I am trying to find such a function or a proof, which shows that there is no such function in general. I know, that the other direction of this statement is true. (I prooved it using only the definiton). But here I have no idea, how to show it. Thank you
So I had an exam today and one of the questions were: Give an example of a function $f$ which is nowhere continuous but $|f|$ should be continuous at all points. At first I had no idea how to do it then I came up with this, even though I know it's wrong:  $$f(x)= \begin {cases} \ \sqrt{x}&amp;\text{if }x &lt;0\\ \sqrt{-x}\ &amp;\text{if }x &gt; 0\\ \end {cases}$$  Like I said I know it's wrong..but can someone give me an example of this? Thanks.
Put a where clause around a stored procedure I cannot edit Why is glass transparent? Once I asked this question from my teacher and he replied "Because it passes light.". "And why does it pass light?" I asked and he said, "Because it is transparent.".  The same question again, Why glass is transparent? Why does light pass through it, while for opaque objects, it does not? Using "nor" in a list without "neither" is a one-by-one-matrix just a number (scalar)? I was wondering. Clearly, we cannot multiply a (1x1)-matrix with a (4x3)-matrix; However, we can multiply a scalar with a matrix. This suggests a difference.  On the other hand, I was, for example, in an econometrics lecture today, where we had for a (Tx1)-vector $\underline{û}=\left( \begin{array}{c} û_1\\ \vdots\\ û_T\end{array}\right)$:     $S_{ûû}:= \sum_{i=1}^T û_i^2$ shall be minimized. We see see that   $S_{ûû}=\underline{û}^T\underline{û}$.   Well, formally, shouldn't it be $(S_{ûû})=\underline{û}^T\underline{û}$ or $S_{ûû}=\det(\underline{û}^T\underline{û})$, to ensure that we stay in the space of matrices and not suddenly go to the space of scalars? So here, the professor (physicist) not only treats $\underline{û}^T\underline{û}$ like a scalar, but also calls it a scalar. Is this formally legit or a wrong simplification (though it does not seem to have any impact, and surely makes life easier)? Design Review: 3.3V Logic to 12V Logic (Uni-directional and Bi-directional) I'm looking for feedback and improvements on my design below. Specific questions are at the end. I created this as an attempt to answer my own, . From my feedback there, it seems like I needed to be more clear in my requirements. These are screenshots from Eagle. If there's a better way to share, please let me know so I can correct it. Entire board  The overall purpose of this board is to translate between 12V logic, and 3.3V logic. The top portion of the board represents the 12V side. The LEDs are placeholders to indicate whether the 12V signal is HIGH or LOW. In practice, these would be replaced with more , requiring up to 3A. The switches are also placeholders, allowing one to manually turn the 12V signal on and off. They are only for test purposes, the &quot;real&quot; 12V signal would be coming as the output from other relays. The bottom half is the 3.3V side. This will be connected to a  (BBB). The board will connect to 2 output GPIO pins and 2 input GPIO pins of the BBB. Overall, I want to translate the 3.3V I/O from the BBB to the 12V signals on the other side (to control more relays and read their signals). I have designed 3 modules to control both directions individually, and together. 3V3_TO_12V Module  This module converts the 3.3V GPIO output from the BBB to a 12V signal on the other side. When the 3.3V signal is low, the 12V signal is low. When the 3.3V signal is high, the 12V signal is high. To do this, the 3.3V GPIO output is connect to a , which turns a  relay on and off. This switches the 12V power as output of the module to be used elsewhere. 12V_TO_3V3 Module  This module converts a 12V signal to 3.3V signal, to be read by a GPIO input from the BBB on the other side. When the 12V signal is low, the 3.3V signal is low. When the 12V signal is high, the 3.3V signal is high. To do this, the 12V signal simply turns a  relay on and off. This switches the 3.3V power to be read as input by the BBB. DUAL_12V↔3V3 Module  This module combines the previous two modules to create a bidirectional translation. If the 12V side is high, the 3.3V input to the BBB GPIO should be high. If the 3.3V output from the BBB GPIO is high, then the 12V side should be high too. It's similar to a logical OR, if either side is high, the corresponding signal on the other side should be high too. A single 12V signal has to be split into individual input and output signals on the 3.3V side for the BBB. Questions  Is the  and  relay combination overkill for having the BBB GPIO output control the 12V power line? I like the isolation and safety it provides, but it seems too much (in terms of cost and board space) Is there a better solution for the 12V to 3.3V conversion. I like the simplicity of the  relay switching a 3.3V signal, but it takes up lots of room. Does the DUAL_12V↔3V3 Module (which combines each translation direction) even make sense? This seems wasteful to use 2 relays and a high side driver, but I haven't found simpler solution that achieves the same result. Should I add pulldown resistors for the BBB GPIO inputs, or are the internal pulldown resistors good enough?  Any other feedback is welcome. I'm new to electronic design. I'm trying to solve the following equation:  $$x^3-y^3=xy+61$$  I got:  $$(x-y)(x^2+xy+y^2)=xy+61$$  But I can't go any further. I am looking for a solution in integers.  I need some hints to proceed, please! I can't seem to find an answer to this simple question, which I need for some compliance documentation.    On a default install of CentOS 6.5 (OpenSSH 5.3p1-94.el6), after how long of being idle will a user's SSH session be terminated?  I believe the following can be set to increase the idle timeout, but they are commented out by default.  $ grep -i alive /etc/ssh/sshd_config #TCPKeepAlive yes #ClientAliveInterval 0 #ClientAliveCountMax 3   Also, is there a command to dump a list of the current sshd settings?  