How to make printed paper depth-of-field effect? Does anyone know where I can find a tutorial on how to make the graphic below? I'm not sure what it's called. A lot of times it really looks like it's been printed on paper and it's just a photograph.  article is helpful, but it is lacking the depth of field.
How to get this blur texture effect in photoshop? I'm trying to get an image to look similar to this photo:    I'd guess they took a picture of the monitor with a regular camera. But I'm more interested to know what effects / filters they used to get the blur and texture. Any suggestions would be appreciated
Let $L$ denote the set of all lines in the Euclidean plane $\Bbb R^2$. We say that two lines $L$ and $M$ are parallel if either $L = M$ or $L$ and $M$ have no points in common.  Using Euclid’s Parallel Postulate prove that parallelism is an equivalence relation on the set $L$.  I need some help determining if I have the right idea about this.  $L=L$ which means that $L$ is parallel to itself. So this is reflexive.  Suppose we have $L || M$. Then Either $L=M$ or $L$ and $M$ share no points. So Then $M=L$ or $M$ and $L$ share no points. Then $M||L$. So this is symmetric.  Suppose we have $L || M$ and $M || N$. So then either $L=M$ or $L$ and $M$ share no points and either $M=N$ or $M$ and $N$ share no points. So we have that either $L=N$ or $L$ and $N$ share no points. So $L || N$. So then this is transitive.  So from all of this, parallelism is an equivalence relation. I'm not sure if this is correct or not. Any help would be appreciated. Which is the right way to do something like 'description' list but with customizable and fixed-width labels? I.e. something like this:  Label:         Text text text text text text                text text text text. Longer label:  Text text text text text text                Text text text text.   The way I see it to use two-column table (first columt for labels and second column for descriptions), but this solution seems ugly. Is there any other way? About $\lim \left(1+\frac {x}{n}\right)^n$ I was wondering if it is possible to get a link to a rigorous proof that  $$\displaystyle \lim_{n\to\infty} \left(1+\frac {x}{n}\right)^n=\exp x$$ How to let the user switch language in playframework 2 I shall assume that the sun is at rest, so before the half mass disappear, the orbit of earth is an ellipse. How to avoid perceived circularity when defining a formal language? Suppose we want to define a first-order language to do set theory (so we can formalize mathematics). One such construction can be found . What makes me uneasy about this definition is that words such as "set", "countable", "function", and "number" are used in somewhat non-trivial manners. For instance, behind the word "countable" rests an immense amount of mathematical knowledge: one needs the notion of a bijection, which requires functions and sets. One also needs the set of natural numbers (or something with equal cardinality), in order to say that countable sets have a bijection with the set of natural numbers.  Also, in set theory one uses the relation of belonging "$\in$". But relation seems to require the notion an ordered pair, which requires sets, whose properties are described using belonging...  I found the following in Kevin Klement's,  (pages 2-3).  "You have to use logic to study logic. There’s no getting away from it. However, I’m not going to bother stating all the logical rules that are valid in the metalanguage, since I’d need to do that in the metametalanguage, and that would just get me started on an infinite regress. The rule of thumb is: if it’s OK in the object language, it’s OK in the metalanguage too."  So it seems that, if one proves a fact about the object language, then one can also use it in the metalanguage. In the case of set theory, one may not start out knowing what sets really are, but after one proves some fact about them (e.g., that there are uncountable sets) then one implicitly "adds" this fact also to the metalanguage.  This seems like cheating: one is using the object language to conduct proofs regarding the metalanguage, when it should strictly be the other way round.  To give an example of avoiding circularity, consider the definition of the integers. We can define a binary relation $R\subseteq(\mathbf{N}\times\mathbf{N})\times(\mathbf{N}\times\mathbf{N})$, where for any $a,b,c,d\in\mathbf{N}$, $((a,b),(c,d))\in R$ iff $a+d=b+c$, and then defining $\mathbf{Z}:= \{[(a,b)]:a,b\in\mathbf{N}\}$, where $[a,b]=\{x\in \mathbf{N}\times\mathbf{N}: xR(a,b)\}$, as in  question or  on Wikipedia. In this definition if set theory and natural numbers are assumed, then there is no circularity because one did not depend on the notion of "subtraction" in defining the integers.  So my question is:     Question Is the definition of first-order logic circular?   If not, please explain why.   If the definitions are circular, is there an alternative definition which avoids the circularity?   Some thoughts:   Perhaps there is the distinction between what sets are (anything that obeys the axioms) and how sets are expressed (using a formal language). In other words, the notion of a set may not be circular, but to talk of sets using a formal language requires the notion of a set in a metalanguage. In foundational mathematics there also seems to be the idea of first defining something, and then coming back with better machinery to analyse that thing. For instance, one can define the natural numbers using the Peano axioms, then later come back to say that all structures satisfying the axioms are isomorphic. (I don't know any algebra, but that seems right.) Maybe sets, functions, etc., are too basic? Is it possible to avoid these terms when defining a formal language? elementary ring proof with composition of functions and addition of functions as operations Consider the set $\mathcal{F}=\lbrace f\mid \mathcal{f}:\Bbb{R}\to\Bbb{R}\rbrace$, in which an additive group is defined by addition of functions and a second operation defined as composition of functions. The question asks to verify that the resulting structure does not satisfy the ring properties.     