It is possible to obtain a injective continuous map $f:\mathbb{R}^m \rightarrow \mathbb{R}^n$ when $m > n$?
There is no continuous injective function $f:\mathbb{R}^n\longrightarrow\mathbb{R}^m$
What causes javac to issue the "uses unchecked or unsafe operations" warning For example:  javac Foo.java Note: Foo.java uses unchecked or unsafe operations. Note: Recompile with -Xlint:unchecked for details. Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$. Let $x$ and $y$ be positive integers such that $xy \mid  x^2+y^2+1$. Show that $$ \frac{x^2+y^2+1}{xy}= 3 \;.$$ I have been solving this for a week and I do not know how to prove the statement. I saw this in a book and I am greatly challenged. Can anyone give me a hint on how to attack the problem? thanks given a polynomial $p(x,y)$ from $\mathbb Z[x,y]$. I want to substitute $x=1$ leaving $y$ as it is. The command Value(p,[1,y]) does not work. Can you give me a hint?  After that it gets a little more complicated. Let  $$p(x,y)=x^6+y^6$$ After substituting $x=1$ we have $p(1,y)=1+y^6$. Given a natural number $j$. I want to find all expressions $y^j$ in $p$ and substitute these $y^j$ by $1$ and the others by $0$. In this case (and for $j=6$) we would get $1+1=2$. If $$p(x,y)=x^4y^2+x^2y^6$$ we should get $0+1=1$. Is there any way to do this?  Thanks for reading! edit: Well, it turns out I used the function Value wrong. The right code for my problem would be Value(p,[x,y],[1,y]). So my first question is solved. Ubuntu server shows me that I  use allmost all disk:  Usage of /:   95.5% of 118.12GB   And I try to find big folders and files, run ncdu:  ncdu 1.8 ~ Use the arrow keys to navigate, press ? for help                                                                                                                                                  --- / ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------     5.5GiB [##########] /root                                                                                                                                                                                    2.3GiB [####      ] /var   628.6MiB [#         ] /usr   209.9MiB [          ] /lib    28.2MiB [          ] /boot     8.6MiB [          ] /bin     7.7MiB [          ] /sbin     6.6MiB [          ] /etc   208.0KiB [          ] /run   112.0KiB [          ] /tmp    48.0KiB [          ] /opt e  16.0KiB [          ] /lost+found     8.0KiB [          ] /dev     8.0KiB [          ] /media     4.0KiB [          ] /lib64 e   4.0KiB [          ] /srv e   4.0KiB [          ] /selinux e   4.0KiB [          ] /mnt e   4.0KiB [          ] /home     0.0  B [          ] /proc     0.0  B [          ] /sys @   0.0  B [          ]  initrd.img @   0.0  B [          ]  vmlinuz   According to ncdu I use about 10 GiB of 128 GiB - it is about 10 %. Contradiction.  How to clean my ubutntu server without rebooting?  I thought that ncdu lies and used another apps to find big files and folders. All of them shows the same result as ncdu.  And df -h command shows that disk is full.  # df -h Filesystem      Size  Used Avail Use% Mounted on /dev/xvda       119G  113G     0 100% / udev            2.0G  8.0K  2.0G   1% /dev tmpfs           788M  212K  788M   1% /run none            5.0M     0  5.0M   0% /run/lock none            2.0G     0  2.0G   0% /run/shm   Update  sudo du -sch /* result:  /# sudo du -sch /* 8.7M    /bin 29M /boot 8.0K    /dev 6.6M    /etc 4.0K    /home 0   /initrd.img 210M    /lib 4.0K    /lib64 16K /lost+found 8.0K    /media 4.0K    /mnt 48K /opt du: cannot access `/proc/4470/task/4470/fd/4': No such file or directory du: cannot access `/proc/4470/task/4470/fdinfo/4': No such file or directory du: cannot access `/proc/4470/fd/4': No such file or directory du: cannot access `/proc/4470/fdinfo/4': No such file or directory 0   /proc 5.0G    /root 212K    /run 7.8M    /sbin 4.0K    /selinux 4.0K    /srv 0   /sys 112K    /tmp 629M    /usr 2.3G    /var 0   /vmlinuz 8.1G    total   8.1G  total as usual. But I see cannot access rows, maybe problem because of them.  Then I checked the biggest folder in /. It is /root :  /# sudo du -sch /root/* 96K /root/Downloads 2.5G    /root/Dropbox 36K /root/nohup.out 4.0K    /root/npm-debug.log 4.0K    /root/readonly 980K    /root/redis-2.6.16.tar.gz 228M    /root/tmp 2.7G    total Possible Duplicate:           What book would you recommend for an undergraduate wanting to learn the basics of topology? I've come across several books that claim to give an introduction to the subject, but I wasn't sure which one(s) to pick.  Here are some of the books I came across:   Introduction to Topology - Bert Mendelson Basic Topology - M.A. Armstrong First Concepts of Topology - William G. Chinn Topology Without Tears - Sidney A. Morris Topology - James Munkres   They don't go over the exact same topics, some are more in-depth than others, some seem to target slightly different audiences etc. What would be right for me (not necessarily from that list)? To give some more background, I want to learn topology because I feel it will be somewhat helpful in the field of Computer Vision. What's the limit on the no. of partitions I can have? I would like to know how many Primary and Extended Partitions I can create on a x86_64 PC with Linux running on it?     Update  : If there is a limit to the number of partitions, why is that the limit? Word for one who likes to share knowledge when asked Which is more idiomatic in a bash script: `|| true` or `|| :`? I don't do terribly much shell scripting, so I was a little surprised when I was reading  and I saw the syntax they used in this documentation:     A non-zero return from the command in any submodule causes the processing to terminate. This can be overridden by adding || : to the end of the command.   