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Using SQL Server, how do I split a string so I can access item x?  Take a string "Hello John Smith". How can I split the string by space and access the item at index 1 which should return "John"? (Pardon if this seems a bit beginner, this is my first post in math - trying to improve my knowledge while tackling Project Euler problems)  I'm aware of Sigma notation, but is there a function/name for e.g.  $$ 4 + 3 + 2 + 1 \longrightarrow 10 ,$$  similar to $$4! = 4 \cdot 3 \cdot 2 \cdot 1 ,$$ which uses multiplication?   Edit: I found what I was looking for, but is there a name for this type of summation? Given the Lie algebra, what is the systematic way to construct the matrix representation of the generators of the desired dimension? I ask this question here because it is the physicists for whom representation of groups is more important than mathematicians.   Let us, for example, take $SU(2)$ for concreteness. Starting from the generic parametrization of a $3\times 3$ unitary matrix $U$ with $\det U=1$, and using the formula of generators $$J^i=-i\Big(\frac{\partial U}{\partial \theta_i}\Big)_{\{\theta_i=0\}}$$ one can find the $3\times 3$ matrix representation of the generators.  However, I'm looking for something else.    Given the Lie algebra $[J^i, J^j]=i\epsilon^{ijk}J^k$, is there a way that one can explicitly construct (not by guess or trial) the $3\times 3$ representations of $\{J^i\}$? Will the same procedure apply to solve other Lie algebras appearing in physics such as that of $SO(3,1)$ (or $SL(2,\mathbb{C})$)? How do you get \mathbb{1} to work (characteristic function of a set)? Colorimetry is not the same Could the missing antimatter lie outside the observable universe? I dont quite understand how pipes work in bash.  I know that it takes an output from one command as the input in another command.  What an output is I can get because it's what the command prints out to the screen.  But how do I know what input a command will take?  Here is an example I thought would work:  which gem | rm   Unfortunately it didn't.  Which gem prints out /usr/bin/gem so that must be the output right?  I thought that was given to rm so it woud be rm /usr/bin/gem but I was wrong.  So my question is, how do I know what input a command takes? Can I have dynamic custom variables in Word? I'm basically trying to create a variable in a document, let's say the name of a person, so that I can change the value in a single place and it updates through the whole document.  I've been reading about Fields and about a DOCVARIABLE, but I can't find where to edit the value (right clic didn't show an "edit" option). I'm using Word 2011 for Mac (that's what we have at work right now) so I'm wondering whether this version of Word is just not intuitive, or I cannot have variables like that in Word and I'm misinterpreting the documentation.  This is what I intend to do:  Hello, my name is PERSON_NAME, I have PERSON_AGE years old.   You get the idea.  PS: We actually want to modify the variables' values from our app, rather than from Word itself, kind of like injecting values to a .*docx file. Intuitive explanation of the tower property of conditional expectation I understand how to define conditional expectation and how to prove that it exists.  Further, I think I understand what conditional expectation means intuitively. I can also prove the tower property, that is if $X$ and $Y$ are random variables (or $Y$ a $\sigma$-field) then we have that  $$\mathbb E[X] = \mathbb{E}[\mathbb E [X | Y]].$$  My question is: What is the intuitive meaning of this? It seems quite puzzling to me.  (I could find similar questions but not this one.) Order of automorphism group of cyclic group Let $G$ be a cyclic group of order $m$. What is the order of $\text{Aut}(G)$?  I want to know the proof as well (elementary if possible). I would still accept the proof if one answers with $m = p$, a prime. Or on top of that, I would accept the answer with extra assumption: $q \equiv 1$ mod $p$ with another prime $p$. Class of sets of a given infinite cardinality This question was inspired by the question on .  From the discussion in the comments there, it seems there does not exist a set of all sets of a given cardinality.  To me, it seems easy to see that this is true for any nonzero finite cardinality $n$. Given any set $x$, you can always make a set of size $n$ by adding $n-1$ other sets to $x$ to make a set of size $n$, which exists by repeated use of the pairing axiom.   But how would you do this for infinite cardinalities? For suppose $\kappa$ is some given infinite cardinality. To show that the set of all sets of cardinality $\kappa$ does not exist, it seems you would have to show that for any set $x$, there exists a set of that size with $x$ as an element, and then you could take the union of that set to find the set of all sets, and thus a contradiction. But it doesn't seem reasonable to simply say, for a given set of size $\kappa$ if $x$ is in the set, we have no problem. If not, just take an element out of the set and put $x$ in. Something about that seems like it would not be allowed.  So how would you do this for infinite cardinalities? Puzzle: Find largest rectangle (maximal rectangle problem) In bash, read after a pipe is not setting values With ksh I'm using read as a convenient way to separate values: $ echo 1 2 3 4 5 | read a b dump $ echo $b $a  2 1 $  But it fails in Bash: $ echo 1 2 3 4 5 | read a b dump $ echo $b $a     $  I didn't find a reason in the man page why it fails, any idea? Displaying attachments on visual force page I need to display attachments on a visual force page for the Case object.  This is the code I am using. I had it working for awhile, but it somehow broke down. It gets all the attachments, but it will not show the images.   &lt;apex:repeat value="{!Case.attachments}" var="att"&gt;             &lt;apex:panelgrid columns="1"&gt;                 &lt;h1&gt;Image/h1&gt;                 &lt;apex:image url="/servlet/servlet.FileDownload?file={!att.Id}"/&gt;             &lt;/apex:panelgrid&gt; &lt;/apex:repeat&gt; I engaged with some enemy NPCs, and accidentally shot a civilian in the head (though not sure it would've mattered if I hit them somewhere else or not) as they ran across my screen. As a result of this, I was alerted by the game that the NCPD (the police) were automatically en route to 'investigate', and that I could avoid them by leaving the area and &quot;lying low for a while&quot;. How long does it take for the police to stop searching for me, and is there any kind of visual information on the HUD that alerts me to when NCPD is or is no longer looking for me? During my upcoming holiday to the USA I'm thinking about buying a new guitar as the exchange rate is extremely favorable. Excuse my naivety but I have never flown with a guitar before. What is a recommended way to go about this? Could I take it as carry on luggage or would it have to be checked? If checked luggage what kind of precautions should I take to keep it safe? Are there any problems with flying US budget carriers? If I do buy the guitar I'm expecting to have to make two flights with it, one domestic flight with Virgin America and an international flight with Air NZ. Finding total after percentage has been used? Tried my best with the title. Ok, earlier while I was on break from work (I have low level math, and want to be more fond of mathematics)  I work retail, and 20% of taxes are taken out, and I am wanting to find out how much I made before 20% is taken out.  So I did some scribbling, and this is without googling so please be gentle. but lets say I make 2000 dollars per paycheck, so to see how much money I get after taxes I do 2000 * .8 which gives me 1600. I can also do 2000 * .2 which gives me 400 and then do 2000 - 400 (imo I don't like this way since I have a extra unnecessary step)  Anyways, I was pondering how to reverse that to have the answer be 2000, and what I did was 1600 * 1.20 (120%) which gave me 1920, and I thought that is odd so I did 1600 * 1.25 and answer was 2000 exact.  My question is why did I have to add extra 5% (25%) to get my answer? I am sure I did something wrong, and I fairly confident the formula I am using is a big no no.  edit; wow thank you all for your detailed answers. I am starting to like mathematics more and more. Is it possible to put commands in /etc/motd? Can I put shell commands in the /etc/motd login banner file? I have tried:   $(uptime)   and  `uptime`   Is this possible? Keeping tables/figures close to where they are mentioned How to show that every Boolean ring is commutative?