Why is $0! = 1$ the same as $1! = 1$?
Prove $0! = 1$ from first principles
Access NSMutableArray from another class - Objective C How general is the Lagrangian quantization approach to field theory? how to loop through arguments in a bash script Seeking birth record for Jacob Schulthess from Wangen an der Aare in Switzerland? Is it possible to edit the Audit fields on UPDATE? Forward an invocation of a variadic function in C In C, is it possible to forward the invocation of a variadic function? As in,  int my_printf(char *fmt, ...) {     fprintf(stderr, "Calling printf with fmt %s", fmt);     return SOMEHOW_INVOKE_LIBC_PRINTF; }   Forwarding the invocation in the manner above obviously isn't strictly necessary in this case (since you could log invocations in other ways, or use vfprintf), but the codebase I'm working on requires the wrapper to do some actual work, and doesn't have (and can't have added) a helper function akin to vfprintf.  [Update: there seems to be some confusion based on the answers that have been supplied so far. To phrase the question another way: in general, can you wrap some arbitrary variadic function without modifying that function's definition.] Question about Subrings and integraly closed Background  I am a first year calculus student so I would prefer if answers remained in Layman's terms.  It is common knowledge and seems to me a mantra that I keep hearing over and over again to "not treat differentials/derivatives as fractions".  I am of course, in particular, referring to Leibniz notation.  However, aside from a quick response such as "oh, it's because its not a fraction but rather a type of operator", I never really got a full answer as to why we can't treat it as such. It just kind of sits at the edge of taboo in my mind where it sometimes gets used and sometimes doesn't.  Confusion is further compounded when a lot of things seem to just work out if we treat them just as fractions (e.g. u-substitution / related-rates)    Example     Air is being pumped into a balloon at a rate of $100cm^3/s$. We want the rate of change of radius when the radius is at $25cm$.   $$\text{we are given}\ \frac{dv}{dt}=100cm^3/s$$ $$\text{we want}\ \frac{dr}{dt}\ \text{when}\ r=25cm$$ Thus we will solve this by using the relation $v=\frac{4}{3}\pi r^3$ $$\frac{dv}{dt}=\frac{dv}{dr}\frac{dr}{dt}$$ $$\frac{dv}{dt}\frac{dr}{dv}=\frac{dr}{dt}$$ $$100\frac{1}{4\pi r^2}=\frac{1}{25\pi}$$ So the answer is $\frac{dr}{dt}=\frac{1}{25\pi}$ when $r=25cm$  *Note the manipulation of derivatives just as if they were common fractions using algebra.    Question  When exactly can I treat differentials/derivatives as fractions and when can I not?   Please keep in mind that at the end of the day, I am a first year college student. An answer that is easy to understand is preferred over one that is more mathematically rigorous but less friendly to a beginner such as me. SQL Server, convert a named instance to default instance? I need to convert a named instance of SQL server 2005, to a default instance.  Is there a way to do this without a reinstall?    The problem is, 2 out of 6 of the developers, installed with a named instance. So its becoming a pain changing connection strings for the other 4 of us. I am looking for the path of least resistance to getting these 2 back on to our teams standard setup.    Each has expressed that this is going to be, too much trouble and that it will take away from their development time. I assumed that it would take some time to resolve, in the best interest of all involved, I tried combing through configuration apps installed and didn't see anything, so I figured someone with more knowledge of the inner workings would be here. I recently bought a Minolta film camera and it had some film with it. The film is dated 1991 - 1994. Can I use the film? Why General Leibniz rule and Newton's Binomial are so similar? The binomial expansion:  $$(x+y)^{n} = \sum_{k=0}^{n} \binom{n}{k} x^k y^{n-k}$$  The General Leibniz rule (used as a generalization of the product rule for derivatives):  $$(fg)^{(n)} = \sum_{k=0}^{n} \binom{n}{k} f^{(k)} g^{(n-k)}$$  Both formulas can be obtained simply by induction; Newton's binomial also has a combinatorial proof . It's striking how these formulas are similar; is there a possible connection between them? I was thinking that maybe the General Leibniz rule could be obtained using a combinatorial argument as well (hence the binomial coefficients)... What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$ Why do I get "Permission denied (publickey)" when trying to SSH from local Ubuntu to a Amazon EC2 server? DML is not allowed in a constructor. Is there a known reason behind this limit?  