Why does proton and electron attract each other?
Why do same/opposite electric charges repel/attract each other, respectively?
If $(a,b)=1$ then prove $(a+b, ab)=1$. I have set of temp files created in my folder with .bak extensions. How can I make them hide by default in Ubuntu?  I tried adding a .hidden file with *.bak as entry in the file, but that is not working. Any help is very appreciated... How do you evaluate this integral $\int \frac{6x^{3}+7x^2-12x+1}{\sqrt{x^2+4x+6}}dx$ $$\int \frac{6x^{3}+7x^2-12x+1}{\sqrt{x^2+4x+6}}dx$$  I have met this complex integral today, how do you evaluate this? Can you do this in more steps?  Is this an elliptic integral? I don't know how to evaluate this integral at all. Show that Function Compositions Are Associative My intent is to show that a composition of bijections is also a bijection by showing the existence of an inverse.  But my approach requires the associativity of function composition.  Let $f:  X \rightarrow Y, g:  Y \rightarrow Z, h:  Z \rightarrow W$ be functions.  $((f \circ g) \circ h)(x) = h((f \circ g)(x)) = h(g(f(x)))$, and $(f \circ (g \circ h))(x) = (g \circ h)(f(x)) = h(g(f(x)))$.  However, I am having problems in justifying that the two compositions, $(f \circ g) \circ h$ and $f \circ (g \circ h)$, have the same domain and range.  When I consulted ProofWiki, whose link is at the bottom, I got even more confused.  Specifically, for $(f \circ g) \circ h = f \circ (g \circ h)$ to be defined, ProofWiki requires that dom$g =$ codom$f$ and dom$h =$ codom$g$.  First of all, I think that it should be dom$g =$ range$f$ ....  Moreover, as you can see in the example below, you actually have to adjust domains and ranges of $f, g, h$ for the requirement to hold true.  Let $f: \mathbb R \rightarrow \mathbb R$ be $f(x) = 2x$, $g: \mathbb R^+ \rightarrow \mathbb R$ be $g(y) = ln(y)$, $h: \mathbb R \rightarrow \mathbb R$ be $h(z) = z - 10$.   Then $((f \circ g) \circ h)(x) = ln(2x) - 10 = (f \circ (g \circ h))(x)$, with dom$((f \circ g) \circ h) = \mathbb R^+$ = dom$(f \circ (g \circ h))$.  As a result, we need to set dom$f = \mathbb R^+$, range$f = \mathbb R^+$; dom$g$, range$g$, dom$h$, and range$h$ remain the same.  Am I allowed to do that?  This adjustment implies that when we say dom$f = X$, $f$ must be defined for all elements in $X$, but $X$ may not be the entire set of elements for which $f$ is defined. Windows 10 puts my first and last name to lock screen. How to avoid this? After upgrading to Windows 10, I see my LastName and FirstName on the lock screen. Is there a way to change this? On Windows 8.1 there was just my nickname and email address (maybe there were my first name and last name, but not displayed so large as they are now).  I mean the name and surname parameters specified in my Microsoft account.  Another question: I prefer the format FirstName LastName, not vice versa.  Is there any way to change this as well?   Apart from Lock Screen I see it on the Start Menu. Unable to understand the syntax of the command find The find command seems to differ from other Unix commands.  Why is there the empty curly brackets and a backward flash at the end of the following command?  find * -perm 777 -exec chmod 770 {} \;   I found one reason for the curly brackets but not for the backward flash.   The curly brackets are apparently for the path     Same as -exec, except that ``{}'' is   replaced with as many pathnames as   possible for each invocation of   utility Create Generic method constraining T to an Enum Variable wavelength IR Diode? I was thinking of building a DIY IR Spectroscope but for this, I need to find an IR diode that can do variable wavelengths. So far I have looked at Farnell and Mouser but all the diodes I have looked at seem to be fixed on a wavelength.   Is this possible? or would I need some sort of filters and optical equipment, if so which parts would I need?  Thanks. A is similar to $A^k$, then each eigenvalue of $A$ is a root of unity Let $A \in \mathbb{C}(n,n)$ and $k \geq 2$ be an integer such that $$A \sim A^k$$. Show that if $A$ is non-singular then each eigenvalue of $A$ is a root of unity.   Attempt: Since $A \sim A^k$, $$PA = A^kP$$ where $P$ is an invertible matrix. Since $A$ is invertible, $0$ cannot be an eigenvalue of $A$. Suppose $$Av = \lambda v \quad v \neq 0$$ then $$PAv = \lambda Pv$$ $$\therefore A^k(Pv) = \lambda (Pv) $$ but this implies that $Pv$ is an eigenvector of $A$. But the eigenvalues of $A^k$ are $\lambda^k$ $$\therefore \lambda^k=\lambda$$ which gives the conclusion required.   My questions is: Is the logic correct? If so, Am I missing any details? If not, then how could I approach this?   