Merging two same values in python
How do you remove duplicates from a list whilst preserving order?
Are we inside a black hole? I was surprised to only recently notice that      An object of any density can be large enough to fall within its own   Schwarzschild radius.   Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's.  Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards.  Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light.  Or Mt. Everest packed into one nanometer.  Reading on about this , it increases proportionally with total mass.  Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.  Question: For an object the , what would have to be its diameter for it to qualify as a black hole (from an external point of view)?  Would this not imply by definition that:   The Earth, Solar system and Milky Way are conceivably inside this black hole? Black holes can be nested/be contained within larger ones? Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside? Whenever I install vsftpd on centos, I only setup the jail environment for the users and rest is default configuration of vsftpd. I create user and try to connect with filezila ftp client, but I could not connect with passive mode. I always change the transfer settings to active mode to successfully connect to the ftp server otherwise I get        Error: Failed to retrieve directory listing   So is there a way to change any directive in vsftp.conf file and we can connect with passive mode to the server? Assume that $M$ and $N$ are two finitely generated $R$-modules. Then $\operatorname{Hom}_{R}(M,N)$ is a finitely generated $\mathbb Z$-module and/or $R$-module (in this case, assume that $R$ is commutative)?   Note that $R$ is not Noetherian ring. Is there any counterexample (for any cases)? We moved to a new place where the dryer connection is 3-prong instead of 4-prong. The dryer was originally 4-prong, so we bought a 3-prong cord and installed it. It works fine, except I am not entirely sure if I installed the ground wire correctly.   Originally, there was a green wire on the cord itself, and that was connected to the screw on the top of the first picture. This is, I assume, used to ground the case and prevent shocks when touching the exterior of the dryer.  Now with the 3-pronged plug, there is no ground wire on the cord. So where does the existing green wire in the case go? Do I leave it where it originally was like in the first picture or do I connect it to the central terminal like in the second picture?      There's no bonding strap running from the case to any terminal. I can't tell where the green wire is connected to. How can I set conditional formatting on a particular cell that depends on another cell's value? Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line. Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line.   I am trying to argue from the definition of uniform convergence for a sequence of real-valued functions, but am struggling quite a lot. My efforts so far have concentrated on trying to find a sequences, ${a_n}$ which tends to zero, such that   $$|(1+\frac{x}{n})^n -e^x |\leq a_n$$ for all $n$. But I have been unsuccessful thus far. All help is greatly appreciated. Large braces for specifying values of variables by condition How do I produce a conditional expression with large brackets? For example: X = 0 if a=1, 1 otherwise, with a large left bracket and specifying each condition in a line? I am considering purchasing a Mac for my godson who will be using it to run Blender 2.8.  I know very little about this program.  All I can find are requirements for a Mac that will run earlier versions of Blender.  Would someone please recommend a list of requirements for a Mac (or a link to a list of requirements) that I could use to find a model that can run 2.8?  Thank you in advance for all your help! Sincerely, M. Lap I'm trying to execute a string into my bash script. String contains variables (so I could substitute some CLI arguments depending on circumstances).  The problem is when I use variable containing --argument=value, everything breaks up, giving error:  Missing trailing-' in remote-shell command.   Example code:  #!/bin/bash  rsync_path="/usr/bin/rsync -azhrP" rsync_ssh_cmd="--rsh='ssh -o Compression=no'"  `$rsync_path /path/to/file $rsync_ssh_cmd username@localhost:/tmp`   If I just echo the last string from this code, it looks fine. But if i try to execute this string from script, it doesn't executes as expected.  I found a workaround - everything became OK if I try  eval "my-command-string"   instead of  `my-command-string`   or  (my-command-string)   Why does it so? How could I (should I really?) avoid to use eval?  I use bash 4.3.11(1)-release (x86_64-pc-linux-gnu) (Kubuntu 14.04.3). When should I load assets for optimal performance? I'm writing a game using LWJGL and Java, and was wondering if there were best practices for when to load resources.  I have seen examples that load all resources when initializing the game (XNA), ones that load the new resources needed for each level while referencing the already loaded assets again. Prove that, for $p > 3$, $(\frac 3p) = 1$ when $p \equiv 1,11 \pmod{12}$ and $(\frac 3p) = -1$ when $p \equiv 5,7 \pmod{12}$ How do I enter a file or directory with special characters in its name? I am confused. I don't understand the difference a ARMA and a GARCH process.. to me there are the same no ?  