Identify a book featuring Free Energy given by an alien
Novel about a teleportation device and a con artist alien
What really is an indeterminate form? We can apply l’Hôpital’s Rule to the indeterminate quotients $ \dfrac{0}{0} $ and $ \dfrac{\infty}{\infty} $, but why can’t we directly apply it to the indeterminate difference $ \infty - \infty $ or to the indeterminate product $ 0 \cdot \infty $?  Furthermore, why can’t we call $ \infty + \infty $ and $ \infty \cdot \infty $ indeterminate forms?  I’m new to calculus, so please clear up my concepts if you can. Thanks! Finding information on German soldiers from World War I and World War II? Where can I find information on German soldiers from World War I and World War II?   I am curious to find out about my ancestors' role in the wars, i.e. what rank they had, where they where fighting, with whom and anything else. $n$ people attend the same meeting, what is the chance that two people share the same birthday? Given the first $b$ birthdays, the probability the next person doesn't share a birthday with any that went before is $(365-b)/365$. The probability that none share the same birthday is the following: $\Pi_{0}^{n-1}\frac{365-b}{365}$. How many people would have to attend a meeting so that there is at least a $50$% chance that two people share a birthday?   So I set $\Pi_{0}^{n-1}\frac{365-b}{365}=.5$ and from there I manipulated some algebra to get $\frac{364!}{(364-n)!365^{n}}=.5\iff (364-n)!365^{n}=364!/.5=.....$   There has to be an easier way of simplifying this. Allow linking (suggested) edits to one comment As the feature-request  elaborates on, some suggested edits seem too radical without the context of comments they are based on.  I fully endorse this request and would like to take it one step further:  Add the option to "suggest* edit based on this comment" next to comments, which would specifically highlight that comment below the suggested edit, such that edits that otherwise would be deemed "too radical" at first sight can be put into a better context. On approval, said comment would also become linked-to by the revision comment.  Since it makes sense to upvote such a comment due to it providing information justifying an edit, that link could replace the flagging-flag (which is anyway hidden after an upvote) with the edit-pen that indicate edited comments, like so:        (mockup based on a  , coming to cinemas never)  In fact, for the editor's convenience, the clicked-on base-comment might also be added to the bottom of the post and preselected (e.g. for one-key deletion or conversion to a quote)    * The "suggest" would not be shown for users with the required edit privilege (&lt;2k rep or OP), yet this option would allow to link an edit to a helpful comment and include aforementioned preselect-insertion of the comment at the post's bottom for convenience Delete commits from a branch in Git Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$ Let $G$ be a finite abelian group and let $\phi: G \rightarrow G$ be a group homomorphism. I am trying to show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$.  I know that since $G$ is abelian we have that $\ker(\phi^{k})$ and $\phi^{k}(G)$ are normal subgroups of $G$ for any $k$  I also suspect we have the following towers which stabilize at $m$ and $m'$  $$\phi(G) \unrhd \phi^{2}(G) \unrhd \cdots \unrhd \phi^{m}(G)=\phi^{m+1}(G)=\cdots$$  $$\ker(\phi) \unlhd \ker^{2}(\phi) \unlhd \cdots \unlhd \ker^{m'}(\phi)=\ker^{m'+1}(\phi)=\cdots$$  I know that if given a group of the form $HK$ where $H$ and $K$ are normal subgroups of $HK$ and $H\cap K=1$ then $H \times K \cong HK$. I want to apply this to this situation but I am unable to show how write $G$ as a product $HK$  Resolution One of the comments directed me to the following article:  The last part of which answers the question. Below is what is says:  Choose $n=\max(m,m')$, then we have for $x \in \ker^{n}(\phi) \cap \phi^{n}(x)$, this means that $x=\phi^{n}(y)$ for some $y \in G$. This gives:  $0=\phi^{n}(x)=\phi^{2n}(y)$ which means that $y \in \ker^{2n}\phi=\ker^{n}{\phi}$. and then we have that $0=x=\phi^{n}(y)$.  The answer below kindly points out that every element $x$ is contained in one of the cosets of $G/\ker^{n}(\phi)$, this means that $x=k+g$ for some $k \in \ker^{n}(\phi)$ and $g \in G$. We also have that $g=\phi^{n}(h)$ for some $h \in G$. Writing $x=k+\phi^{n}(h)$ essentially shows that $G=\ker(\phi^{n}) + \phi^{n}(G)$. Using the fact above, the claim follows. Showing a bijection between the set of ringhomomorphisms $\mathbb{Z}[i] \to R$ and the set of $x \in R$ for which $x^2+1=0$ I've been reading a Wikipedia article that describes the symptoms of rabies in various species, and I want to add a clarification note about which species (or species) a specific paragraph refers to. How can I make it clear that I'm referring either to the singular or plural of the word "species" when the singular of this word is the same as its plural? "Species or species" is the only grammatically correct way that I can think of, but it seems redundant and confusing. Is there any better way to contrast the singular of "species" from the plural of "species"? Word for someone who pays attention to details Mysterious cord running from wall. Safe? My wife and I are preparing to sell our home and are discovering some weird things. Our home was built in 1958, so it is older. We found this in a corner that had some furniture in front of it.   