How to print the set of 3 from the list?
What is the most "pythonic" way to iterate over a list in chunks?
Why do variable names often start with the letter 'm'? Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists I have to show that set of all $x$ such that $x \in P$ and $x \notin Q$ exists. So, I think I have to assume that sets $P$ and $Q$ already exist. So, with that, I can use  . This axiom is $$ \forall w_1,\cdots, w_n \, \forall A \,\exists B \,\forall x \left( x \in B \Longleftrightarrow [ x \in A \wedge \varphi(x,w_1, \cdots , w_n, A)] \right) $$ So, I will let $\varphi(x, Q, P) = x \in P \text{ and } x \notin Q $. Also, I will let $A = P$ and  $w_1 = Q $. So using universal instantiation, I get the following $$ \exists B \,\forall x \left( x \in B \Longleftrightarrow [ x \in P \wedge \varphi(x, Q, P)] \right) $$ And using, existential instantiation, there exists a set $B$ such that $$ \forall x \left( x \in B \Longleftrightarrow [ x \in P \wedge \varphi(x, Q, P)] \right) $$ Using the definition of $\varphi(x, Q, P)$, this can be simplified as following $$ \forall x \left( x \in B \Longleftrightarrow [ x \in P \wedge x \in P \wedge x \notin Q] \right) $$ $$ \forall x \left( x \in B \Longleftrightarrow [ x \in P \wedge x \notin Q] \right)$$ $$ \forall x \left( x \in B \Longleftrightarrow x \in \{ x \,| x \in P \text{ and } x \notin Q \} \right)$$ Now, using , it will follow that $$ B = \{ x \,| x \in P \text{ and } x \notin Q \}  $$ And, since $B$ exists, this means that $\{ x \,| x \in P \text{ and } x \notin Q \} $ also exists. Is the proof good ? less --quit-if-one-screen without --no-init I'm on a terminal that supports the alternate screen which is used by less, vim, etc. to restore the previous display after exiting. That's a nice feature, but it really breaks the --quit-if-one-screen switch of less since in that case less switches to the alternate screen, displays its data, figures out there is only one screen, and exits, taking the contents of the alternate screen with it.  The commonly suggested workaround is using the --no-init switch to avoid using the alternate screen altogether. However, this is somewhat ugly because I do want to use it in case less actually acts as a pager. Therefore I'm looking for a solution to use the alternate screen only if less doesn't terminate automatically.  I'll mostly use this as Git's pager, so a wrapper shell script that only runs less in case there is enough output would be fine, too. At least if there's no way to do it without one. How can an uneducated but rational person differentiate between science and religion? I recently found myself unable to respond to the statement "But the big bang theory is just another creation myth!" during a science vs. religion argument. I found it very difficult to explain the difference between the big bang theory and creation myths without going through a crash course in Newtonian and then Relativistic mechanics.   This had me thinking of the following scenario: Consider a person who for various reasons never got a formal education beyond basic reading and writing. He/She doesn't know any science or math, and was never exposed to any scientific reasoning and experiments. She/He is however an open minded, level headed, and rational person (I've met more than one such person myself).   How would such a person differentiate science from religion? As far as he/she is concerned science has the exact same structure as religion:    A hard to understand scripture: Science treatises and journal papers.  An ordained clergy with a high entry barrier: Doctors, professors, scientists, etc... Seemingly arbitrary injunctions against certain behaviors: "Don't smoke", "Don't pollute",.... Various metaphysical (from his/her perspective) claims about the world around us: The big bang, other galaxies, blackholes, quarks,... Organizations which control and oversee doctrine: The FDA, The NIH, The NFS,...   From his/her perspective, all of these characteristics are no different than the way organized religion presents itself as being the source of truths about the world.   In particular if such a person were to heed the advice of the :         Do not go upon what has been acquired by repeated hearing (anussava),   nor upon tradition (paramparā),   nor upon rumor (itikirā),   nor upon what is in a scripture (piṭaka-sampadāna)   nor upon surmise (takka-hetu),   nor upon an axiom (naya-hetu),   nor upon specious reasoning (ākāra-parivitakka),   nor upon a bias towards a notion that has been pondered over (diṭṭhi-nijjhān-akkh-antiyā),   nor upon another's seeming ability (bhabba-rūpatāya),   nor upon the consideration, The monk is our teacher (samaṇo no garū) Kalamas, when you yourselves know: "These things are good; these   things are not blamable; these things are praised by the wise;   undertaken and observed, these things lead to benefit and happiness,"   enter on and abide in them.'      Following the Buddha's advice (ironically himself a religious figure), such a rational but uneducated person would have just as much reason to doubt the various results of scientists as to doubt the dogmas of organized religion.    