Does "be on time" focus on the resultant state? My Japanese friend asked me this question today and I really wasn't sure aside from "are" maybe focusing on future tense and "be" focusing on now?
Here are some examples.  "Until the Son of God appear" What I was taught: Subjunctive of indefinite future.  "It is required that the applicant be 18 years old and possess a valid driver's license." What I was taught: mandative subjunctive.  "Where be ye going," said the false knight on the road?" What I was taught: subjunctive of direct discourse.  "If I were you, which we both are thankful I am not, I wouldn't do that. What I was taught: The subjunctive mood is used for supposition contrary to fact.  "I dreamed I were a fireman in my Maidenform bra." What I was taught: The subjunctive mood can be used with words like dream.  "God bless you." I don't remember, so obviously I wasn't taught.  I can live with Pluto's not being a planet, but I must say it's irksome to find that so much of what I was told about English turns out to be nonsense.
Why has this configuration chosen for feedback? Exercise 3.5.12. Let $ f: \mathbb N \times \mathbb N \to \mathbb N$ be a function, and let c be a natural number. Show that there exists a function $a:\mathbb N\to \mathbb N$ such that $$a(0)=c$$ and $$a(n++)=f(n,a(n))\;for\;all\;n\in \mathbb N,$$ and furthermore that this function is unique. Tao gives the hint: first show inductively, by a modification of the proof of Lemma 3.5.12, that for every natural number $N\in \mathbb N$, there exists a unique function $a_N:\{ n\in \mathbb N:n\lt N\}\to \mathbb N $ such that $a_N(0)=c$ and $ a_N(n++)=f(n,a(n))$ for all $n\in \mathbb N$ such that $n\lt N$.  In my opinion, we could solve it by proving that $\forall n\in \mathbb N,a(n)\in \mathbb N$ according to mathematcial induction.  The property P(n) is:$$\forall n\in \mathbb N, a(n)\;is\;unique$$ P(0) is true. And if P(n) holds, P(n++) is true because different natural numbers must have different successors. $$a(n++)=f(n,a(n))$$ $$a(m++)=f(m,a(m))$$ $$n++=m++\Rightarrow n=m\Rightarrow a(n++)=a(m++)$$ It's similar to the proof of  Proposition 2.1.16 (Recursive definitions): Suppose for each natural number $n$, we have some function $f_{n} : \mathbb{N} \rightarrow \mathbb{N}$ from the natural numbers to the natural numbers. Let $c$ be a natural number. Then we can assign a unique natural number $a_{n}$ to each natural number $n$, such that $a_{0} = c$ and $a_{n{++}} = f_{n} (a_{n})$ for each natural number $n$.  This proof indicates both the existence and uniqueness of the function $a$. I don't know why Tao says it's informal.  But regarding the hint, how do we get the function f even if we've got the conclusion from the hint. Also it seems like the function a(n) can be diffentent considering different N. I don't know if the hint is correct. Moderncv package - cventry date width Connecting two relative clauses in one sentence I would like to write an essay which gives information about the charts but because I am not native English speaker, when I started to write down my essay I came across the similar problems that I do sometimes.  Here my sentence:  Figure 1 and figure 2 show the percentage of people, WHOSE age is between 25-44 and over 65, WHO purchased concert, cinema and theater tickets online over the first three months of 2006 in three countries, WHICH are Australia, the UK, Malaysia.  Here is my questions:  1.How can I give the information of age and of what do people buy in one sentence?  2.Such vital and important information on the figures can be used as indefinite relative clause? My input file is,  ami21 ami65 ami67 ami66 ami88 ami76 ami29 ami55  ami54 ami32   Using a single command line I need the output as,  ami22 ami66 ami68 ami67 ami89 ami77 ami30 ami56 ami55 ami33   I used the command  awk -vRS=ami '{$0=$0+1;ORS=RT}++n' inputfile &gt; outputfile   but I got the outputfile as ami21ami65ami67ami66ami88ami76ami29ami55ami54ami32  i.e. all strings are written in same line and without space. Could anyone suggext me some better command line. QGIS Processing - Additional Creation Parameter for GdalWarp I am having a hard time getting the "Additional Creation Parameters" to work when using GdalWarp through the processing toolbox.  I am trying to set the nodata value to 0 for the output raster.  processing.runalg("gdalogr:warpreproject","InRaster.tif","EPSG:32736","EPSG:32736",10,0,"-dstnodata 0","OutRaster.tif")   Has anyone used this functionality and managed to get it to work? How to place a float at the top of a floats-only page? I'm a Windows/Mac/Ubuntu and Android user, so I know what I'm talking about, when I say: How do I open binary image files? (.img) They just won't open, on any OS…  I'm an Android dev… I'm currently working on a ROM, (I also program, using Windows) but I need to extract files, from .img files. I've converted them to .ext4.img but they just aren't recognized by Linux (Definitly not by Android), by Mac OS or Windows. In other words, I can't open, extract or mount them.  