What does this bash syntax means? ETL_PORT="${ETL_PORT:-6090}"
Using "${a:-b}" for variable assignment in scripts
I am trying to prove the following statement but have trouble  comprehending/going forward with some parts! Here is the statement:     If $A$ is any set, then  $|A|$ $&lt;$ $|P(A)|$   Here is what I have so far:  We need to show that there is an injection from $A$ to $P(A)$ but not a surjection.   A natural choice for an injection is the function $ f(x)$ $=$ $\{x \}$, which in plain English, takes any element $x$ (that is in $A$) and sends it to the one-element set $\{x \}$. Thus $f(x)$ is injective!  To show that there is no surjection, for the sake of contradiction, assume there is a surjection. Here is where I start to have trouble. Surjectivity means that every element of the co-domain is mapped to an element of the domain, correct? Consequently, in this particular case, we are "matching" sets (from $P(A)$) to elements (from $A$) right?  If the above is correct, my problem arises here. I am not sure how to prove that $f$ is not surjective. Unfortunately, I am easily confused by notation so please explain in English.  Thank you in advance!! :) Deriving even odd function expressions What is the logic/thinking process behind deriving an expression for even and odd functions in terms of $f(x)$ and $f(-x)$?  I've been pondering about it for a few hours now, and I'm still not sure how one proceeds from the properties of even and odd functions to derive: $$\begin{align*} E(x) &amp;= \frac{f(x) + f(-x)}{2}\\ O(x) &amp;= \frac{f(x) - f(-x)}{2} \end{align*}$$ What is the logic and thought process from using the respective even and odd properties, $$\begin{align*} f(-x) &amp;= f(x)\\    f(-x) &amp;= -f(x) \end{align*}$$   to derive $E(x)$ and $O(x)$?    The best I get to is: For even: $f(x)-f(-x)=0$ and for odd: $f(x)+f(-x)=0$  Given the definition of $E(x)$ and $O(x)$, it makes a lot of sense (hindsight usually is) but starting from just the properties. Wow, I feel I'm missing something crucial. Why are some actors uncredited in certain films? Eli Wallach  in Mystic River. Olivia Williams  in X-Men: The Last Stand. However, neither of them (according to IMDb) is credited in the movie. These two instances are simply examples.  Why are some actors, who are oftentimes quite well known, not credited in certain features? Basically I have a setup like the following:  Array (  [0] =&gt; Array ( [0] =&gt; stdClass Object ( [nid] =&gt; 1 [title] =&gt; title1 [uid] =&gt; 1 [parent] =&gt; 0 [weight] =&gt; -15 [name] =&gt; name1 [value] =&gt; 0 )                [1] =&gt; stdClass Object ( [nid] =&gt; 2 [title] =&gt; title2 [uid] =&gt; 1 [parent] =&gt; 0 [weight] =&gt; -7 [name] =&gt; name2 [value] =&gt; 100 )                [2] =&gt; stdClass Object ( [nid] =&gt; 3 [title] =&gt; title3 [uid] =&gt; 2 [parent] =&gt; 0 [weight] =&gt; -1 [name] =&gt; name3 [value] =&gt; 0 )                [3] =&gt; stdClass Object ( [nid] =&gt; 4 [title] =&gt; title4 [uid] =&gt; 2 [parent] =&gt; 0 [weight] =&gt; 1 [name] =&gt; name4 [value] =&gt; 80 )               )   )   What I need is a way to sort all the arrays inside the parent array by the [value] key in the Object. I've been trying for about 2 days now with usort and different methods but I just can't seem to get my head around it. The [value] key will range anywhere from 0 to 100 and I need all of the arrays sorted in decreasing order (IE: 100 down to 0). Why is df missing 500MB of available space? I've just had a message today from Ubuntu 11.04 that I have only 100 MB left, so I cleaned up some files, and I got 200 MB. Then, after a couple of hours, suddenly I have only 26 MB?! I tried df, du via mount --bind, /forcefsck with reboot - nothing could should what the culprit is - finally I searched big files, realized /var/log/syslog is 100MB+ and /var/log/kern.log is 200MB+ - blanked them with sudo bash -c 'echo &gt; ...' and rebooted, and now I have some spare MB.  