For x,y∈I:=[0,1] define the relation on I as x−y∈Q.  How big (using cardinal number) is the cardinality of the equivalence class [1/√2]?  I have tried to solve it by finding the equivalence class but I'm not sure about the method that I can solve the question.  Please, can you help me to solve it.
For $x,y\in I:=[0,1]$ define the relation on $I$ as $x-y\in \Bbb Q$. How big (using cardinal number) is the cardinality of the equivalence class $[1/\sqrt2]$?  I have tried to solve it by finding the equivalence class but I'm not sure about the method that I can solve the question. Please, can you help me to solve it.
Ubuntu Server 18.04 LVM out of space with improper default partitioning Another word for a troll not on the internet The definition of an internet troll:     In Internet slang, a troll (/ˈtroʊl/, /ˈtrɒl/) is a person who sows   discord on the Internet by starting arguments or upsetting people,   by posting inflammatory,[2] extraneous, or off-topic messages in an   online community (such as a forum, chat room, or blog), either   accidentally[3][4] or with the deliberate intent of provoking readers   into an emotional response[5] or of otherwise disrupting normal   on-topic discussion.[6]      This sense of the word troll and its associated verb trolling are   associated with Internet discourse, but have been used more widely.   Media attention in recent years has equated trolling with online   harassment. For example, mass media has used troll to describe "a   person who defaces Internet tribute sites with the aim of causing   grief to families."[7][8]     What is the equivalent for a person who does this type of thing in real life (non-cyber) troll? I have created 50 spreadsheets for 50 students. Each spreadsheet contains 33 sheets, numbered 1 to 33, along with a couple of other sheets.  Within each of these 33 sheets, there are many protected ranges.  I accidentally protected a range that ought not to have been protected. So, with 50 students each having 33 sheets, I have over 1800 sheets to unprotected.  I want to loop through each sheet, 1 to 33, and remove protection from cell F15. Right now, I (the owner) am the only editor.  Since I'm not an actual programmer, I've clearly not done this properly.  Can someone offer a suggestion of how I can change my Google Script to make this work?  var ss = SpreadsheetApp.getActiveSpreadsheet(); var sheets = ss.getSheets();  for (var i=2; i  &lt;sheets.length; i++) {   var sheet = ss.getSheets()[i];   sheet.activate();   SpreadsheetApp.flush();   var range = sheet.getRange('F15');        var protection = range.protect().setDescription('Protected range');        var me = Session.getEffectiveUser();        protection.addEditor(me);        protection.removeEditors(protection.getEditors());        if (protection.canDomainEdit()) {          protection.remove();          } //end of if statement  } How to add sysadmin to user in SQL Server 2008 when no sysadmin accounts exist I have a SQL server 2008 instance running. Unfortunately during testing I deselected the sysadmin rights for my login and now can't readd it (because I don't have sysadmin rights).  There are no other sysadmin accounts for the instance except SA.  I was set up for just Windows Authentication so I hacked the LoginMode in the registry to 2 so I could login as SA using Sql Authentication. This does indeed set the login mode to Mixed, however the SA user is disabled by default and I can't reenable it because I am don't have sysadmin rights.  How do I enable the SA login so I can get in and reassign the sysadmin to my normal account? Is there a registry setting for this too or is it stored in the master database? past simple or present perfect Please have a look at this sentence:     We haven't gotten a lot of Finnish groups that we liked here at Bananas but I'm pretty happy with this four tracker from Helsinki, apparently recorded in the same place where the Ramones played in the 70's.     The first verb is in present perfect (up to now) and the second is in simple past tense. I don't understand the simple past for the second verb.  Why "like" is not in its present perfect form as the first verb is? What is the meaning of "build off of"? What is the meaning of "build off of"? I Googled it, but can't find any definition!  I encountered it in the sentence in a technical book. The sentence is:     For the application we will build, the todos example is the closest   fit, so we'll go ahead and build off of that example.   There is a link related to it I found by Google, But it didn't give the definition! If $x_1,x_2,\ldots,x_n$ are real numbers larger than $1$, prove that $$\dfrac{1}{1+x_1}+\dfrac{1}{1+x_2}+\cdots+\dfrac{1}{1+x_n} \geq \dfrac{n}{\sqrt[n]{x_1x_2\cdots x_n}+1}$$   Attempt  AM-GM doesn't work here since we will get an upper bound. I don't see Cauchy-Schwarz working either. Thus, I think a substitution might work, but I am unsure of which one to use. Having line color vary with data index for line graph in matplotlib? Is there a word to describe words that can be spelled different ways? Is there a word in English to describe words that can be spelled more than one way?  For example:   colour and color favourite and favorite   However, this shouldn't be limited to words spelled differently in different dialects, though I'm not sure what other case there would be. How can I run a DSLR from AC power? My wife has a Nikon D3100 that I've been using to film, but the battery typically won't last through long shoots.  