I had to look up that || : was a shorthand for forcing a command to exit successfully.  Anytime I've had to make a command exit successfully, I used || true.  Is || : considered to be more idiomatic? Appending to the end of a file with NSMutableString I killed my first wife once I found out there is a mercenary you can marry who gives you up to 300 gold a day (in Whiterun). The only requirement, of course, being that I had to hire her first. So I hired her, and then I popped the question, to which she replied the usual: tell the priest to arrange the wedding.   When we reached Riften I told her to wait, just outside the bee and barb, and arranged the wedding. I went through the process, and the second it finished she left, I followed but as I left she was nowhere to be seen. I have tried going back to my house, the pub where I hired her and that same spot in Riften about 6 times each now, some during the day, some during the night and cannot find her at all.   Now this isn't to much of a problem because I can re-marry...oh wait, to remarry, my spouse has to die, so I can't claim gold off her and can't remarry, and the autosaves have been used up fast travelling to the places I thought she might've been. My last save is something like 6 levels ago, and I don't want to have to load it.   What should I do about this situation? In Windows you have a C-drive. Everything labeled beyond that is with the following letter.   So your second drive is D, your DVD is E and if you put in a USB stick it becomes F and the following drive G. And so on and so forth.  But then, what and where are A and B-drives? Nikkor f/1.8G 35mm or 50mm? I'm new to photography. I got a Nikon D3100 with the 18-55 kit lens.  I was looking to buy a f/1.8 prime lens, and I found two options:   AF-S DX NIKKOR 35mm f/1.8G   AF-S DX NIKKOR 50mm f/1.8G   How should I go for choosing one or the other? Explanation of finite population correction factor? I understand that when sampling from a finite population and our sample size is more than 5% of the population, we need to make a correction on the sample's mean and standard error using this formula:  $\hspace{10mm} FPC=\sqrt{\frac{N-n}{N-1}}$  Where $N$ is the population size and $n$ is the sample size.  I have 3 questions about this formula:   Why is the threshold set at 5%? How was the formula derived? Are there other online resources that comprehensively explain this formula besides  paper? how to get rid of arm64 in apt W: Invalid 'Date' entry in Release file /var/lib/apt/lists/_var_cuda-repo-8-0-local_Release N: Skipping acquire of configured file 'non-free/binary-arm64/Packages' as repository 'http://repository.spotify.com stable InRelease' doesn't support architecture 'arm64' E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-updates/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-backports/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Failed to fetch http://archive.ubuntu.com/ubuntu/dists/xenial-security/main/binary-arm64/Packages  404  Not Found [IP: 91.189.88.161 80] E: Some index files failed to download. They have been ignored, or old ones used instead.   After I installed Jetpack for Jetson tx1, my ubuntu constantly tries to fetch arm updates. Is there a way to disable this?  EDIT:   $dpkg --print-architecture amd64  $dpkg --print-foreign-architectures i386 arm64   I see that arm64 is included in foreign architectures. How do I remove it? I came to this conclusion: the primes that can't be written as the sum of two squares (lets use$p\prime$ to denote) can be written as ${p}\prime \equiv 3 \;(\bmod\; 4)$.  I need a simple proof to show this and am stuck. I would appreciate guidance! Journals selection - alternative criteria to impact factor While trying to select the journals I can submit my present work and future work, I realize the time between the date the authors send the article to the journal and when the revised article is submitted. Usually this is something between 6 months and more than 12 months.  Althought I am focusing on the Impact Factor (IF) to select journals, I think that 12 months to have a feedback that might include "add more variables analysis","this article will be more valuable if you test also model x,y and z", can have a huge impact on you work. It will make you stop what you are currently doing and possible spend up to 2 months making the changes. This might make a big mess on your work if you have deadlines to respect, however this happens to everyone in academia.  My question is, besides the IF journal based selection, how can we select a journal with enought quality with lower IF? What alternative criteria should one use to select the journal? Should we choose newly created Journals? How can I solve this integral using the Residue theorem? $$ \int_{-\infty}^\infty \frac{\sin(x)}{x^2 + 4x + 5}dx$$  What I now is you can use residue theorem, and evaluate this integral  $$ \oint \frac{e^{iz}}{z^2 + 4z + 5}dz$$ and through calculating the residues and using the residue theorem I get that the answer for the above integral is $$\pi e^{-1-2i}$$  However after this I am completely lost.  Any guidance will be much appreciated. I would like to know why I can evaluate the integral as an exponential integral as well. Square roots -- positive and negative Please could someone tell me where can I download Ubuntu 32bit without using a torrent? Thanks What is wrong with this query? (Unknown error parsing query) When I run the following query in query editor I get this error.  Error     Unknown error parsing query   Query  SELECT Id, OwnerId,Account.OwnerId FROM Contact where OwnerId = Account.OwnerId limit 100   Does anybody know what the problem is?