Suppose I bought a call option and the stock rises above the strike price. That is, I now have an ITM call option. Also, I don't have enough money to exercise the option. So to make a profit off of the call option without having to exercise it, I go to the market and sell a call option for the same strike price and expiration date. My question is since I now have two different &quot;trades&quot; sitting in my account: one is the long call and second is the short call, do I have to &quot;link&quot; these two trades together somehow or how does it work? For example, a person who bought my short call option exercises it, which means I will have to procure 100 shares to give it to him. But I have a long call option and no money to buy the 100 shares to give it to him. What happens now? Do I necessarily need to exercise my long call and give it to the short call or does the commission &quot;cancel&quot; these two orders without me having to do anything? Also, what happens if I cannot find an exact same short call (with same strike price and expiration date on the market)? Since I cannot offset the trade, will I be in loss?
Suppose I sold an option on stock X, with strike price Y, and expiry date Z. Suppose I later buy an option on the same stock, with the same strike price, and the same expiry date. Do these two positions cancel out each other (i.e. both contracts cease to exist anywhere), or will I end up with two separate contracts?  Is it the same with the reverse situation? e.g. I bought an option on stock A, with strike price B, and expiry date C. If I later sell an option on the same stock, with the same strike price and expiry date, will I end up with two contracts (one long position, one short position)?
This question is the flip-side of the commonly asked food temperature safety concerns. I'd like to know, if a meat-based soup stock (chicken/pork/beef/etc) were to be held constantly at a safe hot temperature of 165F/73C-180F/82C, how long could it stay at this temperature and still be considered safe to eat?  Obviously, it would reduce over time, but suppose it's reconstituted with water regularly so that it could continue being held... Is there ANY sort of time limit (even completely unreasonable spans like, months, years, etc)? Did Anakin and Obi-Wan use the Force to protect themselves from the heat on Mustafar? While duelling that close to lava, I would suspect that they would get dangerously hot and dehydrated, and possibly burned. Did they use the Force to protect themselves in some way, for example lower their body temperatures and cool the air around them while duelling? I want to make a persistent live Ubuntu USB drive with more than 4GB of storage.   I know there is an option of installing directly on the drive but I don't want to do this as it will restrict the drive from working on different computers.   One option is to make an additional partition with extra space but if I do this how can I get newly installed software to be stored on this partition? With the ls command, is it possible to show only the files created after a specific date, hour...?  I'm asking it because I have a directory with thousand of files.  I want so see all files that were created since yesterday.   I use ls -ltr but I have to wait to see all files...  There is an equivalent of DIRECTORY/SINCE=date from OpenVMS ? How to disable automount in nautilus's preferences I am using Ubuntu 11.10 (64 bits) and I do not want to mount automatically USB thumb drives in my system. I tried the command dconf-editor and gconf-editor but there isn't the icon to disable it in nautilus preferences (apps|nautilus|preferences|media_automount).  Thanks. Is this a valid partial fraction decomposition? Write $\dfrac{4x+1}{x^2 - x - 2}$ using partial fractions. $$ \frac{4x+1}{x^2 - x - 2} = \frac{4x+1}{(x+1)(x+2)} = \frac{A}{x+1} + \frac{B}{x-2} = \frac{A(x-2)+B(x+1)}{(x+1)(x-2)}$$ $$4x+1 = A(x-2)+B(x+1)$$ $$x=2 \Rightarrow 4 \cdot2 + 1 = A(0) + B(3) \Rightarrow B = 3$$ $$x = -1 \Rightarrow 4(-1) +1 = A(-3)+ B(0) \Rightarrow A = 1$$ Thus, $$\frac{4x+1}{x^2-x-2} = \frac{1}{x+1} + \frac{3}{x-2}\textrm{.}$$  The substitution of $x$ ($x = 2, -1$) is a common method to find out the coefficient of the partial fractions. However, the equation on the third line is obtained by multiplying $(x+1)(x-2)$, which is assumed to be nonzero. Here we have a contradiction. Furthermore, the original function is not defined at $x=-1,2$. How can we substitute these value for $x$? So is this method valid and rigorous? How to modify it so that it is rigorous? I've been given a proof that shows the following:  If $f:[a,b]\to \mathbb C$ is a continuous function and $f(t)=u(t)+iv(t)$ then $$\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$$ The proof begins by letting $\theta$ be the principle argument of the complex number $\int_a^b f(t)dt$ and there is one step in the proof I don't understand; can anyone explain to me why $$\int_a^b e^{-i\theta}f(t) dt=\Re\bigg(\int_a^be^{-i\theta}f(t)dt\bigg)$$  Would this not imply that the imaginary part of the left hand side is equal to $0$? I'm not sure why the LHS and RHS would be equal here. A  not only grants me a Sentinel Raven, but also the handy ability to see through its eyes.  