The Maximum possible order for an element $S_n$
Maximal order of an element in a symmetric group
$(12)$ and $(123\dots n)$ are generators of $S_n$ How to use "who" vs. "that" I often get confused when trying to use who vs that.  Some examples that often confuse me:  That     The person that went to the store.      The people that went shopping.      The persons that went shopping.      The group that went shopping.   Who     The person who went to the store.      The people who go shopping.   Please explain when to use either for plural subjects and singular subjects.  Animate and inanimate objects as well. MTG: Sideboard if maindeck has more than 60 cards I have a lidar file (file.las) with the following spatial reference:  Spatial Reference:            PROJCS["NAD83 / UTM zone 11N",     GEOGCS["NAD83",         DATUM["North_American_Datum_1983",             SPHEROID["GRS 1980",6378137,298.2572221010002,                 AUTHORITY["EPSG","7019"]],             AUTHORITY["EPSG","6269"]],         PRIMEM["Greenwich",0],         UNIT["degree",0.0174532925199433],         AUTHORITY["EPSG","4269"]],     PROJECTION["Transverse_Mercator"],     PARAMETER["latitude_of_origin",0],     PARAMETER["central_meridian",-117],     PARAMETER["scale_factor",0.9996],     PARAMETER["false_easting",500000],     PARAMETER["false_northing",0],     UNIT["metre",1,         AUTHORITY["EPSG","9001"]],     AUTHORITY["EPSG","26911"]]   Then I reproject it to WGS84 with las2las:  las2las --a_srs EPSG:26911 --t_srs EPSG:4326 -i file1.las -o output.las   And I get:   Spatial Reference:                GEOGCS["WGS 84",         DATUM["WGS_1984",             SPHEROID["WGS 84",6378137,298.257223563,                 AUTHORITY["EPSG","7030"]],             AUTHORITY["EPSG","6326"]],         PRIMEM["Greenwich",0],         UNIT["degree",0.0174532925199433],         AUTHORITY["EPSG","4326"]]   But when I try to revert the transformation: from WGS84 to NAD83/UTM 11N, I get an error:  las2las --a_srs EPSG:4326 --t_srs EPSG:26911 -i output.las -o wgs2utm.las ERROR 1: latitude or longitude exceeded limits error: Could not project point for ReprojectionTransform::latitude or longitude exceeded limits0.   Why I got this error, if I am just reversing the transformation (originally from NAD83 to WGS84, and then from WGS84 to NAD83)?. How prove this $\lim_{n\to \infty}\sin{n^m}$ divergent. show that $$\lim_{n\to \infty}\sin{(n^m)}$$  divergent,where $m\in N^{+}$  I have kown $$\lim_{n\to\infty}\sin{n^2}$$  to be divergent and dense in $[-1,1]$. This is very  famous problem,the problem is first is post $AMM$( The American Mathematical Monthly,1970-1975) problem,and after some years  $AMM$ post $\sin{(n^{14})}$ in $[-1,1]$ was dense? and this is open problem.so I Guess  $$\sin{(n^m)}$$ is dense in $[-1,1]$. Why doesn't `sudo cd /var/named` work? Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$ I'm undergraduate student of mathematics.  I need to prove: $$\sum_{k=0}^{n} \binom{2n}{2k}= 2^{2n-1}$$ Can you please help me How to add and sync folders outside SkyDrive folder? I have folders with documents all over my hard drive, some which I would like to include in SkyDrive without moving them into the SkyDrive folder.  E.g. my SkyDrive folder is in C:\Users\Name\SkyDrive, but I have some files in C:\Users\Name\SyncMePlz that I also would like to be synced with SkyDrive so that I can reach them from other devices.  How can this be achieved? Can I use my laptop as a second monitor? How can I get grub2 to boot a different option only on the next boot? Let $f$ be an analytic function such that $\operatorname{Im}(f(z))=\operatorname{Re}(f(z))^2$. Prove that $f$ is constant. How to solve this question? Also it would be great if someone could tell me from which book this question is from? Why does magnet attract iron but not other metals? While searching, i found this page:  but it does not have full explanation. So Please tell full explanation of why this happens? Assuming file2 already exists, the command   &gt; file1 &lt; file2 cat   appears to be copying the content of file2 to file1.  But I cannot understand this structure.  I understand that "Nothing" is being directed to file1 (creating or erasing its content). Then the content of file2 is being directed to file1.  Why is cat after file2? How does it know to cat file2 if the operands are not in the correct order? Why are trivial edits discouraged? Looking at  privilege, I find this to be a surprising requirement:  Try to make the post substantively better when you edit, not just change a single character. Tiny, trivial edits are discouraged.  What motivated this, or rather, what does this mean exactly? Does that, for example, include removing stuff like &quot;Hi, all&quot;, and &quot;thanks in advance&quot;? [update] I was led to a  talking about this topic, but it has a million Comments, and doesn't really justify the rule (unless it's hidden in those million Comments). However, looking at Jeff's Comments gives me an idea that this was meant as a general guideline, instead of a hard-and-fast rule: If you edit a post, check elsewhere on that post if there are other improvements that can be made. London Heathrow airport - do I need a transit visa? Error in if/while (condition) {: missing Value where TRUE/FALSE needed Determine the exact value of equations involving more two trig variables $2\cos^2x=1+\sin x$.  Determine the exact values of $x$ such that $0 \leq x \leq 2\pi$.    I am experiencing problems with factoring this question.  First I started by getting everything on to the left side so: $2\cos^2x-\sin x-1=0$.  Then seeing as there are two trig variable here ($\cos$ and $\sin$), I used the pythagorean identity and replaced $2\cos^2x$ with $1-2\sin^2x$ to make it into a one variable question: $1-1-2\sin^2x-\sin x-1=0$.   By collecting like terms it then becomes $-\sin^2x-\sin x=0$.  Now you could factor these with $0$ and $-1$, but then it creates uneven brackets so this musn't work.  I don't think the quadratic formula is necessary, but I am wondering if this could be treated as a difference of squares question.    If you replace the $\sin x$ and make the question into $-x^2-x=0$ it is a little easier to look at, however I am not sure if this is the right approach.  If someone could please clarify my answer, that would be appreciated! Basically the problem is that each time the assembly version changes (i.e. the user installs a new version of the application) all their settings are reset the the defaults (or more accurately a new user.config file is created in a folder with a different version number as the name)  How can I keep the same settings when upgrading versions, since using ini files or the registry seem to be discouraged?  When we used Clickonce it seemed to be able to handle this, so it seems like it should be able to be done, but I'm not sure how. C# AutoComplete What blueprints become available during story? As I progress, I realize that some blueprints open up throughout the story and don't have to be researched. Are these random or are they always the same and is there a list over those? Seems you can easily waste research point if you don't know that.