Multiplication operator has no eigenvalues Let $X=C([0,1])$ be the space of continuous functions on $[0,1].$  Consider $T:X\rightarrow X$ given by $(Tf)(t)=tf(t).$  Then $T$ has no eigenvalues.  My thought :   Assume that $T$ has an eigenvalue $\lambda$.  Then, $Tf=\lambda f$  for a non-zero $f$  So we have $(t-\lambda )f(t)=0$  Then, $t=\lambda\in[0,1]$  Then, my friend told me that if $ t \neq \lambda$, then $f=0$  And $f$ is continuous, so it forces $f$ to be zero.  But I don't quite understand his argument since $t \in [0,1]$.  So can anyone tell me what I am missing here?  Also, I have found similar posts.      But unfortunately, I failed to understand them, so I'm asking here.  Thank you.
Multiplication operator has no no eigenvalues Statement: Let $M_x$ denote the multiplicative operator acting on $L^2([0,1], \, dx)$ by $M_x(f) = xf$. Show that $M_x$ has no eigenvalues  Attempt: Let $M_x(f) = xf$ then we should have $M_x(f) = \lambda f$  then we get $M_x(f) = \lambda f \Rightarrow xf = \lambda f \Rightarrow xf-\lambda f \Rightarrow (x-\lambda)f = 0$  Now $f \neq 0$ so that implies that $(x-\lambda) = 0$ but this is achieved when $x = \lambda$, so I don't see how it doesn't have eigenvalue, when we achieve the desired result.
What is the difference between # and . when declaring a set of styles for an element and what are the semantics that come into play when deciding which one to use? Move data from regular partition to lvm I've read a bit about lvm and decided that I want to switch to using it. It seems like actually setting up lvm can be done from the debian installer, so I suppose that'll be easiest. What I'm not sure about is how to copy all of my files to the new system.   I would like to copy my whole system, not just my home directory or just my packages, I've messed around with a lot of stuff, to the point where I have no idea exactly where all of my config files live. The guides I've found on the internet seem to glaze over this step, just mentioning tools that can do it, not how to use them, i.e. use rsync. Instinct tells me I can't just rsync the root of my backup to the root of my lvm system, I'll copy over something important, like the lvm config files, but I'm not sure what exactly I need to exclude, while being sure not to exclude anything I might have changed. Any tips?  My planned steps, for clarity: I have a 1tb hdd and a 250gb ssd. I want to shrink the partition I have on the hdd, use the free space (I have enough) to make two new partitions, and dd my ssd and hdd partitions to those partitions as a backup. Then I want to wipe the ssd partition and hdd partition I'm currently using, and set up lvm on them (ideally with the debian installer for simplicity's sake, but maybe manually). And then I want to copy everything from the backup partitions to the new lvm partitions, somehow. And then wipe the backup partitions and either resize the existing lvm partitions to include the remaining space, or just make the remaining space another physical volume on lvm and add it that way. How to Hide sections of InfoPath form based on Group membership I need to Hide "Sections" of InfoPath form using SharePoint or AD group membership (either is fine). How can I achieve this?  InfoPath 2010 in SharePoint 2010 SD card not showing files when connected to pc How to change color for a block of texts? Let $C$ be the Banach space of all complex continuous functions on $[0,1]$ endowed with the supremum norm. Let $B$ be the closed unit ball of $C$. Does there exist a $\Lambda\in C^*$ for which $\Lambda (B)$ is open? Note that $C$ is a locally convex space and $B$ is convex, balanced and closed set, by the separation theorem of convex sets,we know there exists $\Lambda\in C^*$ such that $|\Lambda f|\leq 1$ for all $f\in B$ and $|\Lambda f|&gt;1$ for $f\in B^c$. But how about this when we consider some concrete space above? I have a couple of questions about light here, and sorry of they are silly..  So since anything that goes beyond the event horizon can't go out, so what if a light beam was pointed somewhere behind the event horizon to the outside, would light have a slower speed then get sucked back? and what if the light particles were somehow exactly on the event horizon, would the light stand still?  And why can't light stand still? why does it always move at that really high speed? Example of set which contains itself I am trying to understand   How can a set contain itself? Can you show example of set which is not a set of all sets and it contains itself. I had to immediate shut down, and I lost about 20 unsaved tabs, is there any way to recover these? Let $I = \langle 2\rangle$. Prove $I[x]$ is not a maximal ideal of $\mathbb Z[x]$ even though $I$ is a maximal ideal of $\mathbb Z$.   My professor mentioned that I should try adding something to it to prove that $I[x]$ is not the maximal ideal. I want to assume he meant to add $ \langle 2 \rangle$ to $I[x]$? I am trying to find examples of maps between topological space which are local homeomorphism but not covering maps. Especially, how twisted has to be such a counterexample : can it be a local diffeomorphism between connected manifolds which is not a covering map ?   I found here() a nice proposition which state that a local homeo from a compact space to a connected Hausdorff space is a covering map.   I am interested in all type of counterexamples, from non-Hausdorff spaces to surfaces, to get a better picture of the differences between covering maps and local homeomorphisms.  