I don't see anything in man sshd. Is it feasible to build an index of prime factors? Would it be possible to break an RSA key, in for example 1 week of time, if the cracker have already spent X number of years building an index of primes by performing every permutation of existing prime keys up to $2^{2048}$?  I understand this would take an immense amount of time to do, but it would only be done once. Obviously, computing such an index would take a considerable amount of time and would have to be done with someone having the right amount of resource. Given the public key, you would be able to look up what the two primes are, and hence retrieve the private key instantly.  Breaking an 256 AES would then be easier, as AES keys are often generated using the RSA private key.  Would it be possible to build such an index? How long would that take in permutations and perhaps with the fastest computer in the world? \sum caused \sqrt to not be slanted I can say "I feed someone". Am I forced to say "I give someone a drink", or is there a single word for this (as in "I [verb] someone")?  Unfortunately my thesaurus can't really help me. What causes these inconsistent dark bands in some of my photos from an indoor event? Yesterday I took photos of an event at school.  The lighting was poor so I increased the iso to 3200, shutter speed was between 80 and 250 and the aperture between 2.8 and 4.0.  Canon EOS500  about 10% of the photos got this weird horizontal black area. The position of the black area is not the same,  Sometimes it is in the middle, sometimes it is in the upper or lower part of the frame  Is this an artifact from the lighting frequency? or can it be a shutter problem? Why do we use the simple past but not the present or future in the following expressions:  Don't you think it's time we went a little further Don't you think it's time we ate Don't you think it's time we went home How to demystify the axioms of propositional logic? How might I go about getting some intuition on the typical axiom schemes given for propositional logic? They seem rather mysterious at first glance.  For example, these are taken from:    $\phi \to \phi$ $\phi \to \left( \psi \to \phi \right)$ $\left ( \phi \to ( \psi \rightarrow \xi \right)) \to \left( \left( \phi \to \psi \right) \to  \left( \phi \to \xi \right) \right)$ $\left ( \lnot \phi \to \lnot \psi \right) \to \left( \psi \to \phi \right)$ Is there any value in full 'beginner's kit bundles'? Metric is continuous function Let $X$ be a metric space , $d$ is the metric , show that $d$ is a continuous function from $X\times X$ to $R$.  I think the definition is all we need , but I just don't know where to start , can anyone help me. This has come up    : migrating old questions causes problems.   The most popular solution to this to date has been to . This is do-able, but frankly it feels like treating a symptom, and doing so in a way that penalizes folks who answer what are by all appearances valid, on-topic questions.   Migration works best as a way to salvage good but off-topic questions and give them new life on a site where they can thrive. But shuffling old, answered, on-topic questions around for the hell of it is a waste of everyone's time.   Therefore, I think the real solution is much simpler: just disable the migration of old questions. They're rarely welcomed or heavily improved post-migration, often overtly disliked by folks on the destination site, and can end up causing a rather bad experience for folks who were participating in good faith on the original.   I suggest that questions older than 601 days should not be eligible for migration, either by normal user close-votes or by moderators. In extreme cases, we can perhaps provide an alternate means of moving old questions, but under normal circumstances these should be done quickly or not at all.   1 60 days is actually based on a  introduced this past spring: migrated and then rejected questions older than 60 days cause the authors to suddenly gain (permanent) reputation on the destination. Ubuntu n00b here.  I have created several disasters of the first order already.  I am getting ready to try to install opera - it is a very long and arduous process.  I am afraid - no - I am absolutely certain that I will damage something important.  How do I create a system restore point?  Does such a thing exist? A cashier wants to work five days a week, but he wants to have at least one of the Saturday and Sunday off.  In how many ways can he choose the days he will work?  So, in this case, what should I count first?  How do I start?  I know how to solve this if the cashier doesn't want a weekend off, but what do I do if the cashier do?  Thanks! Changing deleted partition back to NTFS without having to recover to another drive Recently, I accidentally deleted a partition off of my external hard disk. I had a copy of Minitool Power Data Recovery left over when the same drive had become RAW about a year ago. When I selected lost partition recovery, it immediately identified my deleted partition and allowed me to access and recover the files that were there.  My question is this. Is there any way to change the deleted partition back to NTFS without having to have a drive that you need to recover the files to and then move them back after formatting, as I don’t have any space left on either the computer or on my other external hard drive, so that I don’t need to buy a new one. The files on the disk were really important.  I am using Windows 7 Home Premium.  I appreciate any help in solving this crisis. How to clear the interpreter console? Like most Python developers, I typically keep a console window open with the Python interpreter running to test commands, dir() stuff, help() stuff, etc.  Like any console, after a while the visible backlog of past commands and prints gets to be cluttered, and sometimes confusing when re-running the same command several times.  I'm wondering if, and how, to clear the Python interpreter console.  I've heard about doing a system call and either calling cls on Windows or clear on Linux, but I was hoping there was something I could command the interpreter itself to do.  Note: I'm running on Windows, so Ctrl+L doesn't work.