Replace element recursive in list F#
F# insert/remove item from list
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$ What does the underscores in _servicename_ mean in AngularJS tests? Retrieve Preview Image URL of Salesforce Image Files Should I put a comma before the last item in a list? Should I put a comma before the last item in a list?     I would like crackers, cheese and some soda.   I would like crackers, cheese, and some soda. Is "a total of 10 payments" singular or plural? A total of 10 payments were made.   OR     A total of 10 payments was made.   Which is correct? Or can both be correct? I haven't seen this behavior out in the wild much, but it happened again recently and I was wondering if a flag could be automatically raised when this happens:   User posts answer Answer is down voted User deletes answer User posts exact same text as a new answer User effectively ditched down votes   Got down voted again? Wash, rinse and repeat. Profit (perhaps after modifying the post, which is what you should have done to begin with)    I feel that this should raise a duplicate content flag, with slightly stronger wording. Would this be possible to implement? Or, perhaps, don't let users post new answers if they have a deleted answer to a question. Rather, force them to edit and restore the deleted answer instead, unless locked by a moderator.  I do have a link, but I don't want a lot of people to descend on it and create an even bigger disruption. It happened exactly as I described. Summer in Saint Helena The Winter Bash site is located at http://winterba.sh/.  Only one problem:   . Saint Helena is in the Southern Hemisphere. It's Summer in Saint Helena.   So shouldn't it be the Summer Bash? Don't forget our Aussie/Kiwi/South African/Southern Brazilian/Argentine/Uruguayan/Zimbabwean/Swazi/Tokelauan/Tuvaluan/Pitcairn Islander/ friends! I am wondering how to show that $\mathbb{Z}[\sqrt {10}]$ is not a UFD.    My only idea is to show that there are two factorizations of $10$, say, $ab, uv$ such that $a$ is not a unit times $u$ or $v$. In this ring $10=2\cdot5=\sqrt {10}\cdot \sqrt {10}$, so it suffices to show $2$ is not a unit times $\sqrt {10}$. Suppose $2=\sqrt {10}(a+b\sqrt{10})=a\sqrt{10}+10b$. Then $a=0$ since $\sqrt{10}$ is not rational. So $10b=2$, which has no integer solutions. So $\mathbb{Z}[\sqrt {10}]$ is not a UFD.  Is my reasoning correct? What are the flaws? Are there any advanced options for Google Chrome's history search? How do you configure an OpenFileDialog to select folders? In VS .NET, when you are selecting a folder for a project, a dialog that looks like an OpenFileDialog or SaveFileDialog is displayed, but is set up to accept only folders.  Ever since I've seen this I've wanted to know how it's done.  I am aware of the FolderBrowserDialog, but I've never really liked that dialog.  It starts too small and doesn't let me take advantage of being able to type a path.  I'm almost certain by now there's not a way to do this from .NET, but I'm just as curious how you do it from unmanaged code as well.  Short of completely reimplementing the dialog from scratch, how do you modify the dialog to have this behavior?  I'd also like to restate that I am aware of the FolderBrowserDialog but sometimes I don't like to use it, in addition to being genuinely curious how to configure a dialog in this manner.  Telling me to just use the FolderBrowserDialog helps me maintain a consistent UI experience but doesn't satisfy my curiosity so it won't count as an answer.  It's not a Vista-specific thing either; I've been seeing this dialog since VS .NET 2003, so it is doable in Win2k and WinXP.  This is less of a "I want to know the proper way to do this" question and more of a "I have been curious about this since I first wanted to do it in VS 2003" question.  I understand that Vista's file dialog has an option to do this, but it's been working in XP so I know they did something to get it to work.  Vista-specific answers are not answers, because Vista doesn't exist in the question context.  Update: I'm accepting Scott Wisniewski's answer because it comes with a working sample, but I think Serge deserves credit for pointing to the dialog customization (which is admittedly nasty from .NET but it does work) and Mark Ransom for figuring out that MS probably rolled a custom dialog for this task. Can “does” be contracted? What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely? Range of A and null space of the transpose of A So I'm complete stuck with something. I know it the following statements are true (or at least the seem to be from the results that I got from messing around with it a bit on MATLAB), but I don't understand why they are true or how to show so. Let $A$ be and $m$X$n$ matrix. Show that:  a) if $x \in N(A^TA)$ then $Ax$ is in both $R(A)$ and $N(A^T)$.   For this one I messed around with it with my own examples and I got $Ax=0$, therefore satisfing the statement, but I don't understand what's actually going on.   b) $N(A^TA)=N(A)$  again, makes sense when I see the results in MATLAB, but don't undestand why it works.  c) $A$ and $A^TA$ have the same rank  d) If $A$ has linearly independent columns, the $A^TA$ is nonsingular.  For the last two I have no idea on how to even start showing the relationship. I feel like I'm missing some crucial relationship between $A$ and $A^TA$, but I'm just not seeing it.   I would greatly appreciate any help of sugestions on how to show that these statements are true.   Thank you very much. I'm looking for one word which describes what a student who missed classes needs to do in order to complete his missing.   For example if he missed biology class he needs to seat with the teacher and study this missed class together with her and then he get the mark for this missed class. Someone -who isn't native English speaker- told me that it's called "rework". But I looked for it in some dictionaries (such as ) and I didn't find such definition.   : "SCHEDULE of reworks of missed classes" What new capabilities do user-defined literals add to C++? How should a family with young children apply for UK visas? Java logical operator short-circuiting How to prove that the center of the dihedral group $D_{2n}$ is $\{1,r^{n}\}$ and the center of $D_{2n-1}$ is $\{1\}$?  I don't know how to prove it in this general case. Differences between longtable and xtab I have a pretty simple table that needs to span multiple pages. This seems like a job for either the / package or the  package.   The voting on the answers to this  suggest that longtable is the preferred package, yet xtab is much newer and has been revised since that question was asked.  What are the differences between xtab and longtable and when is one preferable to the other? Complex zeros of the polynomials $\sum_{k=0}^{n} z^k/k!$, inside balls this is a question from a Temple prelim exam, and i'm trapped in it! We have $p_n(z)=\sum_{k=0}^n\frac{z^k}{k!}$ and we have to prove that $\forall r&gt;0 \quad \exists N\in\mathbb{N}$ s.t. $p_n(z)$ has no zeros in $B_r(0)$ for $n&gt;N$.  I tried to use Rouche's theorem observing that $1+\frac{z^n}{n!}$ has the nth roots of $n!$ as complex zeros, which are outside a fixed ball for n sufficiently large, but i'm having trouble proving that $|1+\frac{z^n}{n!}|&gt;|z+\cdots+\frac{z^{n-1}}{(n-1)!}|$ in $|z|=r$ (if this is true). If anyone could help..