I am reading a computer science paper and have come across some notation that I am unfamiliar with.  it says to consider functions from $\mathbb{R}^N$ to $]-\infty,\infty]$  is this the same as writing $(-\infty,\infty]$?  to use another example, is this true:  $x \in ]4,6] \iff 4 &lt; x \leq 6$
I have frequently encountered both $\langle a,b \rangle$ and $[a,b]$ as notation for closed . I have mostly encountered $(a,b)$ for open intervals, but I have also seen $]a,b[$. I recall someone calling the notation with $[a,b]$ and $]a,b[$ as French notation.   What are the origins of the two notations?  Is the name French notation correct? Are they used frequently in France? Or were they perhaps prevalent in French mathematical community at some point? (In this  Bourbaki is mentioned in connection with the notation $]a,b[$.)      Since several answerers have already mentioned that they have never seen $\langle a,b \rangle$ to be used for closed intervals, I have tried to look for some occurrences for this. The best I can come up with is the article on , where these notations are called Czech notation and French notation. Using $(a,b)$ and $[a,b]$ is called English notation in that article. (I am from Central Europe, too, so it is perhaps not that surprising that I have seen this notation in lectures.) I also tried to google for  or . Surprisingly, this lead me to a  where this notation is used for open interval.
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Let $(E,D)$ be an encryption scheme that uses $n$-bits keys to encrypt $l(n)$-length messages. $(E,D)$ is computationally secure if    $$E_{U_{n}}(x_{0}) \approx E_{U_{n}}(x_1)$$   And then it introduces the secure game (e.g. CPA, CCA)? I think it is a part of provable security.  "Unconditional security" (or "information-theoretic security" or "perfectly secrecy") and "computational security" are two opposite classes of security. But I do not think "computational security" and "provable security" are two independent classes of security. I know that computational security emphasizes the power of attacker is bounded (polynomial-time algorithm). And the provable emphasizes the mathematical assumptions or cryptography primitives. But it also related to the computational power. Total of attribute field of point layer per polygon layer I have a polygon shapefile of many lakes, I also have a point shapefile of locations on those lakes where fish were caught.  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I am trying to set the CRS for the project to display Decimal Degrees, where it is defaulting to Feet. I can change it in the Properties Dialog, but it does not change it, it is just staying on Feet. How do I change it?  Edit: this layer was imported from a shapefile where it was internally set to Feet. I was able to get the vendor to supply one with Decimal Degrees so my problem is gone. Still would love to know if there was a way to do it myself from within QGIS. How do you protect a camera and lens while photographing in rain or snow? I've been trying to photograph lightning lately, as we have had some great storms in Colorado. I've had some difficulty getting a good vantage point, however, as almost all of these storms include rain as well. To keep my camera from getting drenched (I have weather-sealed lenses, but my camera body, a Canon 450D, is not weather sealed as far as I can tell), I've had to shoot under the eve of a building or under a thick canopy of trees, however that has greatly limited my ability to adapt to the changing weather and get get a vantage point on the best lightning.  Is there any equipment, something I can purchase or something home-made that has easy-to-find parts, that can help me protect my lens from the rain while still being able to shoot? Additionally, I've been getting rain on a UV filter I have on the front of my lenses, simply to prevent rain from getting on the front lens element itself. However, once a storm really gets going, so does the rain. Is there a simple solution to keep rain off the front of the lens? Is there a "do ... while" loop in Ruby? I'm using this code to let the user enter in names while the program stores them in an array until they enter an empty string (they must press enter after each name):  people = [] info = 'a' # must fill variable with something, otherwise loop won't execute  while not info.empty?     info = gets.chomp     people += [Person.new(info)] if not info.empty? end   This code would look much nicer in a do ... while loop:  people = []  do     info = gets.chomp     people += [Person.new(info)] if not info.empty? while not info.empty?   In this code I don't have to assign info to some random string.  Unfortunately this type of loop doesn't seem to exist in Ruby. Can anybody suggest a better way of doing this? Why do you cast downvotes on answers? I've recently run into many questions where to author asks several related questions in one post, many of them asked before.   I'm wondering what out policy is on such questions:   Should I vote-close them as being not constructive? Should I vote-close them as duplicates? Should I leave them be? Or even suggest an answer?    - Each of the questions: Waiting for an AJAX request with selenium, and headless browsing in selenium have been asked here before, but he asked both in one.  I've done my best to search for similar questions here in meta but I was unable to find any, reading appreciated. Heroku and Twisted Center a column in align I have the following type of code in my document:  \begin{align*}        (-m)+m &amp; \stackrel{\mathrm{Ax 1.1 (i)}}{=}  m+(-m)\\   &amp;\stackrel{\mathrm{Ax 1.4}}{=}  0 \   I want to align on the = but that is complicated by the fact that there is something hovering over it.  It would seem to be easier to align their centers (no matter what, that is where the = will be).  How can I center a column in align (or align* to be honest, I am not that clear on the difference) Was Kylo Ren's Blaster Bolt Freezing Really Force Telekinesis? In this questions answer its stated that Kylo Ren freezes the blaster bolt in midair with telekinesis:       Because he is extremely skilled in Force telekinesis, Kylo Ren is able   to freeze not just objects but even blaster bolts in midair.   But as a commenter already pointed out, this seems nonsense (even in star wars force physics). The blaster bolt is, as far as I know, a cloud of plasma. If it is stopped by telekinesis, why should it continue its old path with its old speed after it is released? Wasn't it more a completely new force ablility like "time freeze"? While I admit in a case of time freeze the bolt should not have flickered all the time. Also the plasma should have expanded and vanished or simply cooled down releasing its energy to the surrounding air.  So when it was force telekinesis Kylo must have done the following:   Stop every atom in the plasma cloud Keep the cloud compressed and in form and shape. 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