Prove: If $f:[a,b] \to \mathbb{R}$ is Riemann integrable, then $f$ is bounded.  My class did this using proof by contradiction and epsilon-delta definition (which I have hard time understanding).   Is there an alternative proof (perhaps easier)? Can someone explain the proof by contradiction method?   I did not post the class proof because it's way too long. Thanks.
Most statements regarding Riemann integrals (at least the ones that I have encountered) begin with the statement "for $f(x)$ bounded on $[a,b]$." I am wondering if Riemann integrability implies boundedness. I think that this has to be the case, but I am not sure. If Riemann integrability does imply boundedness, are improper integrals considered Riemann integrals? I would think that improper integrals wouldn't be Riemann integrals since improper integrals are allowed to be equal to $+\infty$ or $-\infty$. Or are improper integrals that are not equal to $\infty$ considered Riemann integrals?   I am confused.
How can I install an app given only its APK file? What is the reasoning behind the design decision to allow users to create a display name which matches another existing users exactly?    This is opposed to the common practice of enforcing unique user names, and I'd really like to learn something. I have got codes like the following (generated by Kile). How can I add a caption. I guess I should have used the table environment. Is there any solution now?  \newcommand{\mc}[3]{\multicolumn{#1}{#2}{#3}} \begin{center} \begin{tabular}{rccll}      &amp;   &amp; \mc{3}{c}{Colin}\\      &amp;   &amp; a &amp; \mc{1}{c}{b} &amp; \mc{1}{c}{c}\\\cline{3-5} Rose &amp; \mc{1}{c|}{A} &amp; \mc{1}{c|}{(1,2)} &amp; \mc{1}{c|}{(2,5)} &amp; \mc{1}{c|}{(4,4)}\\\cline{3-5}      &amp; \mc{1}{c|}{B} &amp; \mc{1}{c|}{(7,4)} &amp; \mc{1}{c|}{(3,5)} &amp; \mc{1}{c|}{(0,6)}\\\cline{3-5} \end{tabular} \end{center} Is there any way to backtrack to previous areas? Proving $\tan(\theta_1+\theta_2+\cdots+\theta_n)$ has the form $\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$ $$\tan(\theta_1+\theta_2+\cdots+\theta_n)=\frac{S_1-S_3+S_5+\cdots}{1-S_2+S_4+\cdots}$$  where  $S_i$ denotes the sum of product of tangent of angles taken $i$ at a time.     For example,$$\tan(\theta_1+\theta_2)=\frac{S_1}{1-S_2}=\frac{\tan\theta_1+\tan\theta_2} {1-\tan\theta_1\tan\theta_2}$$   (This formula is given  in my textbook with no derivation or background)  How to derive this? Ways of getting a number with $n$ dice, each with $k$ sides Assume the dice are numbered from $1$ to $k$. My hunch is that this will form a normal distribution with a median at $n\cdot\frac{k}{2}$. However, I have no idea as to    turn this fact into an answer (I have a minimal knowledge of stats, but I know that I am missing the standard distribution) and this is probably the wrong approach   How can I approach and solve this problem? (Aside, this is not for a class, stats or other, so any and all approaches welcome).  *Edit: * I want to find the number of ways that the sum of the numbers that are rolled has a particular value, if $n$ dice are rolled, and each has $k$ sides, numbered $1$ to $k$. Detect edits to add [SOLVED] or [RESOLVED] to the title and direct the user to add an answer Users often ask questions that they answer for themselves. Good for them. And good for us.  Symptom  The correct procedure seems to be:   Write new answer to own question  Wait two days Accept own answer   The incorrect, but fairly popular, procedure seems to be:   Edit the question to include the solution Put "[SOLVED] or [RESOLVED]" in the title   Proposed solution  Users should be warned when using the word "solved", delimited in any way, in a question title. This could be "[SOLVED]", "(solved)", or even "Solved - ". I imagine this:   The user tries to submit an edit that adds "solved" such that the word "solved is delimited. The user is brought to a warning page. If the only edit to the question was appending new lines (such as adding an "edit:" paragraph), that edit is copied into a text box The page mentioned in 1 is shown as follows:     $StackSite marks questions as answered when you accept an answer. You can accept an answer by clicking the green check mark next to that answer. There's no need to put "SOLVED" or "RESOLVED" in the title!      Are you answering your own question?      Create a proper answer to your question:         Move your edit to a new answer.   Write your answer.   If nobody writes a more correct or thorough answer after two days, come back and accept your answer.         By doing this, you remove your question from the Unanswered Questions list. You also allow other $StackSite users to vote your answer up. Thanks for helping out!      TEXT BOX WITH EDITS GOES HERE, FOLLOWED BY "POST YOUR ANSWER" BUTTON      Not answering your own question?      Sorry for slowing you down.      OVERVIEW OF EDIT, FOLLOWED BY "SAVE EDITS" BUTTON    Discussion  This would likely reduce the number of [RE]SOLVED questions that appear. However, it's unclear whether this should be a community moderation issue or a feature request issue. The increased engineering work required in building in the interstitial page is probably quite nontrivial, whereas this type of question makes up well under .  Note: Google also provides a . Rogue DHCP Server Can't be found Over the last 3-4 weeks I have been trying to find a rogue DHCP server on my network but have been stumped! It is offering IP Addresses that do not work with my network, so any device that needs a Dynamic Address is getting one from the Rogue DHCP and then that device stops working. I need help to find and destroy this thing! I think it might be a Trojan of some sort.  