As an Example, I want to refer to this  where there are many conditional sentences. Some of them drop the "then", some of them use it. When I change that (drop it where it was used or add it where it was dropped) then some still sound correct, but some sound a little odd, though all of them are still grammatically correct.  Originals:     If you heat water to 100 degrees, it boils. If the sea is stormy, the waves are high. If it's raining here now, then it was raining on the West Coast this morning. If it's raining now, then your laundry is getting wet. If it's raining now, there will be mushrooms to be picked next week. If he locked the door, then Kitty is trapped inside.   Changed:     If you heat water to 100 degrees, then it boils. If the sea is stormy, then the waves are high. If it's raining here now, it was raining on the West Coast this morning. If it's raining now, your laundry is getting wet. If it's raining now, then there will be mushrooms to be picked next week. If he locked the door, Kitty is trapped inside.   Questions:    Is there a term for dropping "then" in conditional sentences? Are there any guidelines on when it can be dropped and when it must be retained?   EDIT: There is an existing question (  ) but that is more of an "YES/NO" type of question and it has been answered with "YES". Here, the question "When" in terms of guidelines : When it is useful to drop ; When it is useful to retain.
I have the following sentence:     If T had still been alive, there is the great possibility that either T or C ...   My teacher says that the word "then" must appear after the comma, but I think that it's implied and unnecessary. Who is right?
Stuck on two valid squares in minesweeper How to solve? The 1 indicates that ones of the two questioned flags is a mine and 3 also indicates the same. How to choose logically between any one of them? Forcing SSL and www in .htaccess I'm looking for a way to force SSL and www.  I've been able to force both separately but together I keep running into redirection issues. The following code works when handling a URL in this format: http://example.com and properly redirects to https://www.example.com but when the incoming URL is https://example.com it will not forward to https://www.example.com - Any suggestions?  EDIT: it should also send http://www.example.com to https://www.example.com.  RewriteCond %{REMOTE_ADDR} !127\.0\.0\.0 RewriteCond %{SERVER_PORT} 80 RewriteCond %{HTTP_HOST} !^www.example\.com$ RewriteRule ^(.*)$ https://www.example.com/$1 [R,L] I was reading . They are performing a logistic regression (with R). At some point they calculate the probability of getting a residual deviance higher than the one they got on a $\chi^2$ distribution with degrees of freedom equal to the degrees of freedom of the model. Copying-pasting from their website...   &gt; glm( cbind(using,notUsing) ~ age + hiEduc + noMore, family=binomial)  Call:  glm(formula = cbind(using, notUsing) ~ age + hiEduc + noMore,            family = binomial)   Coefficients: (Intercept)     age25-29     age30-39     age40-49       hiEduc       noMore       -1.9662       0.3894       0.9086       1.1892       0.3250       0.8330    Degrees of Freedom: 15 Total (i.e. Null);  10 Residual Null Deviance:      165.8  Residual Deviance: 29.92        AIC: 113.4        The residual deviance of 29.92 on 10 d.f. is highly significant:  &gt; 1-pchisq(29.92,10) [1] 0.0008828339       so we need a better model     Why does it make sense to compute 1-pchisq(29.92,10) and why does a low probability indicate that something is going wrong with their model? How long will foods that have "Best by: XX-XX-XX" on the product last past that date?  I have tried looking online, and all I can find is anecdotal evidence, which isn't very assuring for me since there seems to be no specific "x food will expire y weeks after its best by date".  Is there a rule of thumb or some guide out there that can tell me how long a "best by" food will last? Or is it safe to assume that they never expire, since it's not actually labelled on the product? Map bounded if composition is bounded Whether the players killed a mage and got his spellbook(s) or they met with a nice wizard who let him or her learn a spell from his spellbook, can a player prepare a spell from a spellbook that isn't his or hers?  I'm asking because the PHB p. 114 says:     [...] Preparing a new list of wizard spells requires time spent studying your spellbook and memorizing the incantations and gestures you must make to cast the spell: at least 1 minute per spell level for each spell on your list.    emphasis mine   Further, the block on the left as a Copying a Spell into the Book ("the" Book as in "your" Book, since it appears in the block titled Your Spellbook), which explains how you can copy a spell from one book to another, assuming the book is from a stranger, it cost more and takes more time. It actually says:     [...] deciphering the unique system of notation used by the system of notation of the wizard who wrote it. [...]   It continues saying that you have to learn the various parts of the spell (verbose, material, gesture.)  This makes it sounds like a wizard would have a really hard time to prepare a spell from another's spellbook. Is that the case? Is it possible to repeat my track object along a path? I tried using the method shown here  using an array and then a curve modifier, but this happened when I added the curve modifier and chose the path as the curve object. From what I've seen it looks to me like Libav's avconv is thought to become a successor of ffmpeg — is that correct?   