How can the position of 'only' change the meaning of a sentence?
Where to place 'only'
I can show that for $x &gt; 0$ and $r_{i} &gt; 0$ we have $$ \left(\, x + r_{1}\,\right)\ldots\left(\, x + r_{n}\,\right)\ \geq\ \left[\, x + \left(\, r_{1}\ldots r_{n}\,\right)^{1/n}\,\right]^{n}.$$ However, I can't do this using straight up induction, strong or weak. Can someone do this?   You can show the inequality holds for $n$ if it holds for $n+1$ using $r_{n+1} = (r_1 \cdots r_n)^{1/n}$, so going down isn't a problem, but going up has eluded me. Additionally, you can show that if it holds for $n=a$ and $n=b$ then it holds for $n=ab$. Using powers of two and the above is sort of a way to prove the above by induction but it certainly isn't "normal".  You can also prove the above using Lagrange multipliers (which isn't surprising). The last proof I know is where you compare coefficients of $x^k$ and use the AM-GM inequality. Unable to get Excel to recognise date in column I constantly have problems working with dates in Excel, I must be doing something wrong but I don't understand what.  I have a spreadsheet, exported from our exchange server, that contains a column with dates on. They have come out in US format even though I'm in the UK.   The column in question looks like this  04/08/2012 04/09/2009 04/01/2010 04/21/2011 04/05/2012 08/30/2009 08/29/2010 08/28/2011   In Excel, I have highlighted the column and selected Format Cells.... In this dialog box, I have selected the Date, selected English (United States) as the locale and chosen the matching date format from the list. I hit OK and try to sort the data by this column.   In the sort dialogue I choose this column, select sort on Values but the order only gives me options for A to Z, not oldest to newest as I would expect.  This in turn sorts the date data by the first two digits.  I am aware I could re-format this data to ISO and then the A to Z sort would work but I shouldn't have too, I'm obviously missing something. What is it?  EDIT: I messed up the bounty but this should have gone to @r0berts answer, his first suggestion of Text to Columns with no delimiter and choosing 'MDY' as the type of data works. Additionally, if you have a time (i.e. 04/21/2015 18:34:22), you need to first get rid of the time data. However after that the method suggested by @r0berts works fine. Putting a table next to a figure Clicking on a spoiler tag to reveal the text shouldn't navigate you to another page This is an issue I noticed when reading . On multiple occasions I ended up inadvertently clicking a link that I could not see when I was just trying to reveal the spoiler text.         Can links be deactivated in spoilers until the text is revealed?  (Edit: this issue seems particularly to apply to those using touch screen devices with the "full site" theme) Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$ I want to show that for $\gcd(a,b) = 1$ $a,b \in Z$   $\gcd(a+b, a-b) = 1$ or $\gcd(a+b, a-b) = 2$ holds.      I think the first step should look something like this:      $d = \gcd(a+b, a-b) = \gcd(2a, a-b)$   From here I tried to proceed with two cases. 1: $a-b$ is even, which leads to $\gcd(a+b, a-b) = 2$ 2: $a-b$ is odd, which leads to $\gcd(a+b, a-b) = 1$  My main problem I think is, that I do not know how I should include $\gcd(a,b) = 1$ in the proof.  Any help is appreciated. Thx in advance. Cherio Woltan I built a ZI model and it is producing predicted values that are from a very small range when compared to the observed values. Plus it does not produce any zeros. See the fitted vs. observed graph below.     My model structure is given below. My response is a count variable and the predictor is continuous water level measurements (scaled).   m.u.meanwl.gu &lt;- zeroinfl(GU ~ MeanWLScaled | MeanWLScaled, data = uluabat_wl_fg, dist = "negbin", link = "logit")   I need help to figure out what's wrong and fix it. Thanks in advance. This or That person Computing matrices of linear transformation under different basis Came across a problem in my textbook and I am having trouble with it, the book provides an answer but no workings. Looking to get an explanation of what is going on  help I prepare for an exam. If we let $T : \mathbb R^2 \to \mathbb R^2$ be a linear transformation. Consdider two bases $V$ and $W$ of the vector space $\mathbb R^2$, where $V=\{v_1,v_2\}$ with $ v_1 =  \begin{bmatrix} -2 \\1   \end{bmatrix}$ and  $ v_2 =  \begin{bmatrix} 1 \\1   \end{bmatrix}$ and where $W = \{w_1,w_2\}$ with  $ w_1 =  \begin{bmatrix} -1 \\4   \end{bmatrix}$ and  $ w_2 =  \begin{bmatrix} 0 \\1   \end{bmatrix}$. Suppose that  $ A =  \begin{bmatrix} 1&amp;2   \\-1 &amp;4    \end{bmatrix}$ is the matrix of $T$ under basis $W$. I need to find the matrix $B$ the matrix of $T$ under basis $V$.  