What happens behind the scenes when python adds small ints?
"is" operator behaves unexpectedly with integers
Altium de-highlighting nets after using 'Find Similar Objects...' command List all files in all subfolders In windows, is there any way to get a list of all files in a folder, including all the files within all the subfolders? Change Windows sound volume via the command line Is it possible to change the volume in Windows XP via the command line? Merge flash site into one executable Why is Compactification restricted to Toroids, Calabi-Yau et al? Does the alarm work when my phone is turned off? Will the alarm still go off if I turn off the phone before?  Example: when I have low battery, I have to go to sleep and wake up at X o'clock, and there is no charger around. Should I turn off the phone?   Note: If it makes any difference my phone is Galaxy S running froyo $f: \mathbb{R} \rightarrow \mathbb{R}$ is a continuous function. Assume that $\lim_{x \rightarrow \pm \infty} f(x)$ exist and are finite. Prove that $f$ is bounded.  So to show that $f$ is bounded, I must show that $\exists M \in \mathbb{R}$ such that $|f(x)| \leq M$ for all $x \in Dom(f)$. Assuming that $f(x)$'s limit exist, then I know that $\forall \epsilon  &gt; 0$, $\exists N$ such that for $n &gt; N$, $|f(n) - L| &lt; \epsilon$. But I am having trouble with figuring out how to connect the two ideas together. Prove that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ converges absolutely I'm trying to re-learn my undergrad math, and I'm using Stephen Abbot's Understanding Analysis. In section 2.7, he has the following exercise:  Exercise 2.7.5 (a) Show that if $\sum{a_n}$ converges absolutely, then $\sum{a_n^2}$ also converges absolutely. Does this proposition hold without absolute convergence?  I'm posting about this here because my answer to that last question about whether the proposition holds without absolute convergence is "Yes", but my suspicions are raised by him merely asking the question. Usually questions like this are asked to point out that certain conditions are necessary in the statement of propositions, theorems, etc. I just want to see if I'm missing something here.  Anyway, here's how I prove the absolute convergence of $\sum{a_n^2}$, and note that I never use the fact that $\sum{a_n}$ is absolutely convergent:  Proof: Let $s_n = \sum_{i=1}^n{a_n^2}$. I want to show that $(s_n)$ is a Cauchy sequence. So, let $\epsilon &gt; 0$ and $n &gt; m$, and consider, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |(a_1^2 + a_2^2 + \cdots a_n^2) - (a_1^2 + a_2^2 + \cdots a_m^2)|\\                 &amp;= |(a_{m+1})^2 + (a_{m+2})^2 + \cdots + a_n^2|\\                 &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\   \end{aligned} \end{equation} Now, since $\sum{a_m}$ converges, the sequence $(a_m)$ has limit 0. Therefore I can choose an $N$ such that $|a_m| &lt; \sqrt{\epsilon/n}$ for all $m &gt; N$. So for all $n &gt; m&gt; N$,  we have, \begin{equation}   \begin{aligned}     |s_n - s_m| &amp;= |a_{m+1}|^2 + |a_{m+2}|^2 + \cdots + |a_n|^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n}}\right)^2\\                 &amp;&lt; \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2 + \cdots + \left(\sqrt{\frac{\epsilon}{n-m}}\right)^2\\                 &amp;= \epsilon   \end{aligned} \end{equation} Therefore $(s_n)$ is Cauchy and $\sum{a_n^2}$ converges. And since $\sum{a_n^2} = \sum{|a_n^2|}$, the series $\sum{a_n^2}$ is absolutely convergent. &#x220E;  Am I doing something wrong here? Am I right in thinking that $\sum{a_n}$ need not be absolutely convergent for $\sum{a_n^2}$ to be absolutely convergent? How to find basis of intersection of 2 vector spaces with given basis? Suppose we have vector spaces $\mathbb W$ and $\mathbb V$.  A given basis for $\mathbb W$ is $\{(1, 1, 0, -1), (0, 1, 3, 1)\}$, and a given basis for $\mathbb V$ is $\{(1, 2, 2, -2), (0, 1, 2, -1)\}$.  How to find a basis for $\mathbb W\cap\mathbb V$? Given a set of curved geodesics in 2D space, is there a way to determine the geometrical shape of said space? How to convince airport security that I am not dangerous when having metallic parts in my body? I had an operation some time ago and now I have small screws in my shoulder which will not be removed anymore. When I decided to fly for vacation, I supposed that these will may bring me into trouble at the airport when going through the metal detector.  So I asked my doctor and at the hospital if there is any kind of "passport" or something similar which confirms the screws in my shoulder so that I do not get into many problems. Unfortunately, they told me such things do only exist if you get a new knee or something, not if you just have a few screws in your body.  