I am having problem understanding what the following sentence means exactly:     Bill's and my car had to be towed last night.   I can't quite figure out why the possessive is used in Bill's and what it means.
I want to talk to someone about the house that my wife and I own.  Saying, for example, "My wife's and my house is awesome," sounds a bit funny to me.  What's the best way to express this?  Clarification  I'm asking specifically about the grammar of multiple nouns in possessive form.  I'm particularly curious if it's possible to do this with a first-person pronoun (me).  I am capable of rephrasing this in other ways - my question is not how to express the idea, but about this particular grammatical construction, if it is even legal.
Let $y_n$ be a sequence such that  $\lim_{n\to \infty} y_n= y$ then prove that     $ \lim \dfrac{y_1+y_2+...+y_n}{n}= y$   My try:  As  $\lim_{n\to \infty} y_n= y$ then given $\epsilon&gt;0$ there exists $N$ such that $\forall n\ge N ;||y_n-y||&lt;\epsilon $.  Now $||\dfrac{y_1+y_2+...+y_n}{n}-y||\le n^{-1}\{||y_1-y||+||y_2-y||+...+||y_n-y||\}$  How to make this limit tend to zero? Locking a file in Python How do I change the command that a launcher item launches? Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$ It's not difficult to show that  $$(1-z^2)^{-1/2}=\sum_{n=0}^\infty \binom{2n}{n}2^{-2n}z^{2n}$$  On the other hand, we have $(1-z^2)^{-1}=\sum z^{2n}$.  Squaring the first power series and comparing terms gives us  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}2^{-2n}=1$$  that is,  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$$  My question: is there a more direct, combinatorial proof of this identity?  I've been racking my brains trying to come up with one but I'm not having much success. Error message in my excel formula Make \cite{my reference} show name and year I am trying to figure out how to make author's name and year show up every time I make a reference.  For example:  my_bibtex.bib has this entry:  @article{Franklin1999,  author = {Franklin Allen and Risto Karjalainen}, title = {Using genetic algorithms to find technical trading rules}, year = {1999}, volume = {51}, pages = {245-271}, journal = {Journal of Financial Economics}  }   If in my_paper.tex I use this line:  Important result has been found by \cite{Franklin1999}   My output looks like:  Important result has been found by [1]   But I want it too look like:  Important result has been found by Franklin 1999   I there a way to do it?  My bibliographystyle is set to plain  \bibliographystyle{plain}  \bibliography{my_bibtex} How should an educational institute woo good faculty? What steps must an educational institution wanting to recruit good faculty take? There is a cycle in the academia:    Good doctorates from top universities invariably join other top universities as faculty members.  Good students aspire to study in top universities under excellent faculty members.   Suppose a new educational institution or department springs up and desires to set up a top-quality group, how does it break into this cycle? I suppose this could take some years, but is money-power the only thing that could be wielded by the institute to achieve its end? Up to now I don't understand well what \null actually is and when we need it. I have only known that it can be used to create hypothetical anchors as follows.  \documentclass{article} \usepackage[a6paper,margin=2cm]{geometry} \parindent=0pt  \begin{document} \hfill xport \hfill\null\\ \null\hrulefill{} never \hrulefill\par \hrulefill{} dies. \hrulefill\par \hfill really? \hfill\null\par   \newpage \null \vfill \hfill The End \hfill\null \end{document}    What is \null and when do we need to use it? Why do \hrulefill and \hfill need starting \null when they follow \\ but not need \null when they follow \par? Why does \hfill always need ending \null but \hrulefill not need it? Theorem.  If $\sum_{n=1}^{\infty}c_{n}$ is Cesaro summable, then $c_{n}/n$ tends to $0$.  How to prove it? Match the size of multiple background images In  tutorial in the first couple of minutes it is explained how to set the dimensions of a cube and match the background images to this mesh. I have tried to get it right but till now I did not succeed. This is what the creator of the tutorial says in the comments:      I'm keeping only one mesh and just changing the x and y values of my   background images you can see me add at 3:00. We want all the   background images to match that one mesh.   Here are my images:     I think front and back images match to the mesh. But for the right, left and top view I only get one dimension matching. I don't see how you can match both dimensions matching without changing the mesh What is the intuitive meaning of line integral with respect to x? I know how the line integral is calculated, but I want to know what the meaning of line integral with respect to x is, I mean, intuitively. The integral is $\int_C f(x,y) dx$ or it can be $\int_C f(x,y) dy$. ($C$ is a curve here) Thanks. Why don't wizards always use multiple wands? This question, , seems to indicate $$\nabla_a \sqrt{g}=0.$$ Why is this the case? I've always learned that $$\nabla_a f= \partial_a f,$$ hence surely $$\nabla_a \sqrt{g}=  \partial_a\sqrt{g} \neq 0. $$  Where's the hole in my logic? Proving a function is bounded Hi i was wondering if  anyone could help me with my revision This is a question of a past paper i'm stuck on.  Let $$f:[a,b]\to \Re$$ be Riemann intergrable. Part (a) is to prove that f is bounded and part (b) is to Give an example of a bounded function f that is not Riemann integrable  my attempt for part (a) is since f is Riemann intergrable then it is continuous on [a,b] which means that it must also be bounded? or is this incorrect i find this topic rather difficult  For part (b) i dont really have a clue i cant recall any function like the one they ask for I asked a  recently, looking for examples of an online tool. Per the , I answered my own question with a few examples that I had already found. I did this so that these examples would be included in the answers, along with the rest.  The question has received only down votes and insults saying that this shouldn't be done.   Should I not answer my own questions? Could anyone tell me what is up with so many archives, and how are they differ?  There's at least five that I can think of, .tar.tz, .tar.gz, .tar.bz2, .tar.lz, .tar.z  Which is best for what applications? It just seems silly to make so many variations of the same file but I'm sure there's a reason. How to make bash put prompt on a new line after cat command? What I get:  host:~ user$ cat example.txt some texthost:~ stas$   What I want to get:  host:~ user$ cat example.txt some text host:~ stas$   Is there a way I can make cat behave like this?  I'm using bash on Mac OS X. Latin Square and Graph Theory How many &quot;$1$&quot; can be selected at most, provided that only one from each row and column of the attached matrix $A$ is selected?(That is, when one &quot;$1$&quot; is selected, no other element can be selected than the row and column where that &quot;$1$&quot; is located.)  Answer: I think $6$ can be chosen.  How can I give this answer in connection with graph theory? I think it has to do with the Latin Square(or Rectangle). But I can't connect and explain. Please help me. I thought a lot, but I could not establish the relationship completely. Thanks... Indian passport threading coming off Are there other governments in The Hunger Games world? We know that Panem exists in a post-apocalyptic North America but are there other established governments on other continents?