A permutation can't be both even and Odd. How?? Is their any proof??  Kindly tell me.!  Thanks beforehand
How we can show every permutation is either even or odd,but not both......I can't arrive at a proof for this ..... Can anybody give me the proof...  Thanks in advance...
Identifying a thin, black, worm-like creature with a hammer-shaped head I came across the creature shown in the photo below yesterday evening while walking the dogs. At first, I thought it was an earthworm, but a flashlight revealed it to be something I had never seen before.    It is approximately 12 inches (300 mm) in length and about 1/3 of an inch (10 mm) in diameter at its maximum. It is pitch black and very shiny—like piano black. It moves very slowly, using a snake-like motion. It had a very strange head, like a hammerhead shark.  I live in Durban, South Africa, if that helps to narrow down the possibilities.  Can anyone help in identifying this creature? Always when I'm going to travel to someplace, I book my hostel with precedence. Actually I look only for two Booking sites:      Is there a cheaper site than these two, which has the same service with same quality, with the same number or larger? I have a card with a due date of today. The task is complete, and we've moved it to our "Done" list.  How can I update the card so that the due date icon is not red implying that it is late while retaining the date for historical reference? Why aren't bounties refunded if they are not awarded? Euclidean and induction with prime numbers My professor sometimes asks me to referee papers for him.  Should I list the corresponding journals in the professionals activity section of my CV? What is the gradient of $f(x, y, z) = \sqrt{x^2+y^2+z^2}$? What is the gradient of $f(x, y, z) = \sqrt{x^2+y^2+z^2}$?  I know that $\nabla f = \left\langle\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right\rangle$ or equivalently $\nabla f = \frac{\partial f}{\partial x}\mathbf{i} + \frac{\partial f}{\partial y}\mathbf{j} + \frac{\partial f}{\partial z}\mathbf{k}$.  Eventually, I am going to evaluate this gradient at a point and then dot it with some given unit vector to find a directional derivative. I think maybe what is troubling me is the radical in $f$. Will I have to use the chain rule in order to find the three partial derivatives?  I tried this:  $$\frac{\partial f}{\partial x} = \frac{1}{2}(x^2 + y^2 + z^2)^{-\frac{1}{2}}2x$$ $$= \frac{x}{\sqrt{x^2 + y^2 + z^2}}$$  That result looks ugly to me. However, if I did that partial derivative correctly, then I think I know what I am doing. What is the difference between call and apply? Trouble with batch conversion of .png to .pdf using convert convert /home/bill/TempScan/*.png  myfile.pdf   gives error message:  convert-im6.q16: not authorized `myfile.pdf' @ error/constitute.c/WriteImage/1037.   Any help would be appreciated! I'm a citizen of India and I'm travelling to Nepal by air. Is an Aadhaar Card a valid document used for travelling to Nepal by air? $\lim_{h\to 0}\int \frac{f(x+h)-f(x)}{h}\,\mathrm{d}x = f(b)-f(a)$ 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! I have the amulet of Mara but when I go to talk to maramal about a wedding nothing shows up. WHY is that. Is there a case insensitive jQuery :contains selector? Is there a case insensitive version of the  jQuery selector or should I do the work manually by looping over all elements and comparing their .text() to my string? Change color of links created with \in, \at, etc How to partition my hard drive for Ubuntu use? Till now I was windows user. From now on I want to use only Linux.   I have 500Gb HDD. How do I partition it properly? I read that there is no right or wrong way, but still, I am confused. I did something and I have primary partition mounted on / (160Gb) which I believe is a OS and 350Gb extended partition of which I have 4Gb of swap and 346Gb mounted on /home.  I got used to C:\ and D:\ partitioning, but I don't see file system in that way. I am lost. Where is what? How can I make C:\ partition for OS and D:\ for apps, movies, music, photos. Or what I want is Windows way and I have to get used to Linux way? Do I say "I study computer science," or "I study Computer Science"? Similarly, "I really liked that computer science course," vs. "I really liked that Computer Science course." I'm trying to use ARIMA process to predict the behaviour of a time series, the probleme I face is that I can't get the order of each component of ARIMA, the lag is between 0 and 1, same goes for the acf. The time series has no tendency, and I guess no seasonality.     My question is : Does this mean that ARIMA orders are all 0s, and if so, is the HoltWinters a good (or the best) solution for modelling this kind of TS ? Answer list only displays first 30 answers The answer list only displays first 30 answers, for questions with lots of answers - no pagination or lazy-loading once you reach the bottom, to view the other answers.  Personally counted every answer twice. Laravel - Populating Select List with Derived Values How do you prove ${n \choose k}$ is maximum when $k$ is $ \lceil \tfrac n2 \rceil$ or $ \lfloor \tfrac n2\rfloor $?