It is not really puzzling that Benjamin should have taken such authors seriously; virtually everyone – including the avant-garde – was drinking from the murky waters in the interwar period.   From the preceding paragraph it follows that Benjamin really "took such authors" (the ones with reactionary and right-wing beliefs) seriously. But does not the usage of "should have" in my sentence indicate actually the opposite?
From :      ‘We all believe, up at the Lodge, Rachael, that he will be freed from suspicion, sooner or later.’    ‘The better I know it to be so believed there, my dear,’ said Rachael, ‘and the kinder I feel it that you come away from there, purposely to comfort me, and keep me company, and be seen wi’ me when I am not yet free from all suspicion myself, the more grieved I am that I should ever have spoken those mistrusting words to the young lady. And yet I— ’   We usually use should have to say that something was not done, despite being desirable. But in this example, the mistrusting words were indeed spoken (earlier in the book). How would one explain the use of the should have construction then?   Would the following be fully equivalent to the above quote:     ‘We all believe, up at the Lodge, Rachael, that he will be freed from suspicion, sooner or later.’    ‘The better I know it to be so believed there, my dear,’ said Rachael, ‘and the kinder I feel it that you come away from there, purposely to comfort me, and keep me company, and be seen wi’ me when I am not yet free from all suspicion myself, the more grieved I am that I have spoken those mistrusting words to the young lady. And yet I— ’
What is the difference between "meet" and "meet with"?  For example, which of these should I say?        I met my boss yesterday    I met with my boss yesterday   I'm meeting my friends tonight    I'm meeting with my friends tonight "I who has" vs "I who have." Possible Duplicate:          Am aware it is correct to say "I have written..." and "I am a doctor who has writen..."  I have, however, severally come across the sentence "I, Tertius, who have written...". Shouldn't it be "I, Tertius, who has written..."? This is just a curiosity. I have come across multiple proofs of the fact that there are infinitely many primes, some of them were quite trivial, but some others were really, really fancy. I'll show you what proofs I have and I'd like to know more because I think it's cool to see that something can be proved in so many different ways.  Proof 1 : Euclid's. If there are finitely many primes then $p_1 p_2 ... p_n + 1$ is coprime to all of these guys. This is the basic idea in most proofs : generate a number coprime to all previous primes.  Proof 2 : Consider the sequence $a_n = 2^{2^n} + 1$. We have that  $$ 2^{2^n}-1 = (2^{2^1} - 1) \prod_{m=1}^{n-1} (2^{2^m}+1), $$  so that for $m &lt; n$, $(2^{2^m} + 1, 2^{2^n} + 1) \, | \, (2^{2^n}-1, 2^{2^n} +1) = 1$. Since we have an infinite sequence of numbers coprime in pairs, at least one prime number must divide each one of them and they are all distinct primes, thus giving an infinity of them.  Proof 3 : (Note : I particularly like this one.) Define a topology on $\mathbb Z$ in the following way : a set $\mathscr N$ of integers is said to be open if for every $n \in \mathscr N$ there is an arithmetic progression $\mathscr A$ such that $n \in \mathscr A \subseteq \mathscr N$. This can easily be proven to define a topology on $\mathbb Z$. Note that under this topology arithmetic progressions are open and closed. Supposing there are finitely many primes, notice that this means that the set $$ \mathscr U \,\,\,\, \overset{def}{=} \,\,\, \bigcup_{p} \,\, p \mathbb Z $$ should be open and closed, but by the fundamental theorem of arithmetic, its complement in $\mathbb Z$ is the set $\{ -1, 1 \}$, which is not open, thus giving a contradiction.   Proof 4 : Let $a,b$ be coprime integers and $c &gt; 0$. There exists $x$ such that $(a+bx, c) = 1$. To see this, choose $x$ such that $a+bx \not\equiv 0 \, \mathrm{mod}$ $p_i$ for all primes $p_i$ dividing $c$. If $a \equiv 0 \, \mathrm{mod}$ $p_i$, since $a$ and $b$ are coprime, $b$ has an inverse mod $p_i$, call it $\overline{b}$. Choosing $x \equiv \overline{b} \, \mathrm{mod}$ $p_i$, you are done. If $a \not\equiv 0 \, \mathrm{mod}$ $p_i$, then choosing $x \equiv 0 \, \mathrm{mod}$ $p_i$ works fine. Find $x$ using the Chinese Remainder Theorem.   Now assuming there are finitely many primes, let $c$ be the product of all of them. Our construction generates an integer coprime to $c$, giving a contradiction to the fundamental theorem of arithmetic.  Proof 5 : Dirichlet's theorem on arithmetic progressions (just so that you not bring it up as an example...)  Do you have any other nice proofs? Evaluate the integral $$\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$$ I searched wide and far and couldn't come up with a title for a movie I watched somewhere around the mid-90ies up to early 00's as a rerun in late-night television (in Germany, specifically on Vox; but I'm sure it was an American movie to begin with).  