I have an interesting question that is not a duplicate. I have been pondering this for a while, and I would like to see what MSE's "pro" mathematicians think the answer would be.    Problem: What is $\lfloor 1.\overline{9} \rfloor$?    My thoughts:  There are two solutions which I believe can be applied to this problem, although I'm not sure which one is correct.  Solution 1: $1.9999...$ is $2$, and the floor function would equal $2$.  Solution 2: Floor $1.9999...$ to get $1$, which is the answer.    I am not sure which one is correct. Please state which solution you think is correct and why. Thanks! Max0815.
Are the floor functions of $0.999\cdots$ and 1 equal?  It is true that $0.999\cdots=1$ but how does one justifies the integer part of $0.999\cdots$ being 1 , where it is not, or alternatively without using $0.999\cdots=1$ how can we show that  $\lfloor0.999\cdots\rfloor = \lfloor 1 \rfloor$ ?
Solve $f(x)f(2x^2) = f(2x^3+x)$ Given a PRF $F$ , is $G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$ a PRG? If $F$ a PRF, and we construct $G$ using $F$ in the following way:  $$G(s) = F_s(1)\|F_s(2)\|\cdots \|F_s(n+1)$$ where $|s|= n$.   Is $G$ then a PRG? If so how can I prove this? If not how can $G(s)$ be distinguished from a random $r$? And what if $n+1 &lt;$ range of $F_s$? or it could be for any $n &gt; |s|$. Looking for book: contact with aliens, five different races, mismatched claws, biological imperative to breed Auto mount a disk drive in ubuntu 14.04 LTS (Bookmark directory not found) Opening Chromium on Ubuntu VPS Ubuntu noob here. I recently got a VPS running Ubuntu, and decided to install Chromium, my preferred browser, on it. After installation completed, I got a message stating that I cannot open Chromium with root privileges. How would I go about opening Chromium? Editing a post during review doesn't show an "edit not possible" message While reviewing First Posts on Super User, I noticed that I couldn't edit this question (see below). Clicking the &quot;edit&quot; link simply does nothing. Editing is not possible for me right now because I have already five suggested edits pending. It used to be the case that the link would've been grayed out (and the reason shown as a popover). , and while I'm not sure it's an improvement, the current implementation needs some fixing at least.  This bug appears regardless of the actual reason that the edit isn't possible; for instance,  is another user experiencing the same bug who couldn't suggest an edit because of an already pending one. Apparently, I'm far from the only one who experiences this issue. As of last Sunday morning,  have been posted networkwide (and are still alive) and  is #16. Evaluate the following limit of finite sum Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function. Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.  I know that for $f$ is differentiable in $(a,b)$ and that it has one-sided derivative $f_+' (a)≠f_-' (b)$ at the endpoints. If $C$ is a real number between $f_+' (a)$  and $f_-' (b)$, then there exists $c∈(a,b)$ such that $f' (c)=C $. How can I use this to prove the above? I want to make a logistic model from my survey data. It is a small survey of four residential colonies in which only 154 respondents were interviewed. My dependent variable is "satisfactory transition to work". I found that, of the 154 respondents, 73 said that they have satisfactorily transitioned to work, while the rest did not. So the dependent variable is binary in nature and I decided to use logistic regression. I have seven independent variables (three continuous and four nominal). One guideline suggest that there should be 10 cases for each predictor / independent variable (Agresti, 2007). Based on this guideline I feel that it is OK to run logistic regression.    Am I right? If not please let me know how to decide the number of independent variables? Send Gmail calendar invite from alternate email Ellipse formula from points Question: Best way to derive an ellipse formula when given bunch of points (say 60 points which when connected draws an ellipse)?  Background: Using R Momocs library function  which returns confidence ellipse coordinates. Would be nice to abstract those points into a formula.  You can see my ellipse points in the image below;    Any suggestions much appreciated, Thanks Why is the Star Trek 2009 reboot called a reboot? I've created a series of DEM files using the  tool from LAStools; however since I don't have a licensed version they have black streaks running across them. Does anyone know a good method for removing these streaks? What do two question marks together mean in C#? Ran across this line of code:  FormsAuth = formsAuth ?? new FormsAuthenticationWrapper();   What do the two question marks mean, is it some kind of ternary operator? It's hard to look up in Google. Which has the heavier tail, lognormal or gamma? (This is based on a question that just came to me via email; I've added some context from a previous brief conversation with the same person.)  Last year I was told that the gamma distribution is heavier tailed than the lognormal, and I've since been told that's not the case.   Which is heavier tailed? What are some resources I can use to explore the relationship? What's the appropriate reaction to an answer that doesn't attribute the source it's copied from? I have designed a VF page to create a new record in which I am trying to display the value of a pick-list field. I have set a default value for this pick-list field. When trying to create the record using the salesforce native page, the value with which pick-list loads is the one I set as default but when creating the same record using VF page, the pick-list loads with "--None--" as default value.  Can anyone suggest If this is salesforce related bug or Am I doing anything wrong ? Show that the series $\sum(\exp(\frac{(-1)^n}{n})-1)$converges, but not absolutely. Show that the series converges, but not absolutely. $\sum_{n=1}^{\infty}( $exp$(\frac{(-1)^n}{n})-1)$.   My Try:  Let $a_n=$exp$(\frac{(-1)^n}{n})-1$. I was going to use alternating series test because the sequence $\{a_n\}$ is alternating. But $\{|a_n|\}$ is not decreasing to $0$. So, I am stuck now. Can anybody please give me a hint? Down arrow button for choosing the desired site When searching for the desired SE site, the down arrow key (down) should work in order to choose the site one is looking for and hit enter to visit it, instead of using the mouse point to choose it. Would be pretty convenient. Is there a way to display the number of messages for any label in the Gmail label list? The Gmail sidebar displays the list of our labels (or some of them, according to settings). Next to every label name there is a number showing how many unread messages we have for that label.  Is there a way to display also the total number of messages for each label?  Example:  [to answer] (0/36) [to do] (0/55) [waiting answer] (0/7) cooking (2/48) family (6/352) friends (1/1828) website (2/412) work (12/12801)