Difference between Seem and Look
Differences among "It feels...", "It looks...", and "It seems..."
How to force the Y axis to only use integers in Matplotlib? Let $M$ be the space of all $m\times n$ matrices. And $C=\{X\in M|rank(X)\leq k\}$ where $k\leq \min\{m,n\}$. How to proof that C is a closed subset of M? If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light? I know that as the velocity increases, the mass of the object also increases so it becomes tougher and tougher to move the object which ultimately leads to a requirement of infinite energy to accelerate an object to the speed of light. But I have a doubt.  As far as I know only the observable mass (Relativistic mass) increases but not the Proper Mass or Intrinsic Mass, right? The actual mass of the object will remain the same. So if the actual mass ($m_0)$ remains the same and only the observable mass increases, why is more and more energy required? I know that even if the object exceeds the speed of light, we will not be able to say that it is moving faster than the speed of light but is it possible to make it move faster than light?  If rest mass does not change with $v$ then why is infinite energy required to accelerate an object to the speed of light?  I quote Igor Ivanov (a stackexchange user from this question ) to give an insight into my question.     The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference. I strongly suggest to  popular article by Lev Okun, where he calls the concept of relativistic mass a "pedagogical virus".   EDIT  After reading the answers I have a doubt.  SO can I say that only the overall energy of the system increases while the mass remains constant? But then if mass remains constant, then why is more and more energy gradually required? I mean there should be a reason for that requirement of infinite energy. Apply display settings to all user accounts? I predicted the formula by finding total number of non-isomorphic labelled trees of order 1 is 1 , order 2 is 1,order 3 is 3,order 4 is 16,order 5 is 125.But how do i prove it ? I am beginner in graph theory so i will be very thankful if i get some simple approach to solve the problem(Not by using some difficult theorems). C# 3.0 auto-properties — useful or not? Note: This was posted when I was starting out C#. With 2014 knowledge, I can truly say that auto-properties are among the best things that ever happened to the C# language.  I am used to create my properties in C# using a private and a public field:  private string title; public string Title {     get { return title;  }     set { title = value;  } }   Now, with  3.0, we got auto-properties:  public string Title { get; set; }   I know this is more a philosophical/subjective questions, but is there any reason to use these auto-properties except from saving five lines of code for each field? My personal gripe is that those properties are hiding stuff from me, and I am not a big fan of black magic.  In fact, the hidden private field does not even show up in the debugger, which is OK given the fact that the get/set functions do nothing. But when I want to actually implement some getter/setter logic, I have to use the private/public pair anyway.  I see the benefit that I save a lot of code (one vs six lines) without losing the ability to change the getter/setter logic later, but then again I can already do that by simply declaring a public field "Public string Title" without the need of the { get; set; } block, thus even saving more code.  So, what am I missing here? Why would anyone actually want to use auto-properties? I made a skin by using Skincraft and I exported it to minecraft.net. I chose my skin and uploaded it. At the top it says,      "Your skin has been changed! Please wait a few seconds for it to   update."   I went to Minecraft, clicked singleplayer and chose a random world at the top. I looked at my character, but it's still default. Multiplayer won't load for some reason. I don't know what I've done wrong! This came up in proving non-regularity of a certain language (powers of 2 over the ternary alphabet). Any clue to the above equation could help me move forward.  Edit: Of course, $x = 1, y = 1$ is a solution. I am looking for non-trivial solutions. Index not created in pdf output, even though idx file is present I have a document that has \usepackage{makeidx} and \makeindex in the preamble and \printindex inside the document body. An .idx file is created when I compile, no errors are signalled, still there is no index listing in the PDF document that is produced. There used to be one until all my files were deleted except the .tex file, after that I could not get the index to appear in my output. How can one troubleshoot this thing? I have changed all the "%bm" with "%tm" wherever I could find it in the build profiles (Tools -> Options -> Clean), as Thorsten Donig suggested on this website (in an answer to another posting regarding problems with the index creation). It did not solve my problem. I am using the TeXnicCenter editor on Windows XP, with the MiKTeX 2.9 distribution. Determine whether $712! + 1$ is a prime number or not Let $n = 712! + 1$ If $n$ was a prime number then, by Wilson's theorem:  $ (712!)