I've gathered from searching around that I can't charge the camera with USB, but I wondered if there's ANY way to do that. It seems at least possible that an adapter could exist that would fill in for the battery and plug into the wall, but I haven't been able to find such a thing.  Is there such a product or technique? It would be nice to not buy a second battery, I'm really hoping for a "set it and forget it" solution. How to add a subclass as a subview so that background of subview is set in front of superview Debugging scripts, what is the difference between -x to set -euxo pipefail? The main way I know to debug scripts is adding -x to the shabang (#!/bin/bash -x).  I recently came across a new way, adding set -euxo pipefail right under the shabang, as in:  #!/bin/bash set -euxo pipefail   What is the main difference between the two ways of debugging? Are there times you would prefer one above the other?  As a freshman, , I couldn't extract such conclusion. For me, it is pretty clear that $a + \overline{a}*b = a + b$, because the first $a$ in the or will make sure that if the second term must be 'evaluated', $a$ will always be false, and therefore won't matter in the and - probably because I'm a programmer and it is very common to see this unnecessary cluttering in long if-else structures.  I can easily prove it with the truth table as well, just make both expressions', and turns out they are identical.  But I was looking for a 'algebraic' way to prove it. That is, something using the basic operations properties like the fact that they are transitive, commutative, associative, etc. For example, if I was to prove this other simple identity $a + a*b = a$ I would simply do something like:  $a + a*b = a*(1 + b) = a*1 = a$.  Is there a way to also prove the former using this algebraic operations, without resorting to the truth table? What are the pros and cons of flip lock vs. twist lock on tripods? I am in search of a tripod. While doing a bit of research myself, I came to know that there are two broad variants of leg locks, viz. flip and twist lock. In many forums, I find people expressing conflicting views preferring each one over the other. This seems to confuse me even more while not being aware of what each type of lock operates. What are the prime considerations in choosing a particular lock system? Where does the extra kinetic energy of the rocket come from? Consider a rocket in deep space with no external forces. Using the formula for linear kinetic energy $$\text{KE} = mv^2/2$$ we find that adding $100\ \text{m/s}$ while initially travelling at $1000\ \text{m/s}$ will add a great deal more energy to the ship than adding $100 \ \text{m/s}$ while initially at rest: $$(1100^2 - 1000^2) \frac{m}{2} \gg (100^2) \frac{m}{2}.$$ In both cases, the $\Delta v$ is the same, and is dependent on the mass of fuel used, hence the same mass and number of molecules is used in the combustion process to obtain this $\Delta v$. So I'd wager the same quantity of chemical energy is converted to kinetic energy, yet I'm left with this seemingly unexplained $200,000\ \text{J/kg}$ more energy, and I'm clueless as to where it could have come from. Often I have a question, in a specific area (say Math SE or English SE) that is appropriate for the child meta of that site.   Then I realize it is not particular to the meta for that site but for Meta for all sites (like this question itself; I wanted a link to Meta Stack Exchange from meta.english, but realized no meta sites had such a link).  Wouldn't it be nice to have a link in all meta sites to Meta? Why are there so many close votes to review and so few of the others? In the SO Review page , I see the following stats for questions awaiting review:   Close votes:  51.8k (and rising) Suggested edits: 10 (fluctuates, but rarely goes above 20) Everything else: 0 (occasionally see some if you're really lucky)   My question is: Why?  Why are there so many close votes waiting for review? Close votes should expire after four days. And even if there's a good reason for them hanging on longer (ie they're not being viewed), there surely has to be a cut-off eventually after which they can be safely dropped?  And yes, I saw , which is asking basically the same thing. But that was several months ago, and it seems that the queue has hardly moved since then. It seems to me that there's a massive backlog that will never be cleared, and apparently will never expire either. That's not good.  And on the flip side, why are there hardly ever any new user posts or low quality posts to review -- there are always new users posting things, and I recall before this new review system was launched that the list of low quality posts to review was always pretty big. Why is the unit for capacitance so large? What is the default root password? I installed  (Precise Pangolin), 64 bit. Nowhere was I asked to set password for root.  I just installed  software. It was installed under the /root folder by default. Now I try do something on that folder. I tried with su to switch to root, but I don't know its password.   Should I always use sudo or get the default root password, if any?  How do I create a  for software installed inside the /root directory? How to understand linux versioning I need to understand the Linux versioning system and distribution concepts. what are public, stable or final terms for versions?