Basically, what I remember from the story revolves around a crew in a space station or maybe space ship of some sort. Some crew members murder other crew members and there is some kind of door they are not supposed/unable to go through. Late in the movie they do go through the door and I'm pretty sure one of the first views is a skeleton of a dead security guard. It turns out the whole thing was some kind of simulation gone wrong and they find themselves to be in a (nuclear?) wasteland. And that's pretty much the revelation/wrap-up of the movie, as I recall it.  I would be delighted if somebody had any idea what movie this could be :) Thanks!  EDIT: The whole movie was in color and I think it was feature-length, not just 45 mins. What are the most important things I need to do to encourage Google Sitelinks? What lifetime can be expected of the typical hard disk? Or are there big differences between different types? And does it make a difference if it is used heavily instead of never being connected to system (for example serving as a backup medium)? Good-morning Math Exchange (and good evening to some!)  I have a very basic question that is confusing me.   At school I was told that $\sqrt {a^2} = \pm a$  However, does this mean that $\sqrt {a^2} = +2$ *and*$-2$ or does it mean: $\sqrt {a^2} = +2$ *OR*$-2$  Is it wrong to say 'and'? What are the implications of choosing 'and'/'or'  Any help would be greatly appreciated. Thanks in advance and enjoy the rest of your day :) I've got an iPhone app with icon file Icon.png.  This icon shows up properly when the app is on the phone itself, but it doesn't show up in the applications pane in iTunes.  What do I need to do to get it to show up properly? Name of short sci-fi story involving a musician who is punished for listening to Bach When drag force ($bV$) equals to object's weight (mg) then upward and downward force becomes equal. As a result the object comes to rest. If this is true, how is a body moving with constant velocity? What is the agreed upon definition of a "positive definite matrix"? How to suppress certain .bib fields (e.g. year) only for certain entry types (e.g. inproceedings) Why could the pictures and paintings in Hogwarts talk and the photos of Harry's parents couldn't? It's my understanding that "easily" is the regular adverb for "easy", e.g. "He makes friends easily".  But in some collocations one still uses "easy", e.g. "Take it easy", "Rest easy" or "Slow down easy". Is there any rule when "easy" would be used over "easily", or does one just have to know these collocations? Zsh says "no matches found" when trying to download video with youtube-dl I downloaded youtube-dl using pip on CrunchBang (a Debian Wheezy distro). When I run   youtube-dl {video URL}   I get  zsh: no matches found: {video URL}   I guess it has something to do with zsh, because I found some users on Arch forums complaining about it. When I switched to bash it worked. Best Algebraic Topology book/Alternative to Allen Hatcher free book? Allen Hatcher seems impossible and this is set as the course text?  So was wondering is there a better book than this? It's pretty cheap book compared to other books on amazon and is free online.   Any good intro to Algebraic topology books?  I can find a big lists of Algebraic geometry books on here. On a very old thread on Maths overflow someone recommended that a person should read James Munkres Topology first, then you should read Allen Hatcher book.   It just seems like Rudin's book but crammed with ten times more material. Unusual integral I got a clock as a gift recently. It has a very novel face in that the hour positions are given by a complex formula. For the most part, I have been able to verify the calculations presented as accurate, but the two o'clock identity has me stumped.  $$ \frac{\gamma}{\displaystyle{\int_0^\infty\frac{e^{-x^2}-e^{-x}}{x}\,dx}} $$  I know that $\gamma$ is the . And WolframAlpha tells me that $\int_0^\infty\frac{e^{-x^2}-e^{-x}}{x}\,dx=\frac{\gamma}{2}$ which  makes sense because  $$ \frac{\gamma}{\displaystyle{\int_0^\infty\frac{e^{-x^2}-e^{-x}}{x}\,dx}}=\frac{\gamma}{\displaystyle{\frac{\gamma}{2}}}=2 $$  It is not clear how I would show $\int_0^\infty\frac{e^{-x^2}-e^{-x}}{x}\,dx=\frac{\gamma}{2}$. Could anyone shed some light on this or point me to a source (book, article, etc...) where I can read up on this. The usual internet (listed above) resources have not been helpful to me. What counts as "entering a zone"? There are many actions that create persistent zones and have a trigger for their effect of among others: "...enters the zone..." What are the things that qualify as entering the zone?  Things that would seem to fit this would be:   Willing movement into the zone. Forced movement into the zone. Teleporting into the zone. Appearing inside the zone. Having the zone moved to include the square you occupy.   Do any of those listed not count as having entered the zone and why? And are there any that are not listed that would count as having entered the zone?  This is for D&amp;D 4e. Seeking GeoServer tutorials? What are sources where I can learn how to use GeoServer?  I know of these two sites:    - which in fact is not working (at least at the moment)  - not only (tutorials) for GeoServer   But I am interested in more complex information, and not to read only documentation.