The solution is:   $ B = P^{-1}AP$ = $   \begin{bmatrix} -30&amp;22   \\-48 &amp; 35    \end{bmatrix} $  But I don't know why. I am attempting to return an integer (itemcount) of the items within a SP2013 list. I have done this easily using the stock standard json method. However I have a need of counting the splist items which contain a certain value. My silly knowledge immediately lead me to try and use filtering with the ItemCount parameter only to find out that it will always still return the count for all items and it will completely ignore the filter. I have searched for a way of doing this but have found absolutely nothing other than a single page with a comment stating that it is not possible with the REST api and that it can ONLY be done using CSOM.  My question is, firstly, is it true that there is NO way to filter itemcount with REST? If so, how else can I obtain my item count using this type of filtering? (Examples or sources will help vastly) Thanks.  Below is my attempted request:  var itemid = item.id;           MyService.ensureFormDigest(function (fDigest) {               $http.get(                   MyService.appWebUrl + '/_api/web/Lists/getbytitle(\'Items\')/ItemCount?$filter=SubjectsID eq' + itemid,                   {                       headers: {                           'Accept': 'application/json; odata=verbose',                           'X-RequestDigest': fDigest                       }                   }).success(function (d) {                       item.itemcode = d.d.ItemCount;                       alert(item.itemcode);                       callback();                   }).error(function (er) {                       alert("Error getting List Item Count: " + er);                   });           });       }   On another note, I was advised to try it as such: /Items?$filter=SubjectsID eq 3&amp;$select=Id  Then in the JS, in my success method:  data.d.results.length New three-tiered badge idea: Explainer →Refiner → Illuminator The difference between a poor or meh question and a stellar question can often simply be someone understanding it and providing it a great answer. I can't begin to count the number of times I've justified re-opening a question as a moderator by saying:     Look at the answer it got, though. This isn't something we want deleted, this is something we want fixed, because it's obviously valuable. Someone with domain knowledge can easily edit that question based on the answer it received.   This doesn't only apply to borderline-poor or poor questions – sometimes a good edit means the difference between 100 and 10,000 people finding something through typing things into Google. Good titles are hard.   We think we've come up with a way to provide incentive for good, opportunistic edits to happen more often, ideally without questions needing to go through closure or collecting a centimeter of dust before they do. What if we simply rewarded folks that answered and edited questions with a special, relatively difficult to earn badge?  Let's say that you answer something, and:   You edit the question 12 hours before or after answering it. This allows you to edit now, answer later &mdash; or answer now and edit later, when you have the time. Your edit isn't rolled back, or outright rejected if it was a suggested edit The question is not closed for any reason, even simply being a duplicate Your answer has a score of 1 or higher   &hellip; then you've done something that we probably want to recognize. You understood something, you provided the knowledge that you have, and then you provided an edit to make sure that more people in need of this knowledge can find it, while raising the overall quality of the site.  Here's the proposed tiers for the badge (within the above stated criteria):   Explainer (Bronze): Answered &amp; edited 10  questions Refiner (Silver): Answered &amp; edited 50 questions Illuminator (Gold): Answered &amp; edited 500 questions   We think this is going to be pretty hard to game. You can't go leaving streaks of terse snark all over the place on questions you know are going to be closed anyway, and junk edits aren't going to fly.  We're talking about rewarding folks that take a tiny bit more time out of their day just to write a more descriptive title so that folks can find the awesome answer that they wrote. Just doing that alone can make a big difference. Sure, it's a tad hard to get at the gold level, but it's supposed to be. If you routinely edit questions that you answer and have done so for some time, you'd probably get it the day we roll it out.  While this is technically something that we came up with on the quality initiative ( | ) &mdash; this badge could be earned on all of our sites.  What do you think? What did we miss? What could be better about the idea? This may be a generic OOP question. I wanted to do a generic comparison between an interface and an abstract class on the basis of their usage.   When would one want to use an interface and when would one want to use an abstract class? In recent versions of PostgreSQL (as of Dec 2013), can we share a query between two or more cores to get a performance boost? Or should we get faster cores? Prove the map has a fixed point I got this problem from my teacher as a optional challenge. I am open about this being a given problem, however it is not homework. The problem is stated as follows. Assume we have an infinite tetration as follows $$x^{x^{x^{.