But now, I realize I have another problem with df:  $ df -h Filesystem            Size  Used Avail Use% Mounted on /dev/sda5             9,7G  8,8G  385M  96% / none                  963M  696K  962M   1% /dev none                  969M   12K  969M   1% /dev/shm none                  969M  252K  969M   1% /var/run none                  969M     0  969M   0% /var/lock /dev/sda6             9,7G  8,1G  1,1G  89% /media/disk  $ df -h --block-size M Filesystem           1M-blocks      Used Available Use% Mounted on /dev/sda5                9845M     8960M      385M  96% / none                      963M        1M      962M   1% /dev none                      969M        1M      969M   1% /dev/shm none                      969M        1M      969M   1% /var/run none                      969M        0M      969M   0% /var/lock /dev/sda6                9845M     8235M     1110M  89% /media/disk   Note so for /, it says there are 9845M total; and Used 8960M - then remaining would be 9845-8960 = 885 M, however, here I have only 385M Available.  Also, for /media/disk, it says total 9845M, Used 8235M - then remaining would be 9845-8235 = 1610, however, here I have only 1110M Available.  In both cases, there is exactly 500 MB difference.  Where did this difference come from - and can I reclaim it?  Here is also lsof | grep 'deleted' - can't see nothing suspicious here:  $ lsof | grep 'deleted' nautilus  1911 user   21u      REG        8,5   142760     260562 /home/user/.local/share/gvfs-metadata/home (deleted) nautilus  1911 user   22w      REG        8,5    32768     268807 /home/user/.local/share/gvfs-metadata/home-fe882154.log (deleted) python    1919 user    8u      REG        8,5     4096     392258 /tmp/ffiqRK968 (deleted) python    2165 user    5w      REG        8,5        0     132261 /home/user/.[SNIP].lock (deleted) python    2166 user    5w      REG        8,5        0     132261 /home/user/.[SNIP].lock (deleted) python    2185 user   21r      REG        8,5   142760     260562 /home/user/.local/share/gvfs-metadata/home (deleted) python    2185 user   22r      REG        8,5    32768     268807 /home/user/.local/share/gvfs-metadata/home-fe882154.log (deleted) gnome-ter 2279 user   27u      REG        8,5      640     392575 /tmp/vte5KDX2X (deleted) gnome-ter 2279 user   28u      REG        8,5     4936     392605 /tmp/vteKRDX2X (deleted) gnome-ter 2279 user   29u      REG        8,5      648     392947 /tmp/vteMZDX2X (deleted) ubuntuone 2544 user   17u      REG        8,5     4096     392335 /tmp/ffiMErq0V (deleted) bamfdaemo 3235 user   12r      REG        8,5   143868     269077 /home/user/.local/share/gvfs-metadata/root (deleted) bamfdaemo 3235 user   13r      REG        8,5    32768     272310 /home/user/.local/share/gvfs-metadata/root-18092a02.log (deleted) firefox   5291 user   59u      REG        8,5    33288     132262 /var/tmp/etilqs_YdeZiWSd5iQwJ4U (deleted) firefox   5291 user   60w      REG        8,5    32768     132271 /var/tmp/etilqs_MNLXhEaEqoXMm9b (deleted) firefox   5291 user   70u      REG        8,5    34952     132297 /var/tmp/etilqs_yXDdwVeMxmmdpNz (deleted) Prove that, $f'(0) \ge -\sqrt{2}$ for a function $f$ satisfying some conditions on $(-1,1)$. Let $f:(-1,1)\to \mathbb{R}$ be a twice differentiable function such that, $f(0)=1$, $f'(x)≤0$, $f(x)≥0$ and $f''(x)≤f(x)$ for all $x≥0$. Prove that, $f'(0)≥-\sqrt2$   Progress: I was able to prove $f'(0)≥-2$. For this I have applied Cauchy MVT for $f'$ and $g$ on $[0,x]$ for any $x\in (0,1)$ where $g: [0,x]\to\mathbb{R}$ is defined by, $g(x)=\sqrt{x+1}$. But, couldn't find another approach to get $-\sqrt{2}$. Updating the SubscriberKey on the All Subscriber table through the API I'm trying to update an existing Subscriber in the All Subscriber Table through the API; i've set up the AppId in the App Center and have connected and created Subscribers, but i'm still having issues updating.  What call do I need to be making to do this? These are the ones i've been trying. Changing plurality in parentheses If a set of parentheses lies between a subject and its verb, and the parentheses contain an substitutive subject whose singularity/plurality disagrees with the original subject, whose singularity/plurality should be chosen for the verb?  In other words, in the following example, should "questions" (and its verb "are") be singular, or should they remain plural as shown?     Many (if not every) questions on this StackExchange are answered.   