To make the above a bit more readable, it's this question: How can I get $\sum_{k=0}^n\binom{n}{k}(pe^t)^kq^{n-k}=(pe^t+q)^n$?. And the quote is: "How can I get $$\sum_{k=0}^n\binom{n}{k}(pe^t)^kq^{n-k}=(pe^t+q)^n \text{ ?}$$ I'm having a real problem, trying to figure out this equation. Can you, help me with that ?"
@MichaelHardy Ok, I voted to undelete. Maybe it will not hurt if we let a bit more time to the OP. (After all, they can edit the question and get it reopened.) I am not sure whether this is what you wanted to achieve...
@MichaelHardy my problem with that argument is this: the OP uses binomial coefficients. How does the OP define a binomial coefficient? I was first taught they followed from the binomial theorem, contrary to your claim of a lack of knowledge of the binomial theorem
@MartinSleziak thanks
Er, yeah, I guess I'm not supposed to say thanks to things like that
If you had never seen the binomial theorem, then where would you have even begin to consider anything involving binomial coefficients?! — Simply Beautiful Art1 min ago
I do not believe in such extreme coincidences either: consider the likelihood one managed to scramble together an almost exact copy of the binomial theorem without knowledge of It? — Simply Beautiful Art9 secs ago
@MartinSleziak : There are various different ways to introduce binomial coefficients without ever mentioning the binomial theorem. For example, the number of size-k subsets of a size-n set. Since "binomial coefficient" is a standard name for those, a person may hear that name without knowing the binomial theorem.
@MichaelHardy it still does not explain the second comment which I've linked here
@MichaelHardy as I mention on the linked question, it is more so likely that one would learn of the binomial theorem before such combinatorial definitions.
Well, I am not sure whether it is really relevant to this discussion, but I'll mention that in an introductory combinatorics course that I taught we were dealing with binomial coefficients long before binomial theorem. I'm a bit too tired now (it's quite late here) to search now for the syllabus on grammar schools to see what order is supposed to be there.
@MartinSleziak ah, okay. I don't know how most combinatorics courses are taught, but I would've thought that such a progression would be logical, and it was the way I was personally taught
Also, whoever starred my comments in here should do so on the main site
@SimplyBeautifulArt : I disagree about "much more likely". It's done both ways. And there is more than one good reason for doing the combinatorics first. One such reason is that you can then do a combinatorial proof of the binomial theorem.
@MichaelHardy I understand that you may not agree with me on this (and that people over here do not always agree as well on other posts), but here is my reasoning regarding this specific post. The idea of asking for context (no matter how brief) is that questions do not arise in a vacuum. Either they come from a book (then state the book) or course material (then say so) or homework (then you agree it's off-topic) or something they read (then say where) or personal exploration (then give motivation)
2
, and in my honest opinion a question that comes as a totally bald question should be removed from this site, as it encourages people to have a sense of entitlement to be answered on Math SE even without personal effort put in. I have also read a number of Meta posts including yours, where you can see clearly the striking difference between your own questions (of which many of them are out of curiosity) and the kind of questions like the one we are now discussing.
@Jack: Anyway from the revision history I see that you chose to undelete. What was your reason?
@user21820 I can't speak for Jack, but I've decided to vote to undelete so that the OP has a chance to react to the comments. (From their profile it seems that they were not on the site since the question was closed.) Seeing that there already are two delete votes, maybe the OP will no have the chance.
I lean towards deleting, so if Jack does not explain his undeletion soon I'll just delete. Notice from the history of the question that it was originally the worst kind of PSQ possible; a picture of the equation and just 1 line "I'm having a real problem trying to figure out this equation. Can you help me with that ?".
BTW if we see that the OP has abandoned the question, then maybe the users who want the question to remain on the site can try to improve it. Quote from the above link: "A question can be justified by the fact that a good answer can be written." But it is probably too soon to consider the question already abandoned.
@MartinSleziak I saw that comment but strongly disagree with it, since as I've stated before I strongly disapprove of encouraging cheating of any sort.
My main point is that if the OP abandoned some question and if the answers are useful, then the question can be improved by others to meet the standards. (Or simply an analogous question with better quality can be posted by more experienced users.) I think this was done a few times in the past.
The quote was included mainly to show that there is at least one user who wants the post to stay on the site and who considers the answers posted there to be useful.
I know that, but I do not agree with it no matter how many times it was done in the past. Just as I don't agree with cheating even if the whole school does it.
My comment is just to show why I disagree with the justification you quoted from that (at least one) user.
As for specific reasons for that instance, it's as I stated above to Michael.
@user21820 Well, than we disagree on this (general) issue, it seems. (I'm not talking about this specific instance now.)
In the past I have tried to improve some questions in order to get them reopened (and to save the answers which seem useful).
I believe Jyrki Lahtonen mentioned something like this (editing posts by other users) in a few posts on meta, I was able to find quickly this one, but I believe he also mentioned it in some other answer.
I have also made several questions mainly with the intention: "this might be useful to have on the site". And perhaps one or two questions where I basically asked the same thing which was previously closed or deleted but they seemed interesting to me - here is one which I remember.
@user21820 Ok, so maybe our disagreement on this is not that big as I thought :-)
I leave questions alone when at least one answer gives some insightful point.