Here is the (G)ARCH(p, q) process  $$\sigma_t^2 =      \underbrace{     \underbrace{      \alpha_0       + \sum_{i=1}^q \alpha_ir_{t-i}^2}     _{ARCH}        + \sum_{i=1}^p\beta_i\sigma_{t-i}^2}     _{GARCH}$$  And here is the ARMA($p, q$):  $$ X_t = c + \varepsilon_t +  \sum_{i=1}^p \varphi_i X_{t-i} + \sum_{i=1}^q \theta_i \varepsilon_{t-i}.\,$$  Is the ARMA simply an extension of the GARCH, GARCH being used only for returns and with the assumption $r = \sigma\varepsilon$ where $\varepsilon$ follows a strong white process? Disk full, du tells different. How to further investigate? Please add TeX rendering in titles on the iOS app TeX support works fine in question and answer bodies, and comments can be rendered manually by tapping and selecting Render MathJax. See related question .  However, the titles are not rendered which makes the browsing experience less than perfect. See screenshot below.   Are there any plans to implement MathJax support in titles?  (I'm running Stack Exhange iOS App Version 1.0.0 on an iPhone 4S with iOS 7.1.1)    EDIT: I was just informed about  asking for the same functionality for the Android app. I guess I shouldn't hope too much then... I am struggling to understand zero inflated distributions. What are they? What's the point?  If I have data with many zeroes, then I could fit a logistic regression first calculate the probability of zeroes, and then I could remove all the zeroes, and then fit a regular regression using my choice of distribution (poisson e.g.).  Then somebody told me "hey, use a zero inflated distribution", but looking it up, it does not seem to do anything differently than what I suggested above? It has a regular parameter $\mu$, and then another parameter $p$ to model the probability of zero? It just does both things at the same time no? Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces The following is a well-known result in functional analysis:     If the vector space $X$ is finite dimensional, all norms are equivalent.     Here is the standard proof in one textbook. First, pick a norm for $X$, say  $$\|x\|_1=\sum_{i=1}^n|\alpha_i|$$ where $x=\sum_{i=1}^n\alpha_ix_i$, and $(x_i)_{i=1}^n$ is a basis for $X$. Then show that every norm for $X$ is equivalent to $\|\cdot\|_1$, i.e.,  $$c\|x\|\leq\|x\|_1\leq C\|x\|.$$ For the first inequality, one can easily get $c$ by triangle inequality for the norm. For the second inequality, instead of constructing $C$, the  is applied to construct a contradiction.   The strategies for proving these two inequalities are so different. Here is my question,      Can one prove this theorem without Bolzano-Weierstrass theorem?   UPDATE:     Is the converse of the theorem true? In other words, if all norms for a vector space $X$ are equivalent, then can one conclude that $X$ is of finite dimension? I have noticed that the confidence interval for predicted values in an linear regression tends to be narrow around the mean of the predictor and fat around the minimum and maximum values of the predictor. This can be seen in plots of these 4 linear regressions:    I initially thought this was because most values of the predictors were concentrated around the mean of the predictor. However, I then noticed that the narrow middle of the confidence interval would occur even if many values of were concentrated around the extremes of the predictor, as in the bottom left linear regression, which lots of values of the predictor are concentrated around the minimum of the predictor.  is anyone able to explain why confidence intervals for the predicted values in an linear regression tend to be narrow in the middle and fat at the extremes? Motivation: I once had one surplus card on my hand, and knew the robbers would come soon. So I gave it to someone for free, to avoid losing more cards when they hit. I was surprised by how badly this was received. Two of the three other players (the hosts of the game) acted upset, like I had tried to cheat. I had to take the card back, get robbed the next turn and 'giving cards away for free' was banned immediately. (Oh, how I hate mid-game additions to the rules. But that's beside the point.)  So now the question: Is this really illegal in Settlers of Catan? Is it generally considered underhanded in any way? If so, why?   My reasoning was like this:        Consider players A and B.   A wants to give B a sheep.   A trades a sheep and one rock to B, in exchange for wheat.   A trades the received wheat for the (formerly his) rock.   A and B now both have the same resources they had in the beginning, only the sheep has moved from A to B. Unable to post - login problems with Area 51 ... again I recently signed up for Area 51 with my stackexchange network account/ID, verified the account and logged in.  I see the main page  where I confirm that I am logged in.  I click on the discuss link on the black menubar at the top, which takes me to the discussion zone. From here I click on ask question, which asks me to add  a login even though I have already logged in with my stackexchange ID.  Here if I choose the stackexchange login option then it takes me back to the main page, from where the cycle begins again.