My Main Router is the only valid DHCP Server and is 192.168.0.1 which offers a range of 192.160.0.150-199, and I have this configured in my AD as Authorized. This ROGUE DHCP claims to be coming from 192.168.0.20 and offering an IP Address in the range of 10.255.255.* which is messing up EVERYTHING on my network unless I assign a static IP Address to it. 192.168.0.20 does not exist on my network.  My network is a single AD Server on Windows 2008R2, 3 other physical servers (1-2008R2 and 2 2012R2) about 4 Hypervisor VM's, 3 laptops and a Windows 7 box.  I can't ping the rogue 192.160.0.20 IP, and I can't see it in the ARP -A output, so I can't get its MAC address. I'm hoping that someone reading this post has come across this before. Install MySQLdb (for python) as non-compressed egg The install instructions are:  $ python setup.py build $ sudo python setup.py install # or su first   This gives me an .egg file. How do I tell the install to dump the files as a normal, uncompressed library?  Thanks! I know there are some similar posts on adding review queues to the mobile web page. However, this is regarding the Stack Exchange Android app. I really would like to review posts and edits from the Android app, however this isn't included in the app yet. I'm not sure how it would be implemented; maybe there could be a button or something for review. Could we please see this? What are WPF Preview Events? Can we have a list of all the Stack Exchange domains somewhere, for firewall purposes? I work behind an really annoying firewall, and I just want the net admin to add all the SE websites to the whitelist. Right now I've lost access to Stack Overflow's authentication, but not Meta's... so I have to come here before I log in there.  It's driving me nuts. Basically I just want to add an exclusion rule for all SE domains; not only the website domains, but also the content domains such as gravatar.com, quantserve.com, the domain that holds static content, etc... Service or services? I've read many articles that use the term 'emergency services ' and ' location services' .   Why not service instead? Why must it be plural? Thank you Time limited and band limited signal What Happens to electrons after Alpha Decay and Nuclear Fission? Where do the electrons go? In alpha decay do 2 electrons follow the alpha particle and make stable Helium or does the larger daughter nucleus become an anion?  Also what do the electrons do in the mixture of fission and alpha decay? With Beryllium-8 it decays into two alpha particles and 4 lonely electrons or do you get two Helium atoms?If someone could add an entry to Holocron it would be greatly appreciated, thanks. What is the meaning of p values and t values in statistical tests? Lazy evaluation in C++ C++ does not have native support for lazy evaluation (as Haskell does).  I'm wondering if it is possible to implement lazy evaluation in C++ in a reasonable manner. If yes, how would you do it?  EDIT: I like Konrad Rudolph's answer.  I'm wondering if it's possible to implement it in a more generic fashion, for example by using a parametrized class lazy that essentially works for T the way matrix_add works for matrix.  Any operation on T would return lazy instead. The only problem is to store the arguments and operation code inside lazy itself. Can anyone see how to improve this? How do you create a bootable USB stick using windows 7 I've downloaded Ubuntu desktop (the .iso file that is) on a windows 7 machine and want to create a bootable USB stick in order to install it onto a laptop which currently has no OS. Is there a way to do this? I need to insert 800000 records into an MS Access table. I am using Delphi 2007 and the TAdoXxxx components. The table contains some integer fields, one float field and one text field with only one character. There is a primary key on one of the integer fields (which is not autoinc) and two indexes on another integer and the float field.  Inserting the data using AdoTable.AppendRecord(...) takes > 10 Minutes which is not acceptable since this is done every time the user starts using a new database with the program. I cannot prefill the table because the data comes from another database (which is not accessible through ADO).  I managed to get down to around 1 minute by writing the records to a tab separated text file and using a tAdoCommand object to execute  insert into table (...) select * from [filename.txt] in "c:\somedir" "Text;HDR=Yes"   But I don't like the overhead of this.  There must be a better way, I think.  EDIT:  Some additional information:   MS Access was chosen because it does not need any additional installation on the target machine(s) and the whole database is contained in one file which can be easily copied. This is a single user application. The data will be inserted only once and will not change for the lifetime of the database. Though, the table contains one additional field that is used as a flag to indicate that the corresponding record in another database has been processed by the user. One minute is acceptable (up to 3 minutes would be too) and my solution works, but it seems too complicated to me, so I thought there should be an easier way to do this. Once the data has been inserted, the performance of the table is quite good. When I started planning/implementing the feature of the program working with the Access database the table was not required. It only became necessary later on, when another feature was requested by the customer. (Isn't that always the case?)   EDIT:  From all the answers I got so far, it seems that I already got the fastest method for inserting that much data into an Access table. Thanks to everybody, I appreciate your help. Equivalent of "former" and "latter" for more than 2 items Former and latter are valid only when there are two choices.  If I have a list of more than two items, is there an elegant way to say the first one or the last one?