! \equiv -1 \pmod{712}$  The double factorial makes it seriously more difficult...  But We can require:  $$712!! + 1 \equiv 0 \pmod{712}$$  $$712 = 2\cdot 356$$   Hence: $712!! = 2^{356} 356!$  Lets compute: $356! \pmod{712}$. Obviously:  $$356! = (356 \cdot 2) \cdot (355!/2)  = 712 \cdot 355!/2$$  Then: $356! \pmod{712} \equiv 0$.   Now, $2^{356} \pmod{712}$  $2^{356} = 2^{6 + 350}$  Nevermind, what should I do? Evaluate the integral $\int e^{-x}x^n dx$ Evaluating the integral $\int_{0}^{\infty}  e^{-x}x^n dx$ where n=0,1,2 ...   1st Integration by part: let $a=x^n$, $da= nx^{n-1} dx$, Also $db=e^{-x}$, $b=-e^{-x}$ We have $$ -x^n e^{-x} + n\int x^{n-1}e^{-x} dx$$  2nd: let $a=x^{n-1}, da= (n-1)x^{n-2}, db= e^{-x}, b= -e^{-x}$ We have $$-x^n e^{-x} + n\left[x^{n-1}(-e^{-x}) - \int(n-1)x^{n-2}\cdot -e^{-x}\right]$$  How would you find the general form? What would it be? Detail in bijection between Inn(G) and G/Z(G)? Can someone provide a proof that every quadratic residue, when working in $\mathbb Z_p$, where $p$ is a prime, has exactly two roots? Indeed, there cannot be only one root as for any $a^2$, we know $a$ and $-a$ are both roots. So then we need only show that there cannot be more than two- does this follow from some argument for the number of roots a quadratic can have modulo a prime? I'm not well-acquainted with the theorems pertaining to prime moduli. Bind an element to two sources I currently have two text boxes which accept any number. I have a text block that takes the two numbers entered and calculates the average.   I was wondering if there was a way I could bind this text block to both text boxes and utilize a custom converter to calculate the average? I currently am catching the text changed events on both text boxes and calculating the average that way, but I am under the assumption data binding would be more efficient and easier. When updating, I get the following error message:   W: The repository 'http://ppa.launchpad.net/mc3man/trusty-media/ubuntu xenial Release' does not have a Release file.   Here, I find another statement on this error:   This recommends removing certain PPAs; and, I'm not sure if I should do that since it might mean not getting the updates that I need.    Is this what I should do? Is there a password manager for Ubuntu What is the most popular open source password manager which I can use on a Ubuntu machine or preferably across Ubuntu/Windows machines with some form of data compatibility. If there is a free web based version, that would be even more preferable. Prove that $n=\dfrac{5^{125}-1}{5^{25}-1}$ is a composite number   My attempt,  Let $x=5^{25}$, so that $5^{125}-1=x^5-1=(x-1)(x^4+x^3+x^2+x+1)$  $=(x^4+9x^2+1+6x^3+6x+2x^2-5x^3-10x^2-5x)(x-1)$  $=((x^2+3x+1)^2-5x(x+1)^2)(x-1)$  I'm stuck at this point and don't know how to continue anymore. Hope someone can provide a detailed solution. Thanks a lot. how to solve $\int_{-\infty}^\infty e^{-x^2-x{\tau}} \cdot x\ dx$? Access Denied using TakeOwn.exe I have got this file that I can't delete. It happened after a system crash, so the CHKDSK kicked in upon next reboot. After that, I can't delete the file.  THis is on Windows Home Server, and the file is one of those hidden Thumbs.db, and my WHS reports a "File conflict" on the file, the reason: Access Denied"  What I have tried so far, running as an Administrator: Delete: Access Denied TakeOwn.exe : Access Denied Attrib.exe -s -h : Access Denied cacls.exe : Access Denied   (even whe trying to display the current owner) Rename: File not found (its hidden) Re-boot in to safe mode and tried the above: Access Denied Running the above commands as Local System: Access Denied   Tizer Unlocker: Fail (Doesn't find anything locking the file) File Assasin: Crashes ("FindRemoteFileHandles returned NULL value.")  I have used the CHKDSK /f again, rebooted since some suggestions is that the file has been corrupted, but that didn't change anything. Any suggestions ?  Update: In a total separate scenario, I experienced a similar situation; Access Denied when trying to take ownership of a file. It turned out that the file was owned by TrustedInstaler, which is not possible to override just by being an Administrator. In this case, one can use psexec /ids cmd to elevate yourself to System and then TakeOwn.exe /a Variable variable class extensions in PHP--is it possible? Is something like the following possible in PHP?  $blah = 'foo1';  class foo2 extends $blah {     //... }  class foo1 {     //... }   This gives an error.  I want to dynamically set $blah so I can extend whatever class I want.  Edit: The reason for wanting to do this because I wanted to use a function out of another class in a related class. In the end it would have been something like:  Final extends foo1 extends foo2 extends foo3 extends foo4 extends parent { ... }   In the end I decided to instantiate the other class within the class and use it. Not the best options because they both you 2 of the same classes, but this won't be used that often, so it will work for now.