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Multiplicative group $(\mathbb R^*, ×)$ is group but $(\mathbb R, ×)$ is not group, why? $\mathbb R^*$ refers to $\mathbb R$ without zero.  Please explain the statement "$\mathbb R$  is not a group under multiplication, it is a group under addition." in the . Basically:   Why is multiplicative group $(\mathbb R^*, ×)$ a group? Why is $(\mathbb R, ×)$ not group? Why are $(\mathbb R^*, +)$ and $(\mathbb R, +)$ groups? disconnected phone while installing ROM I recently tried to install a custom ROM in my samsung j6+ but halfway through it my PC turned off. Then the problem starts i decided to reboot my phone but it shows this error &quot;No command&quot; &quot; #Reboot recovery cause is [[check_bootmode]RebootRecoveryWithKey]# Block-based OTA Supported API: 3 # MANUAL MODE v1.0.0# E:Failed to mount / cache: Invalid argument  The error message keeps appearing for just a fraction of a second then disappear and appear again I tried to go to recovery mode but no luck i cant get to it I drained the battery to turn off the device then go download mode but after get to it, it also keep restarting help me please. thank you How do I install Ubuntu? reCaptcha v1 is shutting down on March 31, but SEDE still uses it According to this , I thought the new recaptcha API was used network-wide. Though today, when going to  (which for whatever reasons never recognized me automatically), I got this message instead of a usable captcha image.   V1 Unsupported Please direct siteowner to   (Doing a second try doesn't show this message anymore, and the recaptcha v1 works as intended.)  According to , the reCAPTCHA v1 API will stop working on March 31, 2018:  What happens to reCAPTCHA v1? Any calls to the v1 API will not work after March 31, 2018. Starting in November 2017, a percentage of reCAPTCHA v1 traffic will begin to show a notice informing users that the old API will soon be retired. Most websites around the world have already switched to reCAPTCHA v2, where humans pass effortlessly. With our advanced risk analysis engine, reCAPTCHA v2 can effectively separate humans from bots and always stay ahead of the attackers. If your site still uses reCAPTCHA v1, please upgrade to reCAPTCHA v2 immediately. We no longer support reCAPTCHA v1. Any calls to the v1 API will not work after March 31, 2018. Please register a new key and upgrade to v2.  I'm really hoping this will not take  to fix, because we've only got three and a half weeks left! What should I be teaching my two year old? My two year old daughter has never been to a daycare, so everything she knows is something that me, my husband, or her grandparents have taught her. She sees very little interaction with other kids her age, well, except for her 8 month old sister.   I am wondering what people, or even day care centers, teach two year olds. What do they do all day long? Presently, our daughter draws a lot - she has bathtub crayons, wax crayons for paper, and chalk for the driveway/sidewalk. She attempts to draw circles and lines. We try to teach her shapes and colors, and she has a rough idea of what they are. She plays with sand in the sandbox a lot, dumping sand all over her and her sister's head. She goes to her playhouse and uses the slide and the swing.   We sing songs together - the alphabet song or the numbers song. She is able to say the correct word when I say the phonic (i.e. if I say B, she'll say ball; if I say H, she'll say hat). She tries counting, but is still learning (she goes 1, 2, 6, 7, 8...). She enjoys building and destroying towers. We read books and I sing some nursery rhymes. She plays a toy piano and dances around to it. She plays with playdough, but most of the time it just ends up in crumbs everywhere.  She also watches TV - something I know most parents object to. She enjoys watching Dora, Finding Nemo, and Cinderella. She will sometimes watch LeapFrog phonics videos for alphabet and numbers.   I am not trying to give a resume for my daughter, but merely wondering is there something more that kids her age do? Is there something else that I should be teaching her? What do kids her age do at a daycare?   Thanks How could I get the terminal to be launched once I have logged in, so that typing commands is much simpler? Catch multiple exceptions at once? How to edit Parameters for an Object after it is created? Book about a teenager programmed to be an assassin and trying to get back at the people responsible I read this book a few years back (around 5?). It was part of a multibook series but I have only read one book.  It's about this teenager who I think had been programmed to be an assassin but then somehow retained his conscience and was out to get the people responsible for that.  I briefly remember a girl, and this one part where he realizes he can ride a horse and then there's a chase too. I think the guy's name was Jim or Jimmy, but not quite. I'm also quite sure he was either part computer, or had a chip or something in his brain which had been programmed to give him a host of mental and physical abilities which he retained and used as well as the series progressed. How to adjust the breaking in the bibliography? I have been reading about the new Salesforce async triggers. Currently, I tend to handle these sort of needs with a trigger that passes data to a 'Handler class' that would evaluate if a certain change has occurred. If it has then we pass those Ids to a queueable class for further processing.   What advantage do CDC and async triggers offer over using queueable or batch apex? I was wondering if there is such a thing as an shapefile PRJ to PostGIS SRID lookup table?  Something that can translate the most standard shapefile PRJ definitions into the likely SRID.  When using PostGIS and pgAdminIII, if you use the postgisgui to import your shapefiles, the SRID is left as "-1".  It seems like the tool should be able to parse the Esri PRJ and determine the correct (or at least a couple of options) that are the likely SRID, rather than just leave the default.  Or does the importer have the capability to reproject on the fly if you choose another SRID?  It may seem lazy on my part, but to me it seems curious that this function hasn't already been put in place.  Does anyone know if this concept is in the works, or good reason's why it has been left out? Range of values of skewness and kurtosis for normal distribution I want to know that what is the range of the values of skewness and kurtosis for which the data is considered to be normally distributed.   I have read many arguments and mostly I got mixed up answers. Some says for skewness $(-1,1)$ and $(-2,2)$ for kurtosis is an acceptable range for being normally distributed. Some says $(-1.96,1.96)$ for skewness is an acceptable range. I found a detailed discussion here:  regarding this issue. But I couldn't find any decisive statement.   What is the basis for deciding such an interval? Is this a subjective choice? Or is there any mathematical explanation behind these intervals? how does LEA and several instruction work? So, I just finished off the first part of an important task for school and today when I was going to continue, the document with my notes were gone. The only fragment I've got left of my file is the back up file, which doesn't show in the folder where I saved the document, but I can search for it.  Is there anyway which allows me to open the back up file, save it as a text file and continue my task? I don't really have the time for running restoring tools, which never has helped me in a satisfactory way anyway.  I wrote the document in gedit and my version of Ubuntu is 12.10. Can you explain Parzen window (kernel) density estimation in layman's terms? String representation of an Enum Monitor cell value and copy it to another cell Prevent back button after logout In a Silverlight application I'm trying to find out when a property on a usercontrol has changed. I'm interested in one particular DependencyProperty, but unfortunately the control itself doesn't implement INotifyPropertyChanged.  Is there any other way of determining if the value has changed?