But I said that we didn't bring it in just to be put down, so we insisted on x-rays.
Apparently the spine was fine, but one side of the pelvis was broken. However, cats heal bone injuries well, so the prognosis is good.
She is trying to climb everywhere despite our best efforts to keep her quiet.
You're nice! Good job. Sad thing about the story is: it proves that people are incompetent and unless you do all the thinking yourself, jobs don't get done properly : (
Well, I went ahead with my threat to find a question of my own to ask, after our lament about the poor quality of recent questions. It remains to be seen whether this is an improvement. :)
but there might be another way to prove it, encoding lists into numbers.. or something. I could be barking up the wrong tree with thinking about "strong induction"
@Srivatsan That is a possibility. :) And maybe I should have asked it there; however, like I said, it was partly in response to me saying that I would look for questions of my own to ask here.
@MikeSpivey Well, I am ok with the question staying here/going to stats. I pointed it out because I knew you wanted to ask a question in Math.SE after the recent spike in low-quality posts.
@Srivatsan Part of my problem with asking questions on math.SE is that many of the questions I'm interested in would probably get better answers on MO.
Another part of my problem is that for some of my interest areas, like optimization and linear programming, I am by far the most active user on math.SE in that area. There wouldn't be much point in me asking questions about those topics here. Those should get asked at MO or CS Theory.
@Srivatsan I did ask one of those about a year ago and got some good responses. I've been hesitant to ask those, though, because the community hasn't always supported them.
Hindu dude... I was waiting for the day when Asaf would throw some abuses in my direction. Without it, somehow I don't feel I like I belong in this chatroom.
I am slightly irritated that he didn't read my question carefully enough to notice that one of his examples was already in the question. But the new example was good enough that overall I gave him +1.
@Srivatsan Yes, it is, which is why it's so hard to spot. The gender bias example is great. Berkeley was sued in the 1970s because women were being admitted to graduate school at a lower rate than men. The university successfully defended itself by pointing out that when you broke the data down by department, women were being admitted at the same or higher rates than men. The underlying and not immediately apparent explanation was that women tended to apply to more competitive departments.
So the women's overall rate was more heavily weighted by the more competitive departments, and the men's overall rate was more heavily weighted by the less competitive departments. This caused the men's overall acceptance rate to be higher, despite being generally lower at the department level.
@Srivatsan Maybe I should cut him some slack, then. But my comment still stands: He did repeat one of the examples in my question.
A possible counterargument could be that Berkeley was implicitly discriminating by making fewer openings (what's the correct word here?) available in subjects that women want to study, thereby causing them to be more competitive.
@MikeSpivey There are 5 left now, to be done tomorrow. Two of the latest batch actually had something to do with differentials; that's a first,
@HenningMakholm I think the problem was that the departments that women tended to apply to just had a lot more applicants, like humanities programs, so their acceptance rates were lower. It wasn't that there were fewer openings - well, there were fewer relative openings, but that isn't quite the same thing.
@robjohn And your question got some good responses, too, if I do say so myself. :)
@robjohn I said I was only slightly irritated. :) But I accept yours and Srivatsan's reprimands (?) and will cut Mr. Hardy some slack there. Besides, he did give me one new good example I was unaware of, which is what I was after by asking the question.
@MikeSpivey It's not by any means a decisive argument (and I don't personally think it ought to carry the day), but one might still argue that if the university is supposed to size its departments according to student demand, then the disparity indicates that it must have been more responsive to demand in areas favored by men than in areas favored by women. The premise that I've emphasized here is perhaps not easily established, but that can conceivably be hidden away by clever rhetorics.
@MikeSpivey I am not reprimanding, nor do I say that you shouldn't be irritated at all. Mike Hardy is too close to my reputation not to be knocked down a peg ;-)
@JM Thanks for that. Hopefully the question won't get migrated. Simpson's paradox is interesting mathematically, and maybe others here will learn something simply by reading the question.
@JM Murphy's law as applied to non-mathematical induction: If you generalize anything from a small set of examples, the first case you haven't checked before publishing your conjecture will turn out to be a counterexample.
