The question pretty much says it all. Is there any force, or circumstance, or anything that we know of that can affect the measurement of a red shift?
I'm interested if any of the following explanations have enough predictive capability to explain the observations we see today. The claim is that the Universe is not expanding, and that red-shift of light is caused by:    Though a couple of these are simply ridiculous, I'm still interested. Keep in mind that I am not a creationist, but am looking for reasons to see if any of these are valid or invalid.
Prove that the function $f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. Prove  that the function $\displaystyle f(x)=\frac{x}{x^2+1}$ is continuous at $x=-1$. You should give a proof that is directly based on the  definition of continuity.   I saw many similar questions on this website, but none of them gave me a satisfactory answer. I more or less understand how epsilon-delta proofs work but my problem lies more in the algebraic manipulations probably. So here's my "attempt".  Definition of continuity; for $f:A \to \mathbb{R}$     $$\forall \varepsilon &gt;0 \ \exists\delta&gt;0\ \forall x \forall x_0 \in A:|x-x_0|&lt;\delta \Rightarrow |f(x)-f(x_0)|&lt;\varepsilon$$   So from what I understand, the procedure for epsilon-delta proofs are as follows: 1. Plug the point of interest $x_0$ into $|f(x)-f(x_0)|&lt;\varepsilon$ 2. Write $x$ in terms of $\varepsilon$ 3. Then plug $x$ into $|x-x_0|&lt;\delta$ 4. Find $\delta$ in terms of $\varepsilon$. Done    At step 1, we have $\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Step 2 is where I'm stuck because of the 2nd degree polynomial in the denominator. First, I did this: $\left|\dfrac{x}{x^2+1}\right|&lt;\left|\dfrac{x}{x^2+1}+\dfrac{1}{2}\right|&lt;\varepsilon$. Then, I wasn't too sure about what to do, I thought about getting rid of the "$1$", but that would screw up my inequality. I thought about factoring $x^2+1$, but it doesn't have any real roots. I tried inverting the fraction, but that led me to nowhere. And I've already exhausted the tools I have. How do I proceed?  Apparently, epsilon-delta proofs are the most basic building blocks of analysis. And I'm already failing, this is both embarrassing and depressing... When do moderator elections take place? I'm really confused on this. I have no idea on several things:   When do elections begin?   Is there a set time each year?   Do elections actually take place each year?   Can I vote?   Where do I vote?     Etc.  Can someone please help me? Where did Schrödinger solve the radiating problem of Bohr's model? One of the problems with Bohr's theory to describe the hydrogen atom, was that the electron orbiting around the nucleus has an acceleration. Therefore it radiates and loses energy, until it would collapse with the nucleus.  Now Schrödinger describes the electron as a wave function. His theory is able to describe all atoms (in contrast to Bohr's model), but how is the radiation problem solved? I understand that the wave has not an exact position in the time anymore. But the electron still "moves", so it has an acceleration anyway (because of vibrations or so).   Why is in this theory the electron not radiating anymore? And if it is, why doesn't the atom collapse? I want to completely replace Ubuntu with Lubuntu Do characters provoke opportunity attack when they leave another character's reach who is not facing them? "You can make an opportunity attack when a hostile creature that YOU CAN SEE moves out of your reach."   In 5E do you have to specify which way your character is facing at all times?  If an enemy who is behind him leaves melee range but his back is to him does that enemy provoke an opportunity attack?    Are enemies within five feet and 360 degrees of a character considered to be within reach?  For example... Kruska and Atone are attacking Dip.  Dip is facing or only attacking Kruska.    Then Atone moves out of Dip's reach (melee range 5 feet) to engage a silly looking wizard.    Does Atone's move provoke an opportunity attack from Dip even though he's not facing him?  