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Run command on another(new) terminal window Why doesn't the "zig-zag" comb deformation retract onto a point, even though it's contractible? I am starting to read Hatcher's book on Algebraic Topology, and I am a little stuck with exercise 6(c) in Chapter $0$. Unfortunately a picture is involved so it doesn't quite make sense for me to repeat it here - but I'll do it anyways (maybe it helps)     Let $Z$ be the zigzag subspace of $Y$ homeomorphic to $\mathbb{R}$ indicated by the heavier line in the picture:       Show there is a deformation retraction in the weak sense of $Y$ onto $Z$, but no true deformation retraction."   Now the definition for deformation retraction and weak deformation retraction as as follows:  We say that $f: X \to X$ is a deformation retraction of a space $X$ onto a subspace $A \subset X$ if there exists a family of maps $f_t : X \to X$ with $t \in [0,1]$ such that $f_0 = \mathbb{1}$ (the identity) and $f_1 (X) = A$ and also $f_t$ restricts to the identity on $A$ for each $t$.   A weak deformation retraction is almost the same, only that we now relax the conditions $f_1(X) = A$ to $f_1 \subset A$ and, for each $t \in [0,1]$ we require that $f_t(A) \subset A$.  Hence, as far as I understand the question and the concepts involved, I need to show that basically no map can be constructed such that the bold zigzag - line stays put while the thin lines retract to the bold line over a finite time interval $0 \leq t \leq 1$. However, I should be able to show that I can pull the thin lines continously onto the thick line, provided I am allowed to move points on the zigzag line .. is that correct ?  Now, the problem is I can't see why I shouldn't be able to do the former, given that I could find a weak deformation retract. Any help would be great! Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$? We know $$i^2=-1 $$then why does this happen? $$ i^2 = \sqrt{-1}\times\sqrt{-1} $$ $$ =\sqrt{-1\times-1} $$ $$ =\sqrt{1} $$ $$ = 1 $$  EDIT: I see this has been dealt with before but at least with  I'm not making the fundamental mistake of assuming an incorrect definition of $i^2$. There are no interfaces on which a capture can be done What is mirror lockup and what is its primary function? My SLR is equipped with the mirror lockup function. What does it do, and when would I employ such a feature? Cron Job not working in plugin What is the correct way to install proprietary ATI Catalyst Video Drivers (fglrx) directly from AMD? I am planning on doing a fresh install of Ubuntu and want to know what is the correct way to install ATI Catalyst Video Driver?      There are multiple valid answers for this question spanning over several versions of Ubuntu. For your convenience an index of each below: Why should users never use normal sudo to start graphical applications? I've read  and am interested in this line:     You should never use normal sudo to start graphical applications as Root.   Why? What is the difference? Please provide a simple explanation, as I'm just a normal desktop user. OneDrive isn't uploading all my photos from my phone I've got an Office 365 (Microsoft 365) Family license. I've set up OneDrive on my Samsung Galaxy S10 phone. I've verified that it is set up by following the . I've got it set up to upload photos using either Wi-Fi or mobile. And I see photos I've taken with my phone, uploaded to OneDrive from as recently as a few days ago. So, it works. But not all the time or for all my photos. I've scrolled through my photos on my phone's Gallery app. I see some photos from as recently as 4 days ago to several months ago, are not uploaded to OneDrive. Why is that? I read a short story (I think, but it might have been a novel), where most races discover a very easy way to travel faster than light at a certain point in their technological development.   