If that's true, why is that so? What exactly is libav doing better and why would I want to choose it over ffmpeg?   I came to this "issue" while installing Ubuntu 12.04.1 LTS in a VM and when I've installed ffmpeg it came up with a message telling mit ffmpeg is deprecated and I first thought "wtf?".  If I use avconvWill I be able to migrate my scripts depending on ffmpeg more or less easy to libav? I'm mostly using it for writing meta data and doing audio conversion (wav, flac, vorbis, mp3, aac). Friendly way to make previous large calculation results reusable in a new session I want to prove that $xe^{-x}$ is bounded by some constant for all the $x \in [0, \infty)$. So I take derivative of this guy, and found that on $x \in [0, \infty)$, its derivative is positive from $[0, 1)$, $0$ at $x=1$, and negative from (1, in infinity). So  $xe^{-x}$ achieves its maximum in $[0, \infty)$ at $x=1$, which is $1/e$. However, to prove that it's bounded by $1/e$, I need to prove that as $x$ goes to infinity, $xe^{-x}$ converges to $0$. Because otherwise, if it went to some value below $(-1/e)$, $xe^{-x}$ would not be bounded by $1/e$. How can I prove that $xe^{-x}$ converges to $0$? I mean, as $x$ goes to infinity, $e^{-x}$ converges to zero, but at the same time, x diverges to infinity. How can I formally prove that the product term converges to $0$? Do I need to use the epsilon definition of convergence to prove it?  Could you just show me the formal proof of $xe^{-x}$ converges to $0$? Or is there's any other way to approach this question? My professor suggested that I should use the power series for $e^{-x}$...?   Your help is greatly appreciated! Thank you so much!  I hope you enjoy your Saturday! Eigen Values Proof a.) Let A and B be $n$ x $n$ matrices. Prove that the matrix products   $AB$  and $BA$ have the same eigenvalues.      b.) Prove that every eigenvalue of a matrix A is also an eigenvalue of   its transpose $A^T$. Also, prove that if v is an eigenvector of A with   eigenvalue $\lambda$ and w is an eigenvector of $A^T$ with a different   eigenvalue $\mu \ne \lambda$, then v and w are orthogonal vectors with   respect to the dot product.   For a, I know that if their eigenvalues are the same then their eigenvectors must relate too.    For the first part of b, is it similar to proving that the $det(A) =det (A^T)$? And, I do not know how to do the second part. I've just received my new SSD since the old one died. This Intel 320 SSD supports TRIM. For testing purposes, my dealer put Windows on it, but I want to get rid of this and install Kubuntu on it.  It does not have to be a "secure wipe", I just need the empty the disk in the most healthy way. I believe that dd if=/dev/zero of=/dev/sda just fills the blocks with zeroes and thereby taking another write (correct me if I'm wrong).  I've seen the answer , but it looks like it's suited for clearing empty blocks, not wiping the disk.  hdparm seems to be the program to do it, but I'm not sure if it clears the disk OR cleans empty blocks. From its manual page:     --trim-sector-ranges           For  Solid State Drives (SSDs).  EXCEPTIONALLY DANGEROUS. DO NOT           USE THIS OPTION!!  Tells the drive firmware to discard  unneeded           data  sectors,  destroying  any  data that may have been present           within them.  This makes those sectors available  for  immediate           use  by  the firmware's garbage collection mechanism, to improve           scheduling for wear-leveling of the flash  media.   This  option           expects  one  or  more  sector range pairs immediately after the           option: an LBA starting address, a colon, and  a  sector  count,           with no intervening spaces.  EXCEPTIONALLY DANGEROUS. DO NOT USE           THIS OPTION!!              E.g.  hdparm --trim-sector-ranges 1000:4 7894:16 /dev/sdz   How can I make all blocks appear as empty using TRIM? ssh master - execute su remotely I have a server S that I need to connect to.  I'm connecting to S as user asdf with control master and after that I perform some stuff:  ssh -N -f -M -o ControlPath=$SSHSOCKET ${USER}@${IP} -p ${PORT} -i id_rsa ssh -to ControlPath=$SSHSOCKET ${USER}@${IP} -p ${PORT} "su -c whoami &amp;&amp; hostname &amp;&amp; exit"   It works as expected, but second line asks me  for password.  I am trying such fix:  echo 'qwerty' | ssh -t -to ControlPath=$SSHSOCKET ${K3_USER}@${IP} -p ${PORT} "su -c whoami &amp;&amp; hostname &amp;&amp; exit"   but it gets even worse:  muxserver_accept_control: tcgetattr: Inappropriate ioctl for device tcgetattr: Inappropriate ioctl for device Password:   For me, it's mandatory to ssh as asdf first. I also can't make any other ssh control master connections. I also can't modify any config on the target machine.  I just need to switch to root via ssh somehow. Any ideas ? How to test randomness (case in point - Shuffling) First off, this question is ripped out from  question. I did it because I think this part is bigger than a sub-part of a longer question. If it offends, please pardon me.  Assume that you have a algorithm that generates randomness. Now how do you test it? Or to be more direct - Assume you have an algorithm that shuffles a deck of cards, how do you test that it's a perfectly random algorithm?  