Is he assumed to be able to see him? Using --exclude with the du command This is probably something basic but I'm not able to make it work. I'm trying to use DU to get a total size of files minus certain directories. I need to exclude one specific directory called uploads but not every directory called uploads. For example, my file structure looks a bit like this:  /store   /uploads     /junk_to_ignore     /more_junk_to_ignore   /user_one     /uploads   /user_two   I can run the following command:   du -ch --exclude=uploads*    and it gives me the file size minus all the "uploads" directories. However, in trying to exclude certain directories (and all its sub-directories) I fail. I've tried variations of:  du -ch --exclude=./uploads* du -ch --exclude='/full/path/to/uploads/*'   but can't seem to figure it out. How do I exclude a specific directory? Set theory: difference between belong/contained and includes/subset? This is a total noob question.  I am reading , and I'm having difficulty to understand something which seems to be trivial.  In the first chapter he writes:     If $x$ belongs to $A$ ($x$ is an element of $A$, $x$ is contained in $A$), we shall write      $x\in A$   I understand this.  Then, he write:     If $A$ and $B$ are sets and if every element of $A$ is an element of $B$, we say that $A$ is a subset of $B$, or $B$ includes $A$, and we write:      $A \subset B$   I understand this too.  Then he says:     The working of the definition implies that each set must be considered to be included in itself ($A \subset A$); this fact is described by saying that set inclusion is reflexive.   I understand this too.  But then:     Observe that belonging ($\in$) and inclusion ($\subset$) are conceptually very different things indeed. One important difference has already manifested itself above: inclusion is always reflexive, whereas it is not at all clear that belonging is ever reflexive. That is: $A \subset A$ is always true;  is $A\in A$ ever true? It is certainly not true of any reasonable set that anyone has ever seen.   And this is where I don't think I understand anything.  There is not more elaboration on this point in the text.  I tried to skip this but it seems it is quite fundamental for understanding what follows in the book.  Could someone explain what is meant here? Java reading a file into an ArrayList? 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 IE11 making background image text blurry Least expensive way to boost DC voltage How do I find out the number, type, resolution &amp; refresh rate of additional monitors I can attach to my MacBook or MacBook Pro?  This is an attempt at a canonical QA, as per the Meta QA -   to try prevent the myriad "same but different" questions we get on every possible combination of computers, cable &amp; monitors There are perfectly good resources out there that Ask Different should not have to duplicate the efforts of. How do I enforce a password complexity policy? The rank of Jacobian matrix at a point of affine variety is independent of choice of generators Access personal views in a list with PowerShell I am trying to first access and then edit Personal Views for a SharePoint List using PowerShell. However only the public views are returned. In the example below the list called List1 has two views - 1 public and 1 personal created by a regular user account (contoso\user1).  I run the script below via an admin account (contoso\spadmin) -  $url= "http://portal.contoso.com/sites/TEST" $web = Get-SPWeb $url $list = $web.Lists["List1"] Write-Output "Count = $($list.views.count)" $list.views| % {Write-Output "Title = $($_.title)"}   Result -  Count = 1 Title = All Items   I tried the following as well but that did not return the personal views.   [Microsoft.SharePoint.SPSecurity]::RunWithElevatedPrivileges( {      $web = Get-SPWeb $url     $list = $web.Lists["List1"]     Write-Host "Count = $($list.views.count)"     $list.views| % {Write-Host "Title = $($_.title)"} } )    How do I access the personal views for a list with PowerShell? Should not we apply pseudo-forces all the time as the Earth is a non-inertial frame of reference? Why has Earth's core not become solid? What do "watched tags" and "ignored tags" do? To get the character sequences of a particular keyboard shortcut we use showkey -a or verbatim insert (Ctrl+V). What is the opposite of it? How can I get the keyboard shortcut in human readable format from character sequences? I used some keybindings for example ^[^? ^X^U ^[[3;5~ ^[[1;2D ^[[1;2C ^[[1;5C ^[[1;5D ^[[1;6C ^[[1;6D ....  Now I do not remember which key/key-combination they used to represent. How can I find that out? Update 1 I am looking for something which will output Ctrl+R or Ctrl+Delete etc, I mean in human readable format. Any reference to a table which has possible character sequences and their human readable formats will also do. An active access token must be used to query information about the current user