How would it be possible for such a person to distinguish scientific facts from religious dogma?  How can we convince such a person of the validity of ideas like those of modern cosmology or evolutionary biology, without first having to teach them enough biology and physics to understand those concepts? I never want my PNGs to be interlaced. So I wish I could set a bunch of option defaults in the application so that I am saving time when outputting a lot of images as PNG over the course of a day working in Photoshop.  Does anyone know if this is possible in Photoshop without using Actions OR the Save-for-Web option? How is the Integral of $\int_a^bf(x)~dx=\int_a^bf(a+b-x)~dx$ Can Some one tell me what this method is called and how it works With a detailed proof   $$\int_a^bf(x)~dx=\int_a^bf(a+b-x)~dx$$  I've been using this a lot in definite integration but haven't seemed to have realized why it is true.  But whatever it is it always seems to work.  Basically a proof of how it is always true. What to do with sudden wealth? What are the pros and cons of engineered hardwood? Are there any downsides to engineered hardwood? I'm looking to install hardwood in dining room and kitchen areas. 'was' versus 'had been' When I asked the driver/ to come with me to the temple/ he had been reluctant./ No error.   I think instead of 'had been', there should be 'was'. Even the answer key points that the error is in the 'he had been reluctant' part. But I am not sure why exactly is 'had been' wrong.  If we replace the first part with 'when I had asked the driver', would that make 'had been' in the third part correct? Remote desktop without a password I have an HTPC with a user that has no password and autologin.  I want to be able to connect to it via Remote Desktop without a password, so I can login with the original user. (I don't want to add another user just for the mstsc)  Is there a way of doing that?  The OS is Windows 7, 32bit. Rendered image doesn't show what Rendered Viewport shows... (pictures below) How can I add vertices to intersection of two edges? I need to put a point at the intersection of two edges. Below is a picture with red circles around where I need points to be placed. Is there a drupal.org API for retrieving the list of available modules? Prove the inequality and limitation Suppose $\{a_k\}$ ,$\{b_k\}$ and $\{\xi_k\}$ are non negative, and for all $k\ge 0$ , we have $$a_{k+1}^2\le(a_k+b_k)^2-\xi_k^2$$   Prove   1.$$\sum_{i=1}^{k}\xi_i^2\le(a_1+\sum_{i=0}^kb_i)^2$$   2. If $\{b_k\}$ also satisfy $\sum_{k=0}^{\infty}b_k^2\lt+\infty $, then $$\lim_{k\to\infty}\frac{1}{k}\sum_{i=1}^k\xi_i^2=0$$   After doing this transformation:$$\xi_k^2\le(a_k+b_k)^2-a_{k+1}^2$$ $\Rightarrow$ $$\sum_{i=1}^{k}\xi_k^2\le(a_1+b_1-a_2)(a_1+b_1+a_2)+(a_2+b_2-a_3)(a_2+b_2+a_3)+\cdots(a_k+b_k-a_{k+1})(a_k+b_k+a_{k+1})$$ then I can't move forward any more. Why is $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$? First I have checked the search option but found nothing relevant to my problem and also level of math. I just started learning the language of mathematics, on my own and I have trouble understanding why  $  \frac{1}{\infty } \approx 0 $ and  why $\frac{1}{0} = {\infty}$?  I want to know how exactly do I get to these answers. It might sound strange but it's hard for me as a beginner to picture things like this on my own. In addition to the .tex and .dvi or .pdf files, TeX/LaTeX/ConTeXt produces and uses lots of other files. What do they do? Which ones are used to create the document and which ones are automatically created by the compiler. What files can I safely delete? The first given name of an author or editor in my bibliography should be written out, but all further first names should be abbreviated (initials with a period -- and space if there are multiple first names/initials, see below). I am using style=authoryear with BibLaTeX (v. 2.7) and Biber (v. 1.7).  My bibliography looks like this:     Doe, John Arthur Kyle (2013). The secret life of John Doe.   It should look like this:     Doe, John A. K. (2013). The secret life of John Doe.   Minimal example:  example.tex  \documentclass{scrartcl}  \usepackage[ngerman]{babel} \usepackage[babel,german=quotes]{csquotes} \usepackage[backend=biber,style=authoryear]{biblatex} \bibliography{bibliography}  \begin{document}  \cite[123]{Doe} \printbibliography  \end{document}   bibliography.bib  @book{Doe,     title = {The secret life of John Doe},     author = {Doe, John Arthur Kyle},     year = {2013} }   (Worked with said versions of BibLaTeX and Biber, Texmaker (v. 4.0.3) and MiKTeX (v. 2.9.4813).)  I could not find a solution in biblatex.def and firstinits=true abbreviates all first names, including the first one. How do the radian have a unit? and is such interpretation the norm?  When something went from 4 units to 8 units, most authoritative sources seem to agree with the use of "a two-fold increase", even though what was actually increased is more like "one-fold", i.e. the original quantity.  But if the "two-fold increase" is the correct usage, why most people seem to interpret "a 100% increase" the same thing? Is it possible to extend a tourist Schengen visa (12 more days)?