I have to write the definition of uniform convergence. That is, the superior limit in the succession's pointwise convergence's set of the limit for n to infinite of the absolute value of the difference between the n-th function and the limit function evaluated in x. More difficult said than done. The fact is, written in LaTeX this way:  \[\sup_{x\in I}\lim_{n\to\infty}\left|f_n(x)-f(x)\right|=0\]   Results in this:    The range of \sup and \lim are not aligned, resulting in a rather displeasant appearance. I tried adding \vphantoms in the subscripts (just in case the problem is in the capital I), but even putting the same subscript in the  \lim and the \sup changes nothing, the problem is in the p letter of the latter which shifts the subscript lower than the other one.  Can anybody tell me how to ignore it?
Consider the following snippet:  $$\text{d}_{H}(A,B)  = \max\left\{ \sup_{a\in A} \inf_{b\in B} \text{d}(a,b),\sup_{b\in B} \inf_{a\in A}\text{d}(a,b)\right\}$$     In the output, the text under the inf's is significantly smaller then the one under the sup's. The same happens when I have it in an align environment.  You can see the same problem in the wiki definition of the . How can I have the typeset under the inf's and sup's in the same size?
HDD SMART interpretation - Possible impending drive failure I've just had an issue pop up related to my drives.  First things first, I was working in my case when I clumsily shifted the foot of the case off of my desk. Case shifted and hit the desk somewhat hard, but only fell an inch or two. It had been properly shut down so this may not have anything to do with the issue.  After booting up, I noticed that when playing a video from my F: Drive (Seagate), it produced a whine, almost a chirping sound coming from the hard drive bay. I think I may have heard this before the drop, but quieter.  Fearing impending failure I downloaded GSmartControl and inspected the drive information. The Seagate drive displayed a high Raw Read Error Rate, as well as a high Seek Error Rate.  I've read some of these values can be high on Seagate drives from the start. This drive is about 6 months old and the producer of the noise.  I also checked my Toshiba drive, which came with a refurbished prebuilt I bought about a year ago. It showed more normal SMART data, but displayed some concerning statistics (2 "Mechanical Start Failures" and 2 "Reported Uncorrectable Errors").  Both of the drives passed the basic SMART test, but the noise was quite alarming. It would stop as soon as a paused the video and start right up again as soon as I resumed playing.  Here is an album with 3 photos of the SMART data, the Seagate did not display statistics.  Could I please have help interpreting the SMART data, and whether this may indicate an impending failure?   Thank you for your time.   Here are images of the SMART data. Set a polygon's normal's orientation as the objects local rotation orientation (if every polygon is an object) Use Cauchy product to find a power series represenitation of   $$1 \over {(1-x)^3}$$ which is valid in the interval $(-1,1)$.   Is it right to use the product of $1 \over {1-x}$ and $1 \over {(1-x)^2}$ if I know thier expantion (HOW).. Is there another way? If you copy the contents of   httpd.conf   and then paste it into a cat command.. such as this one..  #!/bin/bash cat &gt; /test &lt;&lt; EOF pasted here.. EOF   you run into this error:  -bash: command substitution: line 1: unexpected EOF while looking for matching `'' -bash: command substitution: line 4: syntax error: unexpected end of file   perhaps the solution is to escape the dollar signs and maybe even quotes and so on..  but given that this is such a large file.. can dollar signs be automatically be escaped ?  is my only option to escape them via another program and then give it to the cat command ? Why not brew wine and make beer? Non native speaker so I can't fully discern the difference.  Thanks. Granting access only to standby database One of the physical standby databases in my environment is open in read-only mode and used for reporting purposes . I want to give users access only to this particular standby, not to primary db.   The best approach I found so far is to create AFTER LOGON ON DATABASE trigger which checks v$instance (or maybe v$database), and throws error for depends on  values of host_name/instance_role columns  .   I wonder if there is a better way to do it. For x < 5 what is the greatest value of x It can't be $5$. And it can't be $4.\overline{9}$ because that equals $5$. It looks like there is no solution... but surely there must be? If a charge travels in a circle it must accelerate, thereby producing EM.  However, a wire in a circular loop is analogous to many charges moving in a circle. So, why don't circular currents produce EM? (I have not found any evidence that circular currents can produce EM).  