What I remember:   The guys in wooden ships bounced around subjugating the people without FTL travel. Earth had never figured out the FTL, and so had poured its effort in a different path, achieving present day technology. The aliens were freaking out about handing the humans FTL travel. The story was told from the point of view of the aliens. I read it in the last 10 years, but there is no telling how old it actually was, although I do remember them mentioning F-18s or F-14s. How to connect to wifi using just the terminal? Is there an analog to the Runge-Lenz vector for a 3D spherically symmetric harmonic potential? Why is a normal subgroup of $G_1\times G_2$ with trivial intersections with $G_1$ and $G_2$ is abelian? Let $G=G_1\times G_2$ be a direct product, and let $H\triangleleft G$ be a normal subgroup such that $H\cap G_1=H\cap G_2=\{1\}.$ Then $H$ is abelian.     I considered the commutators of two elements in $H$, trying to show that it must be $1,$ but I don't see how this works. Any hint is very welcomed and appreciated. Thanks in advance. Problem 1.1.5 from Hatcher's I want your advice on my solution of this problem.  problem  Show that for a space $X$, the following three are equivalent:  (a) Every map $S^1 \rightarrow X$ is homotopic to a constant map, with image a point.  (b) Every map $S^1 \rightarrow X$ extends to a map $D^2 \rightarrow X$.  (c) $\pi_1(X,x_0)=0$ $\forall x_0 \in X$.  my solution  $(c) \rightarrow (a)$: Take a map $f:S^1\rightarrow X$, and the constant loop at $x_0$ (which from (c) we know there's only this loop), and take the linear homotopy connecting $f$ and $x_0$.  $(b)\rightarrow (c)$: I am not sure if this is right, but I want somehow to induce some isomorphism from $\pi_1(D^2,y_0)$ to $\pi_1(X,x_0)$ in which case we'll get the required result. So I argued that we take as a map the extension of a map $S^1\rightarrow X$ to a map $D^2\rightarrow X$, but I don't see how to argue that the last map is homeomorphism, any advice?  $(a) \rightarrow (b)$: I am given $f:S^1\rightarrow X$, and it's homotopic to some point $x_0$, so I thought to extend $f$ on the whole ball, by defining the map: $g(x)= f(x)$ if $|x|=1$ and $g(x)=x_0$ if $|x|&lt;1$.  Is any of what I typed right, what do I need to amend?  Thanks. The  specifically says not to ask  for career advice but people do it anyway.  Should I consider the Help Center outdated or only loosely enforced?    And what about a career advice site on the network?  There are 70+ sites, and most of them are for relatively narrow interests (which is not a criticism, I enjoy looking through the many sections).  A career section seems like it would be very popular.  Also, a careers section would help keep career questions off the other sites. I know I've seen somewhere how to typeset 1/2 as ½, but with arbitrary fractions (that is, a macro that takes two arguments and makes the first denominator and the second numerator...). Now I can't seem to find it.  How do I typeset an arbitrary fraction the same way as ½? In which US accent is “again” pronounced /əˈɡeɪn/ with the FACE vowel, not /əˈɡɛn/ with the DRESS vowel? Most dictionaries provide the US pronunciation of “again” as /əˈɡɛn/ (uh-gen) with the DRESS vowel. This is the most common pronunciation in the USA. However, I think I might have also come across /əˈɡeɪn/ (uh-gain) with the FACE vowel. This sounds like the word “gain” with an “a” at the beginning. Is there a US accent where “again” is pronounced this way? How to write a simple jQuery plugin I'm a college student and I just got my first credit card (through Chase). The only reason I got the card is to try and build my credit score. I also have a checking account with Chase, and they let me pay off my credit card any time I want.  For example, right now I have a balance of $92 on my credit card, but my bill won't come until September 2, and the payment isn't actually due until September 27. But through their website I could go ahead and pay it off with money from my checking account.  My question is, is it better for my credit score if I pay off that $92 balance right now, or should I wait for the bill, or does it not matter either way? NOTE: This is a Master Canonical Post for the issues observed on February 25, 2020.  All issues on Feb 25 relating to Python updates not found should be dupe-linked here.  Errors have been seen such as this today, February 25, 2021: Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/p/python2.7/libpython2.7-minimal_2.7.17-1~18.04ubuntu1.3_amd64.deb 404 Not Found  Is there something up with the repositories?