Thanks! I'm struggling a bit with functions(limits, squeeze theorem, etc).  I have done some research and found a list of books on calculus but I'm not sure which one would be better suited for me, so I would appreciate if some experienced people here could advise me which books would be better to master the basics so I can move on with derivatives, etc. Limits is my main problem, so I need a book which explain this in depth so I can master it. Then I'll keep going on with the same book for other chapters.  Below is the list which I found :   Apostol T.M. Calculus Vol. 1 Burn R.P. Numbers and Functions: Steps into Analysis  Courant R. and John F. Introduction to Calculus and Analysis I - One of the better calculus text in print.  Crowell B. Calculus  Dawkins, P Calculus I and Calculus II  Garrett P. Calculus  Ghorpade S.R. and Limaye B.V. A Course in Calculus and Real Analysis  Gill G.S. Calculus Bible  Guichard D. Whitman Calculu.  Hardy G.H. A Course of Pure Mathematics  Hwang A.D. Calculus for Mathematicians, Computer Scientists, and Physicists: An Introduction to Abstract Mathematics  Santos D. Differential Calculus  Shapiro B.E. Calculus and Analysis  Spivak M. Calculus  Strang G. Calculus  Thomas G.B. and Finney R.L. Calculus and Analytic Geometry  Tranter C.J. Advanced Level Pure Mathematics  Tranter C.J. Techniques of Mathematical Analysis  Veeh J.A. Lectures Notes on Calculus  So far I narrowed my list down to Hardy, Spivak and Apostol based on further research, but I haven't got my hands on these books yet to compare them and I'm not sure if these books will be good for me.  Thanks. How do you increase MAXSYMLINKS In a python script, I am creating a bunch of symbolic links chained together.  example: link1->link2->link3->.......->somefile.txt  I was wondering how you can change the max number of symlinks to be greater than 20? Adobe Illustrator: strange behavior while aligning objects The following  (links to pdf) in the  has no provided source. The book  by Ash and Gross seems to use a similar style. Where can I find hints for typesetting publication standard articles/books as above in TeX. I looked around a bit but couldnt find much from else from keyword searches.  Particularly, I am looking at the chapter headings, title page design, and the mirror effect. Sorry for the title, as I dont really know what its called. I can open Thunderbird but as soon as I click on any file thunderbird freezes. Went to tools can see first page of settings but thunderbird freezes.  Ran norton 360 &amp; rebooted too   Went to firefox website to download thunderbird Version 3.1.9 (3) program downloads and then freezes while norton checks for viruses....  Any suggestions? Article "communicated by" What does it mean when it says under a journal article that it has been communicated by "XYZ" where XYZ is not the author but some other scholar with a very strong reputation? What is the relationship to the actual author and/or the content? Is this some sort of seal of approval to get results out and known quickly? (I am specifically wondering in the context of mathematics and mathematical physics.) Limit point of the set $G= \{1/n: n \in \mathbb N\}$? In $\mathbb{R}$ , what is the limit point of the set $G= \{1/n: n \in \mathbb N\}$?  Definition:  A point $p \in X$ is a limit of of E if every neighborhood of $p $ contains a point $q \in E$ $q\neq p$  I do understand $0$ is a limit point but shouldn't it be the case that all the points in [0,1] are limit points by the definition? Does SOQL join not respect OWD /sharing settings? Assuming I have a Czech license and break a minor law in Germany which incurs me a certain number of "violation points" (e.g. speeding), would those points be eventually transferred to my Czech license? I would obviously have to pay the fine (either on the spot or by mail), but it's not clear if EU countries exchange data on traffic points.  I would limit the scope to EU/EEA license holders driving within the EU/EEA, to avoid an overly broad question. Also assume that the person in question is resident in his home country and is only visiting other EU/EEA countries as a tourist. Uxie and Azelf Are Not Appearing in Nameless Cavern How do I disable Dunst and go back to notify-osd? I installed i3, which recommends dunst, but I'm not using i3 at the moment, and the dunst notifications don't really fit with Unity. I'd rather not uninstall dunst totally, since I might want to start using it at some point in the future; is there a way to switch back to notify-osd without uninstalling dunst?