A similar question is: . However, my question asks about circular wires and direct current. Thanks. How can I best describe "making a new discovery"? "Any" followed by singular or plural countable nouns? This question has troubled me for ages despite my several attempts of looking it up in dictionaries or usage books. Do we say, "Do you have any ideas" or "Do you have any idea"? I do see an example where "any" means "it doesn't matter who/which/what", therefore "You can borrow any book you like." Also, does it matter between using it in questions and negatives? Why are packages in the official Ubuntu repositories older than the latest (upstream) versions from Debian Sid, PPAs, the authors, etc.? How can you test what color different people perceive? Turn off buffering in pipe I have a script which calls two commands:  long_running_command | print_progress   The long_running_command prints progress but I'm unhappy with it. I'm using print_progress to make it nicer (namely, I print the progress in a single line).  The problem: Connection a pipe to stdout also activates a 4K buffer, so the nice print program gets nothing ... nothing ... nothing ... a whole lot ... :)  How can I disable the 4K buffer for the long_running_command (no, I do not have the source)? How to set custom keyboard shortcuts from terminal? Obfuscation is one way, but it can't protect from breaking the piracy protection security of the application. How do I make sure that the application is not tampered with, and how do I make sure that the registration mechanism can't be reverse engineered?  Also it is possible to convert a C# application to native code, and  is too costly.  C# provides lot of features, and is the ideal language for my code, so writing the whole codebase again in C++ is out of the question.  Secure certificates can be easily removed from the signed assemblies in .NET. When you have a card like  which reads "Exile Target Creature with power 3 or less", as I understand it, it becomes untargetable if the opponent's creature power increases thanks to a pump spell like .  But what if the Disregard is already on the stack and targeting; and they respond with Brute Strength? I'm pretty sure (and my opponent with Brute Strength was certain) that it won't exile the creature, but I don't know which rule states this, and there's no gatherer ruling on the spell. Can internal forces do work? My Mechanics textbook claims that the sum of the work by internal forces is not generally zero.  translated to English the paragraph reads:     Notice about the work by internal forces: the work by the internal forces is in general not equal to zero although the sum of the internal forces is always equal to zero. Since the work also depends on the relative displacement of the two pointmasses in the material system, the work provided by these 2 internal forces will generally not be equal to zero.   Other sources claim that the work done by internal forces is always zero.  (answer by Mark Eichenlaub)     Then I didn't do any work on the system at all since, by definition, only external forces can do work.        the net work done by internal forces is zero since they do not cause motion of the object.   To me it would seem that these sources contradict eachother. Do they? If so, which one is correct? If not, please explain why they don't contradict eachother. /usr/sbin/grub never finishes I did apt-get upgrade it never finishes at this point:  Searching for GRUB installation directory ... found: /boot/grub Searching for default file ... found: /boot/grub/default Testing for an existing GRUB menu.lst file ... found: /boot/grub/menu.lst Searching for splash image ... none found, skipping ... Found kernel: /boot/vmlinuz-3.2.0-24-virtual Updating /boot/grub/menu.lst ... done  You already have a NoLOADER configuration in /etc/grub.conf Running boot loader as requested Running /usr/sbin/grub  ...    The system does not freeze (Ctrl-Z works, I get my console back) just that that /usr/sbin/grub seems to never complete.  What should I do? What is the symbol ''$\divideontimes$'' (DIVIDE TIMES) for? I looked "$\divideontimes$" up on Google and now I know that it's Unicode U+22c7 but when would it be used?  I am guessing that $5 \divideontimes 5 = 25$ and $1$...? I was solving a few problems from a textbook and I came across this one:     Find the tangent lines to the graph of $x^2+4y^2 = 36$ that go through   the point $P=(12,3)$   I could find the tangency points $$ but my solution was completely messy (I had four equations that I had to go back-and-forth with.  Is there an elegant/simple solution to that?  Tangency points:  $$P_1 = (0,3)$$ $$P_2 = \left( \frac{24}{5} , 3-\frac{24}{5} \right)$$