My intuition tells me that the two words in question should remain in plural forms, since the text in parentheses only interrupts the sentence (and the sentence would be grammatically incorrect if everything in parentheses were removed and the words were in singular form).  On the other hand, when read aloud (assuming one reads the text in parentheses), this has an uncomfortable sound to it, and I've seen others write in what would be the above example's singular-form case, so I'm curious to find out which is correct.  And, thinking about it, I suppose the same question would apply when commas are used in place of parentheses. I just bought a house. Now I'm getting ads in the mail every day or two trying to get me to sign up to pay my mortgage bi-weekly (every two weeks) or weekly instead of monthly. In their words I could cut seven years and thousands of dollars off what I pay in long term. It seems like I would be paying the exact same amount of money, also.  I know "if something sounds too good to be true then probably it is". But I cannot figure out why in this case. What is the catch? Or is this something I should be signing up for ASAP? Give a one-to-one and onto function from $\mathbb{N} \times \mathbb{N}$ to $\mathbb{N}$ Why am I getting "line 1: $' :\r': command not found"? I use Cygwin on my laptop (DOS). I have a collection of scripts from my colleagues, and my own. I am not an IT person, not knowledgeable in Unix. I am following my colleagues' syntax and able to manage a few simple things. The scripts worked well on my old laptop. I just changed laptop and installed Cygwin. When I run my scripts, they do not work. Here is one example of the error message I get: line 1: $':\r': command not found line 5: syntax error near unexpected token `$'\r'' line 5: `fi  Here are the top 5 lines of my script : iter=1 if [ -f iter.txt ]    then rm ./iter.txt  fi    Can someone please explain how I can get around this problem? How to group distinct values from a list using odata rest api the verb in plural with one company Can't get rid of header X-Powered-By:Express Is it acceptable to change the vid column of a term programmatically in the database? I need to move some terms from one vocabulary to another by retaining all their data: translations, aliases, and node references.  Is it acceptable to change its vid column value directly in the database? The terms don't have hierarchy relationships which needs to be handled. In the middle of touching up a new texture, I pressed save and suddenly my textures all turned black on the model and UV texture - just vanished.  I tried reopening the file in another instance of Blender, I tried to CtrlZ too and it just did this weird patchy thing on my texture.   How do I recover it and what did I do wrong? how to set static ip from bash scriptlinux I want to set static IP using bash script what I would to achieve I want to set the same IP to static which is come from DHCP, for example, my eth0 set to DHCP and it picks IP 51.89.84.82 for eth1 it pick 10.0.0.1 I want to set the same IP to static how can I achieve this in centos7. 1 ) find interface name and its ip , subnet mask , gateway. 2 ) loop each interface and set the same ip , subnet and gateway. $2 \times 2 $ Orthogonal Group I am trying to prove that $O(2)$ has two connected components. This is what I have done: Suppose $A \in O(2)$. Then $A^tA=I$, where $A^t$ is the transpose of $A$ and $I$ is the identity. Taking the determinant of both sides of this equation, we get $\det(A^t)\det(A) = (det(A))^2$   which implies $\det(A) = \pm 1$.  And since $\det$ is continuous (which means that the inverse image of an open set is open), we have $O(2)$ is the disjoint union of $O^+(2)$ and $O^-(2)$. Is this right? Would this be sufficient or would this only prove that there are at least two components? How to prove that center of $GL_n(\mathbb R)$ is scalar matrices?  Again what can you say about the center of set of all upper triangular matrices and center of set of all diagonal matrices. How to test whether a file uses CRLF or LF without modifying it? I need to periodically run a command that ensures that some text files are kept in Linux mode. Unfortunately dos2unix always modifies the file, which would mess file's and folder's timestamps and cause unnecessary writes.   The script I write is in Bash, so  I'd prefer answers based on Bash.