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How do I add "citations" at the end of the document as done here? Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric I am pretty sure that this is such a stupid, stupid question, but how do you prove that $d_2(x,y)={|x-y|\over {1+|x-y|}}$ satisfying the third condition to be a metric, which is the triangle inequality.   I know that I should really be able to do this, but I just can't, I keep seeing a contradiction. Please help me. Include the "People Reached" and "Helpful Flags (count)" data in SEDE After my online research on the subject, I learnt that, biologically speaking, many scientists believe that there is no such thing as a race. Homo sapiens as a species is only 200,000 years old, which has not allowed for any significant genetic diversification yet, and our DNA is 99.99% similar. I've read statements that there can be more genetic variation inside a racial group than between different racial groups, meaning that, for example, two individuals from the same "race" can have less in common with each other than with an individual from another "race".  :     Scientists consider biological essentialism obsolete, and generally discourage racial explanations for collective differentiation in both physical and behavioral traits     Q1: If Homo sapiens has no races (according to biologists), why are we so different morphologically? (hair/eyes/skin colour and even athletic performance seem to differ between human populations)  Q2: Is it common for other species too, when genetically close populations have very different morphological traits? Are there any other mammal or animal species that exhibit biological diversity comparable to human diversity, and how do taxonomists treat these species? (excluding intentionally bred domestic species to keep the comparison fair)    The question has been paraphrased to emphasize that it is the biological debate that is in question, not the sociopolitical. I.e., why is there no consensus in evidence and opinions of scientists? How can I change the color of a part of a TextView? Wacom Tablet - Illustrator brush tool I currently got the intuos art wacom tablet so still learning how to use it. I'm currently in illustrator trying to draw out a map and the brush tool is doing something weird and I cannot figure out why. You can see in my image that where there are curves the black slightly spills over and is filling in half the curve with black. Brush setting is set up as a new calligraphic brush and the size is set to pressure, 3pt-3pt. What is your Instagram password when signing in using Facebook? Do this:   On your phone, create an instagram account using Facebook log in. Now on your desktop web browser, log in using Facebook connect.  Now go to delete your account - edit profile -> I'd like to delete my account.    It will ask for your password.   But you never gave it a password in order to create the account.   I tried using my Facebook password, but that didn't work.   Any ideas? The Instagram account management seems quite broken. Hitting arrow keys adds characters in vi editor When I tried to use arrow keys in insert mode in vi editor the following characters are being inserted in the editor:   for ↓ I get B, for ↑ I get A, for ← I get D, for → I get C.   Please help me in resolve this problem. Voting to Close after Accidentally Voting to Leave Open When reviewing on SO, I accidentally pushed the "Leave Open" button on a post that clearly should've been closed. I pushed the back button and saw that in the review panel my vote to keep open had been locked and it said:     PhpMyCoder voted to leave open 1 minute ago   So I clicked on the question heading to go to its page and I clicked the close link on the question page and voted to close for the relevant reason. However, when I returned to the review page (and did a hard refresh) it still said:     PhpMyCoder voted to leave open 2 minutes ago   Is it possible to vote to leave open and vote to close at the same time? I assume not. In which case, I'd say this is a bug because it should've updated to say:     OtherUser and PhpMyCoder voted to close 2 minutes ago To be honest, I have no idea how to even start this problem. I'm sorry I don't have any work to show, but I'm just at a blank. Help?  