I've been reading a camera review which shows a picture with a tiny rectangle highlighted. It then shows that rectangle expanded to the same size as the original picture so that one can see the detail. This is referred to as a 100% crop in the review but that does not agree with the definitions given here. So what is it? I would call it a sectional enlargement!
I use the term "100% crop" to mean a portion of a picture that has been cropped but not resized, but I have also seen some confusion around that term.   Is there an accepted definition for "100% crop?" What is its opposite called?   Here's what I think it means:   If I'm right, what is the proper name for "something else?" If I'm wrong, please include illustrations.  Either way, what evidence supports the definitions?
Gradient Boosting for Linear Regression - why does it not work? Are the WotC archives of d20 Character Optimization forum forever lost? I was looking for the Wizard Handbook but all the links were broken.  Somewhere on the handbooks of other classes (on other forums) I saw a      This was archived by WotC, here's the link   But the link leads to the welcome page of WotC (since it's broken).  Is there a way to get all that info back? Do you know where to get it from? The Wayback Machine did not archive the forums. Calculating $\lim_{x\to0} \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$ Find $$\lim_{x\to0}  \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$$ where $\lfloor\cdot\rfloor$ is greatest integer function   I am a high school teacher. One of my students came up to ask this limit.  For $\lfloor\frac{\sin x}{x}\rfloor$, I have used $\sin x &gt; x$ using increasing decreasing functions.  I tried to prove $x^2 &gt; \sin x \tan x$ using increasing /decreasing  function but I am not getting it. Will I lose previous purchases when I change country in iTunes the slash (/) after a directory name on shell commands I have a little question here.  If I have two files, say filea and fileb, mv filea fileb would   delete fileb rename filea to fileb   Then if I have two directories, say dira and dirb, mv dira dirb would   move dira into dirb (it will become dirb/dira)   Noting that in both cases there are no notice or message, then this is pretty inconsistent to me. I think mv dira dirb should just overwrite dirb with the contents of dira (or merge the two directories under a directory named dirb).  I remember reading somewhere that a directory name with a slash (like dira/) is treated like a directory, and name with no slash (like dira) is treated like a file (to certain extents, of course). Anyway now I want to make the shell (zsh and possibly bash) respect my notation of a directory by using a slash. Is there a terminal option which enable me to enforce that?  To clarify, here is my desired behaviour:   mv dira dirb results in dirb being overwritten with the contents of dira mv dira dirb/ results in dira being moved into dirb (in dirb/dira)   Has anyone thought the same way as me? Or am I just weird? Why screen resolution remains 640x480 when I close a game? Can an illusion give a player partial cover? I'm in an argument with a player at my table, he says hiding behind some bushes while shooting arrows at my monsters gives him partial cover because they can only see his head and shoulders. So they're limited in what they can even aim at. I accepted that. And now he's trying to use minor illusion to create fake bushes/walls and continuing to claim he has partial cover.  I thought cover was based on having a solid obstacle between you and the target... Like, if a magical attack, or penetrating attack can pass through your cover, wouldn't that negate the AC bonus from partial cover? Or is it about "aiming"? What is the relation between linear purity and von Neumann entropy of a state? Why aren't logarithms defined for negative $x$? How to run a complete GUI as root? \clipbox of a \scalebox not working properly in xelatex What is the difference between dpkg and aptitude/apt-get? When installing a software via dpkg -i packageA.deb, will the dependencies required by packageA be downloaded and installed automatically? How is this different from using apt-get or aptitude? PHP __PHP_Incomplete_Class Object with my $_SESSION data What does $b_i\mid b_{i+1}$ mean in this context? In the computational topology literature, the reduction algorithm for computing the Smith normal form of a boundary matrix uses the notation $b_j &gt; 1 \: \text{ and }\: b_j\mid b_{j+1}$ in the context of the diagonal elements of the Smith matrix. Can anyone give me an idea for what it means? How to read exponential expressions, e.g., "2^16"? How do you say the mathematical function in English:     x^y (or xy)   For example, how do you say      2^16  (or 216)   I know ^ means 'power' or 'exponentiate', but that is the name of the operation, not how you pronounce its use.  If y = 2, it is 'x squared', y=3 then 'x cubed'. What if y is some other arbitrary number? Convergence of the sequence $\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots$ I recently came across this problem     Q1 Show that $\lim\limits_{n \rightarrow \infty} \underbrace{{\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+\cdots+n\sqrt{1}}}}}}}_{n \textrm{ times  }} = 3$   After trying it I looked at the solution from that book which was very ingenious but it was incomplete because it assumed that the limit already exists.  So my question is     Q2 Prove that the sequence$$\sqrt{1+2\sqrt{1}},\sqrt{1+2\sqrt{1+3\sqrt{1}}},\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1}}}},\cdots,\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+\cdots+n\sqrt{1}}}}}$$ converges.   Though I only need solution for Q2, if you happen to know any complete solution for Q1 it would be a great help .  If the solution from that book is required I can post it but it is not complete as I mentioned.   Edit: I see that a similar question was asked before on this site but it was not proved that limit should exist. Adding Vertical Reference in Python to ArcGIS feature dataset I was reading a blogpost here:  () One thing that threw me off was that after the first four large displayed equations, there is the statement &quot;it is sufficient to prove that if the theorem holds for $n=m+1$, then it holds for $n=m$.&quot; How is this type of induction valid? I browsed around for things like backward induction, reverse induction, and Cauchy induction, but couldn't find a justification for how this is valid. With the usual forward induction of verifying a base case and proving $P(n)\implies P(n+1)$, it's easy to intuitively understand how induction will show a property holds for all natural numbers (or at least starting at the base case). But with this reverse induction, it seems to me that if you prove $P(m+1)\implies P(m)$, then if you were able to verify a specific case like $P(15)$, then you would only know it's true for numbers up to $15$. How does it actually prove the property for all naturals? I see you have succussfully answered this question previously but it is not specific to my system.  I have downloaded your file and created the relevant dump file but I don't know how to analyse it. Can I upload it to you for some advice please? What will reduce my rendertime? What would reduce the render time? Should I get a better GPU or more RAM?