Can anyone help me? I'm kinda confused… I have what seems to me a very simple proof that $A_{n}$ is the only subgroup of $S_{n}$ of index 2.  Since I've seen other people prove it with what feel like really complicated methods (), I'm wondering if I've overlooked something.  Proof: Let $H$ be any subgroup of index 2 in $S_{n}$.  Then $H\cap A_{n}$ is a normal subgroup of $A_{n}$ and since $A_{n}$ is simple, $H$ is either the trivial or the improper subgroup of $A_{n}$.  If it's the trivial subgroup it doesn't have index 2 in $S_{n}$, and otherwise the theorem is proved. Are there rules for disassembling a slain creature, especially dragon? I am looking for a good GTD (todo/task/project management) app that has cloud sync. I'd like it to be on my iPhone, iPad and Mac. Web app would be nice, too.  OmniFocus is the closest thing I've found but it seems too expensive.  Things don't have clound sync... only WiFi sync is available for Things.  Do you know of any GTD app I'm looking for? Thanks! How to obtain optimal hyperparameters after nested cross validation? Space after LaTeX commands How do I edit an invalid sudoers file? It throws the below error and it's not allowing me to edit again to fix it.  Here is what happens:  $ sudo visudo &gt;&gt;&gt; /etc/sudoers: syntax error near line 28 &lt;&lt;&lt; sudo: parse error in /etc/sudoers near line 28 sudo: no valid sudoers sources found, quitting jQuery not working in Wordpress 3.5 I just came across this glowy ore, and my 'Sharp Silver Pickaxe' won't mine it. I'm playing on the PC version of Terraria, if that helps.  How do I mine the glowy ore block? How to roll perception checks for characters who aren't actively looking without arousing suspicion? This applies to all d20 systems, but with an example from the from the Pathfinder  (emphasis mine):  Stonecunning: Dwarves receive a +2 bonus on Perception checks to potentially notice unusual stonework, such as traps and hidden doors located in stone walls or floors. They receive a check to notice such features whenever they pass within 10 feet of them, whether or not they are actively looking.  In this case, does the GM roll the check in secret or ask the player roll the check? If the GM asks the player to roll for the check, what stops situations like:  GM: (interrupting) &quot;Gimli, Roll a perception check.&quot; Dwarf player: &quot;Oh, it's a natural one, I guess I don't see anything.&quot; Human player: &quot;Okay, I'll roll a perception check for anything unusual in this room. Nice! 19. How about 19, does 19 work for you?&quot; GM: &quot;Gimli, everything looks kosher to you. Aragon, you notice a rock coloured tarp on the ground here, covering what looks like a pit trap.&quot;  In this case, by telling the dwarf to roll his &quot;free&quot; perception check, he's telegraphed to the players that there is something to notice. How can this be fixed, without bluffing checks for nothing in particular to throw off the signal to noise ratio of similar checks? How does one solve the matrix equation $AX+XB=C$ for $X$? It doesn't seem too difficult. I tried many times but failed.  I'm an adult student... I am now vexed about Gilbert Strang - An Introduction to Linear Algebra. I don't even understand a single word in Wikipedia: . If you have ever use some nice workable materials or lecture notes? You can generously upload and share the links of the lecture notes and assignments. Different subjects/ topics are welcome, as long as you deem they are nice and workable.   The problem origins from a system of diff equation, using undetermined coefficients (matrix) to find the particular solution. Try $y_p=X\begin{pmatrix}   e^{\alpha t} \\ e^{\beta t} \end{pmatrix}$  $\dot{y}+Ay=C\begin{pmatrix} e^{\alpha t} \\ e^{\beta t}\end{pmatrix}$   $\dot{y_p}=X\begin{pmatrix} \alpha &amp; 0 \\ 0 &amp; \beta \end{pmatrix} \begin{pmatrix}e^{\alpha t} \\ e^{\beta t}\end{pmatrix}$  substitute $\dot{y_p}$ and $y_p$ into the original differential equation..  $X\begin{pmatrix} \alpha &amp; 0 \\ 0 &amp; \beta \end{pmatrix}+AX=C$ I want to encrypt a USB stick, and be able to decrypt it on Windows as well as Ubuntu. How do I do this &amp; what programs do I need to use? Guest (not logged in) users can only sort questions with specific tag by newest I think this is platform wide (all SE sites).   Logout Choose a tag, eg.  on SO Try to sort questions by something other than newest   No matter what sorting is chosen, questions are sorted by newest