How to ask this as question
How should I phrase a question that must be answered with an ordinal number (e.g., the third prime)?
Sum and product of Martingale processes Given two Martingale processes $(X_t)$ and $(Y_t)$, are their sum $(X_t+Y_t)$ and their product $(X_t \times Y_t)$ also Martingale?  If not, will the two $(X_t)$ and $(Y_t)$ being independent grant their sum and product Martingale? Thanks! Prove Inverses not need be Unique if Associativity fails Let $M=\{x, y, z\}$ be a set and let $\circ$ be a binary operation on $M$ such that the identity element is $x$ and $y \circ y = x = y \circ z$. Prove that inverses need not be unique if associativity fails given the multiplication table below.  $x \circ x = x, x \circ y = y, x \circ z = z$  $y \circ x = y, y \circ y = x, y \circ z = x$  $z \circ x = z, z \circ y = x, z \circ z = x$ Story where radically different cultures live together and are defined by rulesets, some choose not to see each other, a house is used as a spaceship I think this novel came out in the 2000s.  There are many cultures that live close together but are very different, for example some pretend to be pre-industrial.  One of the main characters is a youth who grew up in a pretend pre-industrial society and is now exploring the rest of the solar system? ring-world?   Each culture experiences their own reality that is defined by a ruleset.  One of the rulesets becomes aggressively self-propagating and this is the problem that drives the plot.  At some point a tumbling house, just a normal house, is used to travel across space. Can you save an image with a white background as a transparent image out of Photoshop? What is the difference between Clamav and Clamtk? I know that both of them are antivirus. What are the differences between Generics in C# and Java... and Templates in C++? I mostly use Java and generics are relatively new. I keep reading that Java made the wrong decision or that .NET has better implementations etc. etc.  So, what are the main differences between C++, C#, Java in generics? Pros/cons of each? Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$ I was hoping to find a more "mathematical" proof, instead of proving logically $\displaystyle \sum_{k = 0}^n {n \choose k}^2= {2n \choose n}$.  I already know the logical Proof:  $${n \choose k}^2 = {n \choose k}{ n \choose n-k}$$  Hence summation can be expressed as:  $$\binom{n}{0}\binom{n}{n} + \binom{n}{1}\binom{n}{n-1} + \cdots + \binom{n}{n}\binom{n}{0}$$  One can think of it as choosing $n$ people from a group of $2n$  (imagine dividing a group of $2n$ into $2$ groups of $n$ people each. I can get $k$ people from group $1$ and another $n-k$ people from group $2$. We do this from $k = 0$ to $n$. Can anyone provide me with (or point me to) real life gravitational lensing data that I can plug in to the first equation on this page (the standard lensing equation):   together with the luminous mass and distance to the galaxy(s).  I've looked for papers online and have not found any simple data that can be readily plugged in to the equation (I am not familiar with the details of how exactly the lensing is measured and have gotten lost in the mountains of data in the papers).  Thanks Can file uploads time out in PHP? Hi im quite new to PHP, i have created a form for very large csv files to be uploaded to my server. Some one mentioned to me that the browser can time out due to the uploading file being to big, is this true? and if so, can it be prevented?  Thanks for your help! In attempting to wrap my mind around the basic vocabulary, concepts, and methods of philosophy, I find myself wondering what the difference is between a philosopher and a theologian.   can have two meanings: 1. Theology is a rational study of the existence of God/gods and the nature of religious ideas. 2. Theology is simply a study of a particular religion (or all religions), really more the practice than the theory, but maybe a mixture.  It seems from an immediate reading that definition 1 would lead to the conclusion that a theologian is a philosopher (perhaps that theology is a branch or subset of philosophy), but definition 2 appears to be rather unphilosophical in nature.    So, how does philosophy answer this question?   Is theology considered a proper subset/branch of philosophy overall? Does it depend entirely on which of the above 2 definitions of theology fits a particular theologian as to whether he is a philosopher or not?   I think this answer is simple and fairly self-evident, but somewhere in my gut I feel like I'm missing something.  Is there a treatment of this question in the literature?    