When I flew from Vienna to Amsterdam and back, my fears were confirmed: The security staff inspected me very precise, and I had to explain them my story. Thank god I have some scars left so they believed me!  However this is not a permanent solution for the future. Is there any international "passport" which my doctor and hospital do not know about? If not, what else are my possibilities?  I am not that afraid when travelling within the EU, however I fear that this situation might get quite dangerous when I'm in other countries... Can I visit other Schengen countries on a long-term Schengen visa or residency permit? Polling the keyboard (detect a keypress) in python How can I poll the keyboard from a console python app?  Specifically, I would like to do something akin to this in the midst of a lot of other I/O activities (socket selects, serial port access, etc.):     while 1:       # doing amazing pythonic embedded stuff       # ...        # periodically do a non-blocking check to see if       # we are being told to do something else       x = keyboard.read(1000, timeout = 0)        if len(x):           # ok, some key got pressed           # do something   What is the correct pythonic way to do this on Windows?  Also, portability to Linux wouldn't be bad, though it's not required. Can't install wine on Ubuntu 14.04 I cannot install Wine on Ubuntu 14.04.  When I try to install it on the Ubuntu Software Center I always get a message that says I have unmet dependencies. I tried installing Wine through the terminal and I get this:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  wine : Depends: wine1.6 but it is not going to be installed E: Unable to correct problems, you have held broken packages. Behaviour of return statement in catch and finally What will be total number of solutions of $a+b+c = n$? Please tell me how to find the total number of intergral solutions of $$ a+b+c=n $$ I already know that total number of solutions will be $(n+3-1)c(3-1)$.  But what will be the case when a varies from let $2$ to $6$ , $b$ varies from $2$ to $6$, $c$ varies from $2$ to $6$.There can be other conditions also. Please give the generalized result. It will be really helpful. Upgrade to version newer than repositories I have  about how to upgrade ghostscript to a version that is available on 15.04 but not on 14.04LTS (which I have). On this site there are numerous almost identical question regarding different packages, a few examples include:         So I thought it would be very useful in general to know: is there  a general, automated way to upgrade a package, including all its dependencies, to a version that is newer than Ubuntu's repos? Is this more easily done if the newer version exists in more recent Ubuntu releases? Is it possible to see the history of changes to a particular line of code in a Subversion repository?  I'd like, for instance, to be able to see when a particular statement was added or when that statement was changed, even if its line number is not the same any more. Calculate half life of esters I'm trying to calculate the level of testosterone released from different testosterone esters. Here are some graphs of testosterone levels after single injections of 250mg of each ester.  Testo U    Testo B   Each ester have a specific half life. e.g. testo e have an half life of 4.5 days. testo b 29.5 testo u 20.9  After an injection of an ester, there will be a specific amount in your body. say 250mg.  Those 250mg will follow a normal half life curve for that ester. And I know how to calculate that.  However, when the ester is reduced, the testosterone bound to it will be released.  So over time , more testo will be released from the ester, and the testosterone itself have some sort of half life I assume.  Not doing drugs here ;) working on a medical app.  (sorry for the homework tag but I have no clue what this goes under..) Monty hall problem extended. I just learned about the Monty Hall problem and found it quite amazing. So I thought about extending the problem a bit to understand more about it. In this modification of the Monty Hall Problem, instead of three doors, we have four (or maybe $n$) doors, one with a car and the other three (or $n-1$) with a goat each (I want the car).  We need to choose any one of the doors. After we have chosen the door, Monty deliberately reveals one of the doors that has a goat and asks us if we wish to change our choice.  So should we switch the door we have chosen, or does it not matter if we switch or stay with our choice?  It would be even better if we knew the probability of winning upon switching given that Monty opens $k$ doors.