Rename all files in directory through terminal
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$\mathbb{R}$ \ $\mathbb{Q}$ and $\mathbb{R}^2\setminus\mathbb{Q}^2$ disconnected? Kernel panic after update to 4.4.0-108-generic win 10 home how to rename my home directory and account login Prove without using graphing calculators that $f: \mathbb R\to \mathbb R,\,f(x)=x+\sin x$ is both one-to-one, onto (bijective) function. Prove that the function $f:\mathbb R\to \mathbb R$ defined by $f(x)=x+\sin x$ for $x\in \mathbb R$ is a bijective function.    The codomain of the $f(x)=x+\sin x$ is $\mathbb R$ and the range is also $\mathbb R$. So this function is an onto function. But I am confused in proving this function is one-to-one. I know about its graph and I know that if a function passes the  horizontal line test (i.e horizontal lines should not cut the function at more than one point), then it is a one-to-one function. The graph of this function looks like the graph of $y=x$ with sinusoids going along the $y=x$ line. If I use  a graphing calculator at hand, then I can tell that it is a one-to-one function and $f(x)=\frac{x}{2}+\sin x$ or $\frac{x}{3}+\sin x$ functions are not, but in the examination I need to prove this function is one-to-one theoritically, without graphing calculators. I tried the method which we generally use to prove a function is one-to-one but no success. Let $f(x_1)=f(x_2)$ and we have to prove that $x_1=x_2$ in order fot the function  to be one-to-one. Let $x_1+\sin x_1=x_2+\sin x_2$ But I am stuck here and could not proceed further. How can I create a progress bar with bash?  This is my script :  #!/bin/bash  pass='number1 number12 number13 number14 number15 number16'  chk='number14'  for i in $pass ; do    if [ "$i" == "$chk" ]; then      echo ' Found ^_^'    else      echo 'loading 50%'    fi  done   I want to replace echo 'loading 50%' with anything to create an progress bar. Show that $\deg f$ is even when $n$ is odd. A map $f:S^n\rightarrow S^n$ satisfying $f(x)=f(-x)$ for all $x\in S^n$ is said to be an even map. Show that if $f:S^n\rightarrow S^n$ is an even map, then $\deg f=0$ when $n$ is even and $\deg f$ is even when $n$ is odd. Moreover show that when $n$ is odd, there exist even maps of any given even degree.   My Try:  So $f=(-I)\circ f$. Then $\deg f=\deg (-I)\times \deg f$. If $n$ is even $\deg (-I)=-1$. Hence, $2\deg f=0$, so $\deg f=0$. But how do I show the results when $n$ is odd. No clue at all. This problem is in Hatchers book (A very complicated text). There is a hint but I do not understand it. Can somebody help me to proceed? COUNT(*) vs. COUNT(1) vs. COUNT(pk): which is better? Given that$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$, find $a_7+a_6+a_5+a_4+...+a_1+a_0$ Given that$$(3x-1)^7=a_7x^7+a_6x^6+a_5x^5+...+a_1x+a_0$$find $$a_7+a_6+a_5+a_4+...+a_1+a_0$$  Is there anyway to do the question without using binomial theorem and expanding the expression on the LHS?? What is difference between the different 'flavours' of neutrinos? MBP 13' (mid-2010; 7,1) 2.4 Core 2 Duo P8600 supporting 16 GB RAM under Win7? I’ve got a MBP 13′ (mid-2010) 2.4 Core 2 Duo (full specs below) that I’m now operating solely under Win7 64Bit. It formerly run as well under OS X 10.6.8, relatively to which the firmware seems up to date (MBP71.0039.B0B).  Would my system recognize 16 GB RAM if operated under Win7 64 Bit? Or would it require the latest firmware (MBP71.0039.B0E) of OS-X 10.7.5 (which was never installed on my MBP) anyway?   As far as I have read elsewhere, using 16 GB RAM under OS X seems to definitely require this later version of OS X (including the respective firmware update); so I'd like to know whether this is an issue of OS X or (as I suspect) the firmware.    Modellname: MacBook Pro Modell-Identifizierung: MacBookPro7,1 Prozessortyp: Intel Core 2 Duo Prozessorgeschwindigkeit: 2,4 GHz Anzahl der Prozessoren: 1 Gesamtzahl der Kerne: 2 L2-Cache: 3 MB Speicher: 4 GB Busgeschwindigkeit: 1,07 GHz Boot-ROM-Version: MBP71.0039.B0B SMC-Version (System): 1.62f6 Why did the command ":(){ :|: & };:" make my system lag so badly I had to reboot? Do not run this command to 'test' it unless you are prepared for a crash and/or force-rebooting your system.  I was in my Virtualbox running 12.04 trying to compile an app, and while waiting I happened to chance upon a forum where a comment said:   Try :(){ :|: &amp; };:  Fun, too, and doesn't need root.  Without thinking, I ran it in my gnome-terminal. It made my 12.04(in Virtualbox) lag so badly, I had to shut it down. My question is what does this command do?   :(){ :|: &amp; };: Suppose $\sum{a_n}$ converges. How do I prove that $\sum{\frac{\sqrt{a_n}}{n}}$ converges What happens if you use Polyjuice potion after saving hair or nails? Suppose you cut a five year old's hair, save it for 10 years, and then use it for a Polyjuice transformation. What age do you turn into: The toddler or the teenager? How to remove \xa0 from string in Python? How to reinstall Windows 10 on new hard disk What is spin as it relates to subatomic particles? Position vs Part I'm looking for a word which describes a task which I think is poorly designed and will lead to either mediocre results or failure, but which I have to do anyway, especially in a work setting.   The word "Dilbertian" comes to mind, however this word is obviously made up and is only meaningful to someone who is familiar with the Dilbert comic strip, so I'm looking for something which captures both the futility and compulsory nature of the task in a way which is meaningful to a broader audience. I heard a lot about in-body image stabilization recently and I wonder how this technology works. I don't mean the mechanical part (I understand how the sensor moves along different axes to compensate), but the technique in principle:  When I take my 5D III and a lens like the 70-200 2.8 II IS USM with activated stabilization, the IS will constantly move one glas element within the lens in such a way that it directs the cone of light exactly onto the sensor, so that you can always use the full sensor area.  When the cone of light goes through an unstabilized lens and you need to move the sensor - how can it capture the same amount of light at all? The light enters the lens down a fixed axis right through the center of the lens. When the sensor currently moves down, for example, to compensate for a shake, I can't see how it then is still able to capture the full resolution? When a part of the sensor is below default/calm position, then there must be missing the same part on the opposite site?  There's only one way I could image IBIS to work without resolution reduction: if the sensor area was significantly bigger than the area exposed to light, so that there's still sensor available when it currently moves out of its initial position. But wouldn't this (partly) be the same as digital stabilization because the final image gets calculated from the full sensor area minus the not exposed area?  I really would like to understand this and it would be great if someone could "shed some light on this". New Google SEO benefit with SSL - with only a few sections in SSL, or always on?