Put figure and listing side by side
Placing listing and figure side by side in memoir
Importing single symbol from MnSymbol Shell script to send an alert mail if disk usage exceeds 90% What does limit actually mean? I have been in a deep confusion for about a month over the topic of limits! According to our book, the limit at $a$ is the value being approached by a function $f(x)$ as $x$ approaches $a$.  I have a doubt that in real number line we can never ever reach the closest value to $a$ because always a more closer value will exist.  Now when talking about our methods for calculating limit, what method comes in our mind when we have to calculate where the value approaches? Let's say we have to find what value $f(x)$ approaches when $x$ moves from $[0,a)$.  So we calculate the value of $f(x)$ at $x=0$, say $4$, and then at $x\to a$.   But the problem is that we don't know the value $x\to a$, so we say the value is $a-h$ where $h\to 0$ and calculate the value of $f(a-h)$, say $5-h$.  Now here is where my doubt starts! In the final step we put the value of $h=0$ say in that it is an infinitesimal quantity.  My doubt is that $h$ was tending to $0$ means that it was never equal to zero  maybe it is infinitesimally small, not a stationary value, not an imaginable value, but we know for sure that it is not  equal to $0$. Maybe it is the point closest to zero, but it is not equal to zero and when we use the result $5-h=5$ we are actually making an error which is tending to zero. Maybe the error is very small, but still, there is some error in that we cannot calculate it but we can see that there is this infinitesimal error present.  That means we don't get the exact limiting value or last value of $f(x)$.  $x$ belongs to $[0,a)$ but a value approximate to infinitesimal? Isn't it right! We get an approximated value? I tried this way, I only need to know if this is correct or if there are better ways to solve this:  $2^{1000}$ does not have a factor of $5$ obviously therefore we can assume  $$ 10^{m} &lt; 2^{1000} &lt; 10^{m+1}$$ for some  $m$   Assume $ k = 2^{1000}$, then take log on both sides $\log k = 1000  \log 2 \approx 301.02999 &gt; 301$  Therefore $2^{1000}$ has $302$ digits. Assume there is a public-key encryption scheme $(KeyGen, Enc, Dec)$ with perfect correctness (i.e., for all messages M and valid key-pairs (PK,SK), we have $Dec_{SK}(Enc_{PK}(M))=M$).  Will there always be a function $A$ such that for all messages M and valid public-keys PK, $A_{PK}(Enc_{PK}(M))=M$?  In other words, can a computationally unbounded adversary decrypt the message, having only the public key? How to prove that you have significant ties with family in your home country? How to delete ".."-folder under Windows? I have a folder on my desktop which is named ".." (which itself contains subfolders with an empty name). The folder can't be deleted the usual ways, even not when using the CLI. Does anyone know how I can remove this folder on Windows Vista 64-bit?  Renaming does not work, either (obviously).  This is what "dir /x" echoes:  09.10.2009  15:04    &lt;DIR&gt;                       . 09.10.2009  15:04    &lt;DIR&gt;                       .. 08.03.2007  11:18    &lt;DIR&gt;                       cgi-bin                0 Datei(en),              0 Bytes                3 Verzeichnis(se), 45.866.037.248 Bytes frei I'm currently working on building a predictive model for a binary outcome on a dataset with ~300 variables and 800 observations. I've read much on this site about the problems associated with stepwise regression and why not to use it.  I've been reading into LASSO regression and its ability for feature selection and have been successful in implementing it with the use of the "caret" package and "glmnet".   I am able to extract the coefficient of the model with the optimal lambda and alpha from "caret"; however, I'm unfamiliar with how to interpret the coefficients.    Are the LASSO coefficients interpreted in the same method as logistic regression? Would it be appropriate to use the features selected from LASSO in logistic regression?   EDIT  Interpretation of the coefficients, as in the exponentiated coefficients from the LASSO regression as the log odds for a 1 unit change in the coefficient while holding all other coefficients constant. Understanding 74LVC245 datasheet and current source/sink I'm using a SN74LVC245A () to shift 5V TTL down to 3.3V so I can read the signals with a Raspberry Pi.  However I am getting really weird results (a 60Hz input signal is picked up by the Pi at anything between 110Hz and 320Hz) and I'm really confused about how to read the datasheet to figure out whether I need pullup or pulldown resistors.  