@MartinSleziak Yea. It may sometimes seem so mainly because we don't discuss at length issues on which we agree; we often discuss those on which we disagree. =)
@MartinSleziak By the way, I totally support your method of saving good answers by just reposting them under a proper question.
And here is another example where the main reason for the repost was continuous deleting and undeleting - so I tried whether a post from a user with more reputation and with addition a bit more context has a better chance of surviving.
@MartinSleziak Indeed your re-post was well received, and I think it's best that way. It also shows that good quality answers are not a good enough reason to not close or delete, since their authors can easily move their answers to the better question.
@amWhy Yes, it is always "very nice" to see that someone decides voluntarily to discuss your actions behind your back. The input I would have given, if I had had the chance and if I had decided to give some, is aptly expressed in "And I, for one" Simply's comment on main and in your pair of comments on Will's answer.
@amWhy For the record, the reason I decided to post my comment, is not for MH's sake or for the sake of experienced users, who are (or at least should be) able to discern the dishonesty underlying the wordplay on "off topic" which is at play here, but for the sake of newcomers who might be abused by this rhetoric.
@MartinSleziak I think this may be a questionable practice; at least in some cases. I'd like to know what your criteria is for a post with "if the answers are useful, then the question can be improved by others to meet the standards."
user12692
@user21820 Quite a few messages to real. While I agree that the post has very poor quality (I was the first to vote to close it), I thought it OK to leave the post [on hold] for a while. Now that it is deleted again, I don't have a strong opinion about removing it or not. Just FYI, there is another user who has pressed the undeleted button again.
@MartinSleziak 'BTW if we see that the OP has abandoned the question, then maybe the users who want the question to remain on the site can try to improve it. Quote from the above link: "A question can be justified by the fact that a good answer can be written." But it is probably too soon to consider the question already abandoned.' What criteria to use to define when a question is abandoned?
@MartinSleziak I'd also propose, when and only when a question is abandoned by the OP, if edited, the editor should leave a comment acknowledging there edit, with a link to the review history, because I've seen too many answerers, to problem-statements/unclear questions, modify a question to suit their own interpretation of the question.
Editing/improving questions by other users than the OP was discussed a few times. I have linked to few Jyrki's posts. Here is link to a conversation in this chat room: chat.stackexchange.com/rooms/2165/conversation/… I'm not sure whether we have to reiterate all those discussions again.
You must have encountered this topic a few times on meta - you've been here for quite a long time.
Or maybe I misunderstood what you have in mind @amWhy. Now I noticed that you replied with the message about questionable practice to my message where I mention question which I asked. (Not situation where I edited a post by another user.)
@MartinSleziak I am not, nor have I implied that no question ever should be edited by another. There is currently no consensus on what "a question abandoned by the OP" means. How do we operationalize "abandoned question?" And when a question is useful and worth keeping.
Is there a consensus about anything? And in fact, the question does not have to be abandoned. I cannot find examples right away, but I remember several times when I edited context into the question based on the OP's comments under the question.
@MartinSleziak I'm not talking about unanimity, but when folks want to make a statement to the effect that, when if ever a question is interesting, potentially useful, and in particular abandoned by the OP, then no holds barred.
If you want to see some cases where I tried to edit/improve a question (or ask for an advice how can I improve a question), you can find a few in this room.
@Jack Yes, I've voted to delete. The answers amount to an answer of one's interpretation of a question without enough information provided to warrant either interpretation.
Since @Jack often post here, I have added him to the room owners - so the he can pin, unpin, unstar messages, too.
If, for some reason, some of you think he shouldn't be among the owners you can simply remove his ownership.
@user21820 This one is deleted now - revisions/timeline. I haven't unstarred it - I'll leave it up to you. Maybe you want to keep the messages as a pointer to the problematic users. (Since you mentioned: "This user has a history of posting PSQs.")
I should be a more careful about grammar when talking here in chat. I mean "Jack posts" (not Jack post).
@amWhy I did not understood some of your messages, but it seems you asked me for a clear criterion what is abandoned post and what are useful answers (or useful questions). I do not have such a criterion, I think this is a judgement call.
After all it is the same with closing and deleting. Not everybody would agree with the closing/deletion of posts menioned here. If somebody doesn't agree, they can simply not vote to close/delete, or actively vote to reopen/undelete (or even post on meta or discuss the issue here).
I think it's basically the same with editing/improving posts. If I edit somebody's post, people who disagree with that can say so. And the fact that I mention such cases here in this room makes such actions easier to notice. (I have to admit this does not happen very frequently.)
If you prefer, we can discuss this elsewhere. (If you feel I've digressed too far from the purpose of the room.
Seeing that I wrote I did not understood rather than I did not understand cast doubts upon my language abilities mentioned in your previous message. :-) But let's hope I'll improve with practice.
@MartinSleziak You do very well. I understand your comments, answers, etc. far better than the majority of posts on MSE (or on Meta). Please note most immediate comment prior to this, was not in any way meant sarcastically.
(As you can see, even I mess up when commenting in my native tongue of English.)
I'd like to see this inequation proven wrong, but I can't find proof for it. Do you have an idea?
$n,b,a$ all are $> 0$
Is the statement true?
$$\lim_{n\to \infty}\int_X f_n(x)dx=\int_X\lim_{n\to \infty}f_n(x)dx$$