Thank you ! Can you deliver it [when,after] it [is | will be] assembled? Geometric interpretation of Electromagnetism For gravity, we have    General Relativity, which is a geometric theory for gravitation.  Is there a similar analog for Electromagnetism? I made the jump from Jumsoft's Money app to GnuCash a while back. It appealed to all my OCD tendencies. I don't know how to use Perl, or stuff of the sort, but with detailed instructions I manage to get things done... when I can find them.  I set up Finance::Quote to pull quotes after I set up GnuCash. I even managed to get it to pull quotes for Korean funds. And every thing had been working well, until tonight. I only get back a pop-up that states "There was an unknown error while retrieving the price quotes." That's where I need help. What can I do?  I dug around and found that it seems that it has something to do with Yahoo Finance ending it's API support. I also learned that Finance::Quote can pull data from many sources, so I don't really understand why one missing API would break it. I also saw that someone out there is trying to use AEX to pull the quotes instead for GnuCash specifically. I found Finance::Quote on cpan (I also first heard of cpan), but I don't understand what I'm looking at. But that's all beside the point. I don't know how to fix this.  Any help would be appreciated. I'm on Windows 10, GnuCash version 2.6.17, and have Strawberry Perl 5.18.2.2-32bit installed.  edit Thanks everyone who responded. It seems to be working more or less. The currency and Korean funds still haven't updated, but you've shown this horse to water. I'll do my best to drink it now. ModuleNotFoundError: No module named 'apt_pkg' error I run below command on ubuntu 16.4 :  sudo add-apt-repository ppa:noobslab/apps  of below question:    and get below error:  Traceback (most recent call last):   File "/usr/bin/add-apt-repository", line 11, in &lt;module&gt;     from softwareproperties.SoftwareProperties import SoftwareProperties, shortcut_handler   File "/usr/lib/python3/dist-packages/softwareproperties/SoftwareProperties.py", line 27, in &lt;module&gt;     import apt_pkg ModuleNotFoundError: No module named 'apt_pkg' Error in sys.excepthook: Traceback (most recent call last):   File "/usr/lib/python3/dist-packages/apport_python_hook.py", line 63, in apport_excepthook     from apport.fileutils import likely_packaged, get_recent_crashes   File "/usr/lib/python3/dist-packages/apport/__init__.py", line 5, in &lt;module&gt;     from apport.report import Report   File "/usr/lib/python3/dist-packages/apport/report.py", line 30, in &lt;module&gt;     import apport.fileutils   File "/usr/lib/python3/dist-packages/apport/fileutils.py", line 23, in &lt;module&gt;     from apport.packaging_impl import impl as packaging   File "/usr/lib/python3/dist-packages/apport/packaging_impl.py", line 23, in &lt;module&gt;     import apt   File "/usr/lib/python3/dist-packages/apt/__init__.py", line 23, in &lt;module&gt;     import apt_pkg ModuleNotFoundError: No module named 'apt_pkg'  Original exception was: Traceback (most recent call last):   File "/usr/bin/add-apt-repository", line 11, in &lt;module&gt;     from softwareproperties.SoftwareProperties import SoftwareProperties, shortcut_handler   File "/usr/lib/python3/dist-packages/softwareproperties/SoftwareProperties.py", line 27, in &lt;module&gt;     import apt_pkg ModuleNotFoundError: No module named 'apt_pkg'   Thanks for help How do I run an executable file with a double click? I'm trying to run an executable (testdisk) but double click doesn't work. The only way is to run:  sudo ./testdisk   from terminal. But I'd like to open executables with double click in future. How can I do this? How do I add a notification for process completions How can I add a notification of some sort (like playing a .wav file or creating a pop-up on the status bar) when a process finishes. For example, I am compiling a program that takes a couple of hours to finish. I would like to hear/see some sort of message when it completes compiling. Is there a tool for doing this (like tying an alarm program to the pid of a process) or something like that? While explaining to my nephew about the physics of light, I told him we cannot see infrared color, and he kicked back with a very simple question: why can't we see it? I could not tell him. Is the human eye unable to sense such light or can it indeed but the brain can't understand the signal? any other reason? Given a file like this:  1,768,12,46576457,7898 1,123,435,134,146 2,345,6756856,12312,1311 5,234,567465,12341,1341 1,3245,4356345,2442,13 9,423,2342,121,463 9,989,342,121,1212   I would like to list all rows (in bash terminal) such that the value in column 1 appears at least twice (in column 1). The result should be  1,768,12,46576457,7898 1,123,435,134,146 1,3245,4356345,2442,13 9,423,2342,121,463 9,989,342,121,1212 Does order matter when casting a cantrip with a casting time of a bonus action and another spell? When casting a spell as a bonus action, you can't cast another spell on the same turn except a 1-action cantrip - can the order be "reversed"? Can you cast a cantrip first as a bonus action, then any other spell? If not, would it be broken to allow it?  I'm thinking a Sorcerer casting a Quickened true strike, then casting a leveled spell requiring a touch attack. Seems like a great use of the cantrip + Metamagic feature, but it seems like it is not allowed.