Unlike the telepathic connection with a regular familiar, I don't have to use an action to do so.    If I am blinded, but my Sentinel Raven is not (and within telepathic range), can I use my raven's sight to cast spells that require me to see my target? Would this negate any disadvantage resulting from me being blinded? Or would I still suffer disadvantage, for example, because I have to cast from my raven's perspective and not my own point of view? I have to give low and high bounds for the following:  $$ \sum_{n=1}^\infty \frac{1}{2^n - 3^n } $$  How do I determine an upper bound? How can I show this sum exists?  edit: removed erroneous conclusion. How to concatenate text from multiple rows into a single text string in SQL server? Consider a database table holding names, with three rows:  Peter Paul Mary   Is there an easy way to turn this into a single string of Peter, Paul, Mary? Switch command output language from native language to english I am aware there are many questions similar to this on MSE but I am having trouble following any of the solutions given.   I have the function given by   $f(x) = \dfrac{xy}{x^2+y^2}\;$ for $(x,y)\neq (0,0)$ and $f(0,0)=0$  I have calculated the partial derivatives and found:   $$\frac{\partial f}{\partial x} = \frac{y(-x^2+y^2)}{(x^2+y^2)^2}, \quad \frac{\partial f}{\partial y} = \frac{x(-y^2+x^2)}{(y^2+x^2)^2}$$  Now I need to show the partial derivatives exist for $(x,y) = (0,0)$.  I am also asked to show it is not continuous at $(x,y)=(0,0)$, based on other answers I've seen it seems like this follows from solving the first part but I fail to see how that follows through as well.   I could just copy the solutions with my function in place as I have seen a lot of answers using the definition of the derivative, but realistically I do want to understand what the thinking behind this is.   Any help would be appreciated. Question about the order of the product of two elements in an abelian group My reference for learning abstract algebra says that in an abelian group $G$ the product of two elements (say $a$ with order $n$ and $b$ with order $m$) has order $mn$ if $gcd(n,m) = 1$.   What I don't understand is where the $gcd(m,n)=1$ comes into use in proving this fact? For example, $ a^{mn} = (a^n)^m = (e)^m = e$ (identity element). A similar argument for $b^{mn}$ together with the fact that $G$ is abelian is enough to show that $(ab)^{mn} = e$. From here, how do I conclude for an integer $r &lt; mn$ that $(ab)^r \neq e$  Also, are there any other conclusion that can be drawn if $gcd(n,m) \neq 1$ ?  Thanks for any feedback in advance ! Need clarification on the Draw 4 rule. - Player 1 lays down a Draw 4 Card and says the color is Red. - Player 2 does not have a Red card but has a Draw 4 Card. Can Player 2 lay down his Draw 4 Card and have Player 3 draw 8 cards? Childrens fantasy, blind monk leading boy who can control the elements I have downloaded and extracted the packet tracer file, then I used this command as root  chmod +x install   then I ran (as root)  ./install    Then I used this command   ./set_ptenv.sh   but whenever I run this command   packettracer    it just doesn't start Why is it that Blender will only allow me to render with a CPU (GPU choice is unavailable)? Or is it until I acquire a graphics card that is specially built for such a task?  The images below show a Dell System Diagnostics (Video calibration) and GPU-Z results.      Platform: Dell Inspiron 3521 notebook with Core&nbsp;i3 Intel HD Graphics 4000 How to ask "If you have any problem then ask me" in polite manner RSA is not designed to be used on long blocks of plaintext like a block cipher, but I need to use it to send a large (encrypted) message.  How can I do this? What's the difference between an argument and a parameter? When verbally talking about methods, I'm never sure whether to use the word argument or parameter or something else. Either way the other people know what I mean, but what's correct, and what's the history of the terms?  I'm a C# programmer, but I also wonder whether people use different terms in different languages.  For the record I'm self-taught without a background in Computer Science. (Please don't tell me to read  because I'm asking this for the benefit of other people who don't already have a copy of 's marvellous book.)  Summary  The general consensus seems to be that it's OK to use these terms interchangeably in a team environment. Except perhaps when you're defining the precise terminology; then you can also use "formal argument/parameter" and "actual argument/parameter" to disambiguate.