The datasheet says on page 4 the "high-level output current" is -24mA, and the "low-level output current" is 24mA.  So to me this means that when the device is outputting a high signal, it is able to sink 24mA of current (since outputting a negative amount of current suggests the current is going into the device instead.)  But then if you're outputting a positive voltage, isn't that sourcing current?  Why is the figure listed as a negative value?  Is anyone able to explain what these figures actually mean?  When I disconnect the 74LVC245 output from my GPIO pin, I still get weird signals from the floating input pin so I am assuming this means the 74LVC245 output is also floating in one state, but I don't know in which state it is (i.e. is it left floating on a high output signal or a low one?)  It doesn't really make sense to be floating on a high output signal since it's a level converter and the whole point is to maintain the correct 'high' voltage, so do I need pulldown resistors to handle the low output?  If so, why does the datasheet seem to suggest the chip can both source and sink current?  (In my mind, source current means the device can output a current with a positive voltage, while sinking current means the device takes in anything and connects it to GND, so perhaps that is where I am going wrong.)  Anyway I'm quite confused so any clarification would be much appreciated! How can one format a cell to have word wrap in Google Sheets?  I've tried Shift+Enter, but that doesn't seem to work.  One thing I know works is to place  and then if you edit your cell you can have word wrap in it.  But is there a way to do this without switching modes? How to Micro Manage Manipulator Why do I get more satisfaction out of participating in SO than out of my job? Alternatively, are there good ways to get more satisfaction out of my job, possibly by leveraging my participation in SO? Correct usage of "lest" Which of the followings is/are the correct usage of the word "lest"? How are these different from each other?   ...hesitant to speak out lest he be fired. ...hesitant to speak out lest he'd be fired. ...hesitant to speak out lest he would/will be fired.   P.S. I took point number 1 as the reference for this question from the definition of lest from the Merriam-Webster Dictionary. How to turn off "unread messages" feature on Windows XP login screen? In Windows XP, if you have logged onto Windows Live Messenger at some point, then it'll start displaying how many unread messages on the Windows login screen. How can I turn it off? How is pressure an intensive coordinate? How can you describe someone who gives up too easily? A friend of mine said that he was a cynic. I had told him that he was giving up too easily. In this situation, the worst case outcome was rejection, which logically speaking, was equivalent to not trying in the first place.  I want to say, "No, you aren't cynical, you are X," or "No, you aren't a cynic, you are a(n) X."  The closest I can come up with is unmotivated or intimidated.  What word describes a person who gives up too easily? I recently upgraded Windows 7 to Windows 10. The biggest issue I have now is that the Windows Search service no longer works, making the Start menu mostly unusable.  If I go to Indexing Options in the control panel I see that Indexing is not running and the list of paths to index is empty.  Going to advanced options, the current index path is empty, and the new path is empty too. This is true even if I try to use the "New Index" button.  Using the troubleshooter won't help since the service doesn't start. If I try to manually start the "Windows Search" service, I get the error  "Error 3: Unable to find specified path" (this is the rough translation, the original message is in my language).  What can I do to find out which path/file is missing ? I tried to check with Process Monitor, but the only file (beside system libraries) the SearchIndexer.exe try to access seem to be c:\ProgramData\Microsoft\Search\Data\Application (everytime the service is started the whole folder c:\ProgramData\Microsoft\Search is deleted and recreated) and C:\Windows\System32\config\systemprofile (which exists).  Edit: all available updates are installed, and issuing      SFC /scannow   Doesn't reveal any issue A isometric map in metric space is surjective? Mortarboard badges being awarded as a result of bounties after recalc I keep hearing about tandem breakers, and how they won't work with 240V loads and how they should never be used for a multi-wire branch circuit.  Aside from those issues...  What is a tandem breaker?     (note: they can be thrown independently).