We are wondering    What kind of wiring is this?  Is it safe to handle or remove? $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$ Let $f:[a,b]\to  R$ be integrable and continuous on $(a,b)$. Prove that: $$\lim_{h\to 0} \int_a^b\frac{f(x+h)-f(x)}{h} \,\mathrm{d}x = f(b)-f(a).$$  What I've tried so far: make a change of variables, which didn't help. I also thought of using the intermediate value theorem inside the integral, but the function being differentiable is not specified. Any help, tips? Thanks in advance! What did Auggie's father give to his wife in the movie Wonder? There is a scene roughly in the last third of Wonder where Auggie's parents Nate and Isabel (Owen Wilson and Julia Roberts) spend an evening together while the kids are out. Nate has a surprise gift for his wife. She opens the box just enough to see it, laughs, and closes it again. So I asked myself the question:  What's in the box? Reading notification on website should clear native Android notification I think it would be nice if you read an inbox notification on the desktop version of the site, it should dismiss the native Android notification in the system tray. It seems kind of weird when I come back to my phone an hour later, and find a bunch of notifications I thought a dealt with... and come to find out I really did deal with them. Privacy/Security concers for setting up business email using Gmail app on Nexus devices I need to set up my business email*(non gmail email)* on the mobile devices (Nexus 5 and Nexus7). The business has its own private mail server. The way I can do it is by using Gmail app on these devices. The question I have is does Gmail app on the mobile devices store the IMAP emails(non gmail emails) on the gmail servers? Or Gmail app is just a client and does not bother storing the IMAP emails(non gmail emails) on its servers that are not gmail emails? Thanks for the insight... How do I check if a string is a number (float)? What is the best possible way to check if a string can be represented as a number in Python?   The function I currently have right now is:  def is_number(s):     try:         float(s)         return True     except ValueError:         return False   Which, not only is ugly and slow, seems clunky. However I haven't found a better method because calling float in the main function is even worse. Delete files older than X days + I have found the command to delete files older than 5 days in a folder  find /path/to/files* -mtime +5 -exec rm {} \;   But how do I also do this for subdirectories in that folder? I just installed Ubuntu 14.04 Server and cannot get wifi configured correctly to work with WPA2 personal and could use some help.    There was a simple wizard during install where I selected my SSID from a list and entered my passphrase and that worked great.  Now that the install is done I am having trouble configuring wifi.  My Access Point is setup to WPA2 Personal TKIP or AES. Any advice would be greatly appreciated.  I have been messing around with WPA supplicant ant my /etc/network/interfaces file with no luck.  Thanks Fine-tuning "Open safe files after downloading" how to pass objects between intents I have defined my own language whose syntax is very close to the one of Pascal. I would like to type the following program for instance. Many people use the packages algorithmicx or algorithm2e to print programs, but it seems that we have to use their specific keywords of its syntax like procedure, end while.  I just want to indent spaces when needed, and bold some words when I want (sorry that I could not bold letters in the following figure). Do I have to use  texttt for each line? Also, with verbatim, I could not bold words...  Also, as the program is not large, I would need to put it on the left side of the page, and leave space for some explanasion text on its right hand side. So I  guss I need to get them all together, and use multicols.  Could anyone help?  program test                                      some text here var   i : integer;                                    ...    b : boolean; begin    i := 1;                                        ...    b := true;    while i &lt; 15 do       i := i  + 1;       b := not b                                  some text here    od end   Edit1: Following @Werner's tabbing solution, I have made the code a minipage:  \begin{minipage}[t]{0.48\linewidth}% \begin{tabbing} Werner's solution \end{tabbing} \end{minipage}\hfill \begin{minipage}[t]{0.48\linewidth} a paragraph \end{minipage}   Actually as the code shows, I want the texts to be another separated minipage on the right hand side of the code. I have then 2 questions:   is it reasonable to make 0.48\linewidth instead of 0.5\linewidth? 0.48\linewidth is a conventional choice? is it possible to make a frame around the code, and use \caption and \label to make it a reference (I prefer figures)?