Edit: the answers so far seem to want to redefine theology or other terms - that is fine, but please be clear that you are redfining them, and provide, if possible, sources for why the term should be different than given (support from historical works, other sites, etc.). Word for a modified version of a quote What are the assumptions for applying a quantile regression model? The question has been asked (one time) on CV before, but the answer is really imprecise and does not really answer the question in my opinion.  So: What are the assumptions for estimating a linear regression model via quantile regression?  To my understanding (and as several CV users have mentioned), quantile regression does not assume any specific distribution of the error terms - does that mean that, in a time series model, autocorrelation and heteroscedasticity do not have to be accounted for?  What about the other Gauss-Markov assumptions? I would assume that the assumption of no perfect multicollinearity has to be met when applying quantile regression, but do the parameters have to be linear? The linearity assumption only has to hold for the specific quantile I would assume.  Anyways - I do not find any backup for any of my thoughts in the scientific literature and I would appreciate a comprehensive answer. Thank you! The definition of span Using customized Coordinate System in ArcGIS Desktop? I don't know so much about coordinate systems...  In my office we use to deal with spatial data coming from archaeological sites. Each site has its own x-y-z coordinate system (GCS). Three simple ortogonal cartesian axis. In the last years we have been managing this spatial data through GIS software (ArcGIS), without using specific coordinate system (just leave it as "undefined")  I'd like to know if there exisits any GCS designed to deal with such datasets using simple cartesian orthogonal axis, without grid distortions of the typical GCS. In addition, I'd like to know if this system is suitable for using it in an online mapping application.  By the way, we manage 2D (ArcMap) and 3D (ArcScene) environments and work with "mm" as length base unit.   If such a thing doesn't exists, maybe someone knows how to create it. What are the badges I can earn on each site, and what are the exact criteria for earning each badge? Formerly List of all badges with full descriptions.  What are badge name's requirements? Why didn't I get badge name ? Which badges can I earn multiple times?    Jump to:                    Note: Some badges are awarded based on score. The term score means the total number of upvotes minus the total number of downvotes.  Any badge with a *** next to it is one of 20 badges that count towards the  displayed on a moderator candidate in an election. The candidate score is a total of 40 points: the first 20 are awarded based on the user's rep divided by 1000 and rounded down; the second 20 represents the total number of unique badges earned of the 20 that count. Note that if the same badge is earned multiple times, it will only count once towards the candidate score.  Any badge with a &quot;(retired)&quot; next to it is no longer awarded, but is retained by users who previously earned them. See  for more info on what it means for a badge to be retired.       Visit the  of the  on any site to see a complete list of badges that you can filter by earned, unearned, or type. Compute the radius of convergence of the power series $\sum_{n=0}^{\infty} n!x^n$ Who was the colleague that Erik was going to contact for help? After S.H.I.E.L.D confiscates Jane's work in Thor, the researchers discuss what they'll do next.  Erik mentions two colleagues. The first is reasonably implied to be Bruce Banner, but who is the second colleague he mentions? Transcribed from the film:  Jane Who are these people? Erik I knew this scientist... a pioneer in gamma radiation. S.H.I.E.L.D showed up and... umm. He wasn't heard from again. Jane They're not going to do that to us. I'm going to get everything back. Erik mumbles Please. Let me contact one of my colleagues. He's had some dealings with these people before. I'll email him and maybe he can help. Darcy They took your laptop, too. What is the resolution I need to make a picture to make curves look smooth and not pixelated? I was running a Python script that malfunctioned and used sudo to create a file named &gt;.  How can I get rid of this file?  Of course, when I try sudo rm &gt;, I get the error bash: syntax error near unexpected token 'newline', because it thinks I'm trying to redirect the output of rm.  Its permissions are -rw-r--r--. Smallest Width for Galaxy S and Galaxy S2