I have been searching for the answer &amp; haven't found anything which addresses the question. May be it's not documented anywhere(Or google doesn't know where it is). Please add a system to allow file uploads attached to questions and answers I posted a question and a couple of respondents asked for the source code. I could only post portions of the code.  If attachments were allowed I could have uploaded a .zip file with the whole application.  Will this be a feature in SO? 16 GB USB flash drive capacity down to 938 MB After writing the FreeNAS IMG to a 16 GB USB flash drive, I can now only use 938 MB. I used the Win32 Disk Imager tool to write the IMG to the device. Then later, when I inserted the the USB drive into my Windows 7 computer it said that it had to be formatted, because it couldn't read it. I believe this is normal. So I formatted it inside Windows using the format option when prompted. So in Windows Explorer now, 938 MB is reported as capacity of this device.    Also, when i check the properties dialog box I can see the same numbers.    And when I check with diskmgmt.msc I can see there are several volumes I don't recognize and unallocated space of 12.79 GB.    Now, I have another 2 GB USB flash drive with the same problem. It too was used for FreeNAS, and it too has a reported capacity of only 938 MB. I thought it was broken there for a while, until I saw the same problem with this 16 GB model.  I tried using diskpart on the 2 GB model, and I saw that there were several partitions there (list partitions) just like on this one. So I used the clean option to try to wipe it, but that wiped off everything so it's totally useless now. I'm not sure how to rebuild it.  Is this a standard routine, like part of the whole "user experience", that whenever you make a bootable USB falsh drive with FreeNAS, it messes up your device? I am new to FreeNAS, so i wouldn't know. But it sure looks like it. Maybe it is in fact the format operation in Windows that messes things up... I don't know. It's not very nice.  How do I restore the capacity back to 16 GB-ish (14.9 GiB)? Drawing on an image with TikZ Proving $\tan(\theta_1+\theta_2+\cdots+\theta_n)$ has the form $\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$ $$\tan(\theta_1+\theta_2+\cdots+\theta_n)=\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$$  where  $S_i$ denotes the sum of product of tangent of angles taken $i$ at a time.     For example,$$\tan(\theta_1+\theta_2)=\frac{S_1}{1-S_2}=\frac{\tan\theta_1+\tan\theta_2} {1-\tan\theta_1\tan\theta_2}$$   (This formula is given  in my textbook with no derivation or background)  How to derive this? Lightning component quick action - send parameters to the lightning component I have a lightning component that is available for use as lightning component quick action. I need to use this component from various object actions, for example, I will add a lightning component quick action to account object and to contact object. Now on the lightning component itself, I want to know if it was invoked from the account object or from the contact object, but I cannot find a way to do that. I have found a way to get the record Id by adding &lt;aura:attribute name=&quot;recordId&quot; type=&quot;String&quot; /&gt; (see code snippet below) It is working but not good enough. What I really need is to send a parameter from the lightning component quick action invocation:  And get it in my component: &lt;aura:component implements=&quot;force:lightningQuickAction,force:hasRecordId,flexipage:availableForAllPageTypes&quot;&gt;     &lt;aura:attribute name=&quot;recordId&quot; type=&quot;String&quot; /&gt;     &lt;aura:attribute name=&quot;param&quot; type=&quot;String&quot;/&gt; &lt;/aura:component&gt;  Is this possible? And if not - any workaround for achieving that? How do I fill arrays in Java? I know how to do it normally, but I could swear that you could fill out out like a[0] = {0,0,0,0}; How do you do it that way? I did try Google, but I didn't get anything helpful.