Why Can't We Divide by Zero?
Why does $x$ divided by zero not equal $x$?
All I remember is the guy was sent to a planet to test something or he did something illegal, and time moved really fast on the planet but slow to the outside world. He had to fix something to leave the planet I think. His dad was also dying and he checked how many days he had left every day, but in the end his dad didn't actually die as time was fast. It took place on a sandy planet. Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$ Evaluate $$\int_0^\infty\frac{\ln x}{1+x^2}\ dx$$ I don't know where to start with this so either the full evaluation or any hints or pushes in the right direction would be appreciated.  Thanks. "With who" vs. "with whom" Is this correct?     The person with whom I'm doing the project should be here soon.   If it is, is with always a dative preposition (like mit in German)? Showing margins/frames in beamer slides Proving that expression is equivalent to the definition of derivative Let $f$ be differentiable at $x=a$.   Prove that if $x_n \to a^+$ and $y_n \to a^-$ then:  $$\lim_{n\to \infty} \frac{f(x_n)-f(y_n)}{x_n-y_n}=f'(a).$$  Every option that I think about seems to my very trivial, so I believe that I am doing something wrong.  Both numerator and denominator approach zero as $n\to\infty$ as the case of the formal definition of derivative, but it isn't guaranteed that the limits are equal (“$\frac{0}{0}$”).   Any direction? How to show that a set of discontinuous points of an increasing function is at most countable I would like to prove the following:       Let $g$ be a monotone increasing function on $[0,1]$. Then the set of points where $g$ is not continuous is at most countable.     My attempt:    Let $g(x^-)~,g(x^+)$ denote the left and right hand limits of $g$ respectively. Let $A$ be the set of points where $g$ is not continuous. Then for any $x\in A$, there is a rational, say, $f(x)$ such that $g(x^-)\lt f(x)\lt g(x^+)$. For $x_1\lt x_2$, we have that $g(x_1^+)\leq g(x_2^-)$. Thus $f(x_1)\neq f(x_2)$ if $x_1\neq x_2$. This shows an injection between $A$ and a subset of the rationals. Since the rationals are countable, $A$ is countable, being a subset of a countable set.    Is my work okay? Are there better/cleaner ways of approaching it? I gave a scammer my telephone number, address, and name. How bad is it? Updated question because old one was embarassing: I saw a spam email from "PayPal" and I didn't realize that it was a phishing attempt. I gave the phishing site my name, telephone number, and email. What could he do with them?  Old question: Well, I saw a spam email, but I didn't realize that it's really a scam at first. I gave him my telephone number, address, and name. What would he do with them? Could he ruin ALL of my reputation with it? Discrete mathematics - Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$. Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$.  This is one of the questions we presented in one session to contest preparation PUTNAM. It turns out that I can't get from the problem. Could someone just give me a hint? (Please, don't give me the answer. Simply, an argument that can help me advance in the problem or theorem might suffice.) Example 1) Let's say I have some random creature with protection from white, and my opponent plays , a white card with the effect "Destroy all creatures." Can my creature with protection from white be destroyed by a white card that isn't actually targeting it specifically?  Example 2) I was playing a match with a friend where I had  on the field against his 3 zombies. Is he able to declare his zombies as blockers even though Elite Inquisitor has "protection" from zombies?  If he can declare them as blockers, does protection mean that no damage is dealt by the zombies to  Elite Inquisitor? I have a British passport from 2006 September and going to Florida. The passport in has camera symbol. Is it valid? I am going to Florida in a few days. I have a British passport that I acquired in September 2006. It has a "camera" symbol on front and is biometric. Just seen news items that only passports from October 2006 or later will be accepted by the USA. Is my passport valid for travel to the USA? I do have a valid ESTA. Removing clock from the lock-screen I'm using Ubuntu 18.04.  I want to remove the digital clock from the lock screen because I just want to see a good wallpaper there, unobstructed.   How do I go about this? What are the criteria for questions to be selected for Hot Network Questions? I really like the , where certain questions from the Stack Exchange Network are presented, along with a hotness rating that is described as &quot;arbitrary&quot; in its tooltip. Such questions also appear randomly on the sidebar on sites across the network, under the heading &quot;Hot Network Questions&quot;. How do these arbitrary hotness points work, and how are they used to select questions to appear in those lists? Can players enchant items? I know that the DM can give you enchanted items, but can players spend gold and downtime to enchant their own? Several companies are commercializing tests for telomere length such as this one . I understand the basic mechanism for why telomeres shorten during DNA replication, but how good is the evidence that telomere length is a reliable indicator of healthspan/lifespan? Why is there a big delay after entering a wrong password? I notice a weird (well, according to me) thing about passwords. For example, if I type an incorrect password during login, there will be a few seconds' delay before the system tells me so. When I try to sudo with a wrong password I would also have to wait before the shell says "Sorry, try again".  I wonder why it takes so long to "recognize" an incorrect password? This has been seen on several distributions I use (and even OSX), so I think it's not a distribution specific thing. the problem of using "~\\" and blank line Recently,I found the code that cotains the"~\\" and blank line always shows the warning imformation "Underfull \hbox (badness 10000) in paragraph at lines"  \documentclass{ctexart} \usepackage{color} \usepackage{amsmath} \usepackage{amssymb} \usepackage{graphicx} \usepackage{epstopdf} \hfuzz=\maxdimen   $(A \pm  B)^{-1} \neq A^{-1} \pm B^{-1}$,$(A \pm  B)^* \neq A^* \pm B^*$~\\  $|(A^*)^*|=|A|^{n^2-2 n+1}$~\\  \end {document}   I add the code:  \tolerance=10000 \hbadness=10000 \begin{document}   However,fail to solve it! Are there any places to leave luggage in Brussels, for short and/or long periods of time? How can I prove that prove $n^5 - n$ is divisible by $30$? I took $n^5 - n$ and got $n(n-1)(n+1)(n^2+1)$ Now, $n(n-1)(n+1)$ is divisible by $6$. Next I need to show that $n(n-1)(n+1)(n^2+1)$ is divisible by $5$. My guess is using Fermat's little theorem but I don't know how. how to run the dialog command with proccess Please look on my code – ( bash script )  I want to display both dialogs on the screen on the same time,   one dialog display the:  tail –f from - /var/log/proccess1.log  ,   and the second dialog display the:  tail –f from the file - /var/log/proccess2.log     but the sad fact is that I can display only one dialog and not both dialogs ( because when I run the first dialog , the second dialog will activate only if the first dialog will killed )   So I create process on the second dialog ( ….. ) &amp;    , in order to display both dialogs    But …. the second dialog create process number but not create the second dialog GUI , ( seems that when we create dialog with process , the process not send the dialog to standard output )  So how to  run the second dialog with process but send the dialog GUI to screen ? , or other solution in order to display both dialogs on screen  My code       #!/bin/bash       # this dialog will locate the tail box on the top of the screen      dialog --begin 15 10  --tailbox   /var/log/proccess1.log  13 125         # this dialog will locate the tail box down in the screen      ( dialog --begin 37 10  --tailbox   /var/log/proccess2.log    13 125 ) &amp; How to Store Fresh Herbs What is the best way to store fresh herbs like parsley or cilantro?  I find I have about the same luck with them whether they are left in a plastic bag or I put them in a cup of water.