To add some theory to the problem - A deck of cards can be shuffled in 52! (52 factorial) different ways. Take a deck of cards, shuffle it by hand and write down the order of all cards. What is the probability that you would have gotten exactly that shuffle? Answer: 1 / 52!.  What is the chance that you, after shuffling, will get A, K, Q, J ... of each suit in a sequence? Answer 1 / 52!  So, just shuffling once and looking at the result will give you absolutely no information about your shuffling algorithms randomness. Twice and you have more information, Three even more...  How would you black box test a shuffling algorithm for randomness? What exactly is the cause of RAM incompatibility? I'm looking at rather short QVL lists from manufacturers, and I'm wondering what is the underlying cause of RAM incompatibility aside from the obvious: Obvious Reasons for Incompatibility  RAM Generation (DDR, DDR2, DDR3, DDR4) Form Factor / pin count RAM Type (ECC vs Non-ECC, Registered vs not, Buffered vs not) Minimum speeds on a board that cannot adjust the memory frequency Non-standard voltage range on a board that cannot adjust the memory voltage Channel count (single vs dual vs quad) Bad or inoperable module Mismatched set  Not Obvious Reasons  Brand SKU Max Capacity Speed too high  As in, why can't motherboard manufacturers just list the specifications of the RAM they will accommodate, and support every memory chip of that category instead of listing specific SKUs from specific brands? What happens electrically/physically that causes boards to fail to POST / operate with RAM that is otherwise 'compatible' with all of the specifications of RAM that is on the QVL? Why does Lang describe a field as a union and compositum of its subfields in this manner? I am reading Serge Lang's Algebra, revised 3rd edition, and on page 226, the author makes the following definitions and observations:   If $E,F \subset L$, the compositum of $E$ and $F$ in $L$ is defined to be the smallest subfield of $L$ containing both $E$ and $F$. It is denoted $EF$. If $k \subset E$ and $\alpha_1,\dots,\alpha_n \in E$, then $k(\alpha_1,\dots,\alpha_n)$ is defined to be the smallest subfield of $E$ containing $k$ and $\alpha_1,\dots,\alpha_n$. Observe that $$ E = \bigcup k(\alpha_1,\dots,\alpha_n), $$ where the union is taken over all finite families $\{ \alpha_1,\dots,\alpha_n \}$ of elements of $E$. The compositum of an arbitrary family of subfields of a field $L$ is defined as the smallest subfield of $L$ containing all fields in the family. $E$ is finitely generated over $k$ if there is a finite family $\{ \alpha_1,\dots,\alpha_n \}$ of elements of $E$ such that $E = k(\alpha_1,\dots,\alpha_n)$. Observe that $E$ is the compositum of all its finitely generated subfields over $k$.   My question is regarding the two observations (point nos. 3 and 6). It appears to me that it is enough to take union (and compositum) over all subfields generated by a single element. For example for point no. 3, I can write $$ E = \bigcup_{\alpha \in E} k(\alpha) $$ because $E$ is clearly contained in the RHS, and each $k(\alpha)$ is contained in $E$ and hence so is the union, implying that $E$ contains the RHS. Similarly for point no. 6.  So, why does Lang emphasise to take the union and compositum over all finitely generated subfields? Is there some perspective that he wishes to emphasise that I am missing? Any help in understanding this will be appreciated. If I pass PHP variables with . in their names via $_GET PHP auto-replaces them with _ characters. For example:  &lt;?php echo "url is ".$_SERVER['REQUEST_URI']."&lt;p&gt;"; echo "x.y is ".$_GET['x.y'].".&lt;p&gt;"; echo "x_y is ".$_GET['x_y'].".&lt;p&gt;";   ... outputs the following:  url is /SpShipTool/php/testGetUrl.php?x.y=a.b x.y is . x_y is a.b.   ... my question is this: is there any way I can get this to stop? Cannot for the life of me figure out what I've done to deserve this  PHP version I'm running with is 5.2.4-2ubuntu5.3. Beamer continue block in next column I don't think I ever understood the rationale behind this.  I get that the dot product $\mathbf{a} \cdot  \mathbf{b} =\lVert \mathbf{a}\rVert \cdot\lVert \mathbf{b}\rVert \cos\theta$ is derived from the cosine rule. (Do correct me if I'm wrong.)  However, I never really understood why $\mathbf{a} \times  \mathbf{b} =\lVert \mathbf{a}\rVert \cdot\lVert \mathbf{b} \rVert \sin\theta$. Is there a proof for this?  In addition, how does the vector cross product lead to orthogonal vectors?  I remember learning that they do and I know how to solve equations using the respective formulas, but I never got why is it so. How to install PHP from source with latest cURL package on Linux? I simply have to use the latest cURL version (7.21.3) with PHP on my webserver. (Has to do with specific bug fixes)  It is not available by default on most current Linux variant repositories. (Natty Narwhal by Ubuntu is the only one and it's still in beta stages) - so I cannot simply run "aptitude install php5-curl" or similar to get it (the very latest version of cURL) installed.  How would one go about installing the very latest PHP + cURL packages?  Is it as simple as changing the to-download file for cURL in a repository somewhere? (ie. changing a text file's entry somewhere from  to  or something..?)  Basically I need the very latest cURL library running with PHP on Linux. How would you personally go about doing that?