^{.^.}}}} \, = \, a$$ With a given $a$ find $x$. The next part of the problem was to discuss the convergence radius of a. If a is too big or too small the tetration does not converge. Below is my humble stab at the problem.  My friend said you would have to treat the tetration as a infinite series, and therefore could not perform algebraic manipulations on it before it is know whether it converges or diverges. However my attempt is to first do some algebraic steps, then discuss the convergence radius. I) Initial discussion At the start it is obvious that the tetration converges when $a=1$ (just set $x=1$) Now after some computer hardwork it seems that the tetration fails to converge when a is roughly larger than 3. II) Algebraic manipulation $$ x^{x^{x^{.^{.^.}}}} \, = \, a$$ This is the same as $$ x^a \, = \, a$$ $$ \log_a(x^a) \, = \, \log_a(a)$$ $$ \log_a(x) \, = \, \frac{1}{a}$$ $$ x \, = \, a^{\frac{1}{a}}$$ Now, if we let $a=2$ then $x = \sqrt{2}$. After some more computational work, this seems to be correct, which makes me believe this formula is correct. III) Discsussion about convergence By looking at the derivative of $ \displaystyle \large a^{\frac{1}{a}} $ we see that the maxima occurs when $a=e$, which also seems to correspond to the inital computational work. Now I think, that the minima of $\displaystyle \large a^{1/a}$ is zero by looking at its graph, studying its derivative and the endpoints. So that my &quot;guess&quot; or work shows that it converges when $$ a \in [0 \, , \,  1/e] $$ VI) My questions Can my algebraic manipulations be justified? They seem rather sketchy taking the a`th logarithm and so on . (Although they seem to &quot;magically&quot; give out the right answer) By looking at Wikipedia it seems that the tetration converge when $$ a \in \left[ 1/e \, , \, e \right] $$ This is almost what I have, why is my lower bound wrong? How can  I find the correct lower bound? How do I temporarily disable an app when there is no "Disable" option Show that the polynomial $X^5 + X^3 + \bar{1}$ in $(\mathbb{Z}/2\mathbb{Z}[X])$ is irreducible Number of planks required to stop the bullet dual boot missing files on ntfs I have 3 partitions: one for Windows 7 (ntfs), one for Ubuntu (ext4) and one just for data (ntfs so both operating systems can see them).  My problem is that I had stored some files on the data partition using Ubuntu and when I booted Windows 7 all that data was gone! After that I couldn't find the files even when using Ubuntu.  My files were simply GONE :(  Is there something I can do in Ubuntu or is it just windows problem? If every prime ideal is maximal, what can we say about the ring? Suppose $R$ is a ring and every prime ideal of $R$ is also a maximal ideal of $R$. Then what can we say about the ring $R$? Hoping someone can give me some thoughts on what might be going on here so I can be a bit more informed when I call a plumber.  Situation is, we got our water heater replaced a few years back and ever since this has been an issue. It's more noticeable when it's cold outside it seems, but still seems to be a year round problem. Whenever we  use hot water, we basically run out of it within minutes. In order to get an acceptable amount of hot water (enough to take a 10 minute shower), we literally have to prime the water first. By that I mean I have to turn on the hot water, let it run for a couple of minutes, then turn it off and wait 20 minutes. Then when we go to use the hot water again we'll get hot water for a respectable amount of time. Now I am fairly ignorant to all this, but it seems a 71 gallon hot water heater should be capable of holding enough water to not need to be primed like this. I should be able to take a 30 minute shower, let alone 10 without running out. My shower this morning was decently warm for maybe 2 minutes before it was just warm-ish.   So if anyone can give me some ideas on what might be going on I would appreciate it. We've just put up with this for some years assuming perhaps it was some eco friendly thing. Like the system doesn't maintain much hot water in the tank so it's not always running and only heats water up when you start to use it? I hope that isn't the case though and even so, I should be able to get more hot water out of it. Any help?  UPDATE Sorry everyone, I meant to tell you all that the water heater was gas. The pilot light is lit. I don't recall the specific model though I can look that up if people think it will help. I have actually turned up the thermostat on it above the default and when the water heater is putting out hot water, it can be very hot. Too hot. But again, that requires us to prime it before we get any decent amount of hot water out.  UPDATE 2 Looked it up, I believe this is the model info if that helps anyone: State Select: High Output. Model number: GS675XRRS 300