Chapter 2: Problem 27:  University B, once boasted $17$ tenured professors of mathematics. Tradition prescribed that at their weekly luncheon meeting, faithfully attended by all $17$, any members who had discovered an error in their published work should make an announcement of this fact, and promptly resign. Such an announcement had never actually been made, because no professor was aware of any errors in her or his work. This is not to say that no errors existed, however. In fact, over the years, in the work of every member of the department at least one error had been found, by some other member of the department. This error had been mentioned to all other members of the department, but the actual author of the error had been kept ignorant of the fact, to forestall any resignations. One fateful year, the department was augmented by a visitor from another university, one Prof. X, who had come with hopes of being offered a permanent position at the end of the academic year. Naturally, he was apprised, by various members of the department, of the published errors which had been discovered. When the hoped-for appointment failed to materialize, Prof. X obtained his revenge at the last luncheon of the year. &quot;I have enjoyed my visit here very much&quot;, he said, &quot;but I feel that there is one thing that I have to tell you. At least one of you has published an incorrect result, which has been discovered by others in the department.&quot; What happened the next year?&quot;   Chapter 2: Problem 28:  After figuring out, or looking up, the answer to Problem 27, consider the following: Each member of the department already knew that Prof.X asserted, so how could his saying it change anything? Custom toolbar location XP A few years ago Umber Ferrule wrote that the toolbars in the taskbar are defined in   HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer\Streams.   This looks very plausible but cannot be the entire story.  Deleting this key will in no way affect the taskbar and on rebooting the system the key magically reappears.  Why do I want to know?  Simple.  I would like to export the key to a reg. file as a convenient backup. How do I get the UTC time of "midnight" for a given timezone? The best I can come up with for now is this monstrosity:  &gt;&gt;&gt; datetime.utcnow() \ ...   .replace(tzinfo=pytz.UTC) \ ...   .astimezone(pytz.timezone("Australia/Melbourne")) \ ...   .replace(hour=0,minute=0,second=0,microsecond=0) \ ...   .astimezone(pytz.UTC) \ ...   .replace(tzinfo=None) datetime.datetime(2008, 12, 16, 13, 0)   I.e., in English, get the current time (in UTC), convert it to some other timezone, set the time to midnight, then convert back to UTC.  I'm not just using now() or localtime() as that would use the server's timezone, not the user's timezone.  I can't help feeling I'm missing something, any ideas? I am trying to understand an example from my textbook.  Let's say $Z = X + Y$, where $X$ and $Y$ are independent uniform random variables with range $[0,1]$. Then the PDF is $$f(z) = \begin{cases} z &amp; \text{for $0 &lt; z &lt; 1$} \\ 2-z &amp; \text{for $1 \le z &lt; 2$} \\ 0 &amp; \text{otherwise.} \end{cases}$$  How was this PDF obtained?   Thanks Add sort by relevance to search jobs In Careers 2.0, individuals can choose "search jobs" and sort by date posted, job title, and company name.  However, Careers 2.0 already knows what tags I'm proficient in, and knows the tags associated with the job postings.  A sort option, relevance, should be added so that jobs matching my skill set, as demonstrated on stack exchange, will float to the top. Regionalism or just bad English? I've encountered a particular type of writing occasionally and it being, derp, in writing, it's hard to tell whether there's an accent behind it. The English used seems to me to be simply incorrect, but I can't help but feel that the following features are part of a dialect or a regional style of English. One of the most glaring (and grating) features is the substitution of &quot;saw&quot; with &quot;seen&quot;.  He seen him at the shop the other day. I seen that you were looking for... etc.  The use of &quot;away (to)&quot; is also peculiar, if not incorrect.  He was away to open the door when... He was away to get what he had asked for. etc.  I haven't come across these forms very often, and even then it was accompanied by otherwise mostly correct English, which is what makes me wonder what the hell. This is more intellectual curiosity than anything else. Double dispatch in C#? No margins for Winter Bash popup When opting out the Winter Bash the top bar popup related to snowflake looks like this for me:    Is it intentional that there are no horizontal margins for popup content? Intuition on the Kullback–Leibler (KL) Divergence I have learned about the intuition behind the KL Divergence as how much a model distribution function differs from the theoretical/true distribution of the data. The source I am reading goes on to say that the intuitive understanding of 'distance' between these two distributions is helpful, but should not be taken literally because for two distributions $P$ and $Q$, the KL Divergence is not symmetric in $P$ and $Q$.   I am not sure how to understand the last statement, or is this where the intuition of 'distance' breaks down?   I would appreciate a simple, but insightful example. Show that $A_n$ is the kernel of a group homomorphism of $S_n \rightarrow \{−1,1\}$. Is it legal/well-defined C++ to call a non-static method that doesn't access members through a null pointer?