This is the question 24.10 from Modern Algebra, by Durbin, 4th edition.  So what I have so far is that all of the properties for the additive group (with addition of functions as the operation here) hold, associativity of the composition of functions hold, and that the failure must come from the distributive laws.  My proof of my claim, so far;  $$1\,\,\,\,\,[(\mathcal{f}\circ\mathcal{g})+\mathcal{h}](\mathcal{x})=\cdots=\mathcal{f}(\mathcal{g}(\mathcal{x}))+\mathcal{f}(\mathcal{h}(\mathcal{x})).$$ ...but,  $$2\,\,[(\mathcal{f}\circ\mathcal{g})+\mathcal{h}](\mathcal{x})=$$ $$3\,\,(\mathcal{f}\circ\mathcal{g})(\mathcal{x})+\mathcal{h}(\mathcal{x})=$$ $$4\,\,\,\mathcal{f}(\mathcal{g}(\mathcal{x}))+\mathcal{h}(\mathcal{x}).$$ ...which brings me to my contradiction of the properties of rings that;  $$5\,\,\,[\mathcal{f}\circ(\mathcal{g}+\mathcal{h})](\mathcal{x})\neq[(\mathcal{f}\circ\mathcal{g})+\mathcal{h}](\mathcal{x}).$$  So my question is, is this the correct path to showing the distributive laws are not obeyed when composition is taken as an operation on $\mathcal{F}$? particularly my proceeding from 2 to 3 to 4 is what i feel uncomfortable about, like i may be missing a step in there.  thanks Avoid linebreaks in LaTeX console / log output (or increase columns in terminal) Is it possible to tell the LaTeX command not to use line breaks in its console / log output?  This would make it easier to automate the processing of the log file, e.g. extracting the names of missing graphics files like in this output  ! LaTeX Error: File `figures/triggers/muontriggers/notmu18_medium_mu10_loose/2d map_abs_eta_phi.pdf' not found.   which are otherwise cut into pieces and unnecessarily difficult to grep etc. Formula to add minutes to date+time in Excel If I have a cell formatted as date+time in Excel, how can I add to this in terms of minutes? It would need to work whether I was adding 20 minutes, or 2,500 minutes.   So, for example if I had this spreadsheet, what formula could I put in B5 to get a result of 2013-09-22 09:10?    I tried using =B4+TIME(0,B3,0), but it gives 2013-09-21 09:10 which is a day off. It works fine though if B3 is less than a day's worth. Meaning of 'no earlier than X days after Y' I am having trouble understanding the following notice on the American Airlines AAdvantage (miles account) :     Note: Mileage credit requests can be submitted no earlier than 15 days   after all travel is completed.   What does it exactly mean? Which of the following statements is the correct interpretation?   I have to wait for 15 days after all my travel is completed before I can request my mileage credit If I want to request my mileage credit, I have to do so within 15 days after my travel is completed Something else   In any case, I wonder, is the original statement grammatically correct? Show badges in user profile in iOS app When viewing a user's profile from the iOS app, it would be nice to be able to see what badges they have, instead of just the counts. I just did a clean install of 20.04 and I noticed that no key shortcuts for files manipulation work when my focus in on Desktop (not in Nautilus).   When I have copied a file to clipboard, I cannot Ctrl+V it to Desktop, when I click on a file on Desktop, I cannot Ctrl+C it, or I cannot Delete it with keys. Only ways to do it is either navigate to the Desktop folder in Nautilus, or right-click the file on the Desktop and copy/move to trash/paste...  Sorry if I'm missing something obvious, all the key shortcuts worked normally for me in 18.04. Given a method signature:  public bool AreTheSame&lt;T&gt;(Expression&lt;Func&lt;T, object&gt;&gt; exp1, Expression&lt;Func&lt;T, object&gt;&gt; exp2)   What would be the most efficient way to say if the two expressions are the same? This only needs to work for simple expressions, by this I mean all that would be "supported" would be simple MemberExpressions, eg c => c.ID.  An example call might be:  AreTheSame&lt;User&gt;(u1 =&gt; u1.ID, u2 =&gt; u2.ID); --&gt; would return true Which Mac is suitable for Blender 2.8? I am considering purchasing a Mac for my godson who will be using it to run Blender 2.8.  I know very little about this program.  All I can find are requirements for a Mac that will run earlier versions of Blender.  Would someone please recommend a list of requirements for a Mac (or a link to a list of requirements) that I could use to find a model that can run 2.8?  Thank you in advance for all your help! Sincerely, M. Lap I want to create a 2D game but I'd like to have the character to wear tons of different equipments on different combinations, like a RPG or something.  So let's say the user changes his/her shoulders and pants, this must be shown to the player and all these different equipments must follow the different characters action (hitting, being hit, spelling magic, etc.).  I see a few problems that I'd like to know the best approach/algorithm/architecture to solve.  1 - Sprites or Animations  Should I create different sprites for each equipment in each action animation?  Is it better to just have the equipment sprite and animate it directly on code like rotating and translating (using something like tween on Flash)?  Is there any other better option? (I really don't like the ideas above)  2 - Positions  Let's say during one of the character's move he starts looking directly in front to the player's view but ends his movement showing his right side to the player (like if he swings his sword from one side to the other).  If we consider one part of the user, like his head for example, it starts in front and then turns left.  It means at least 3 different positions for each head equipment (helmet, cap, whatever).  This surely influence the answer of #1 question. How is the best way to achieve that?  3 - Layers  Let's consider a character move where he spins 360 degrees with his arms open. At the beginning of the animation, his right hand is close to the user's view and then, at the middle of the movement, this is probably behind the character's body on the animation.  Whatever is the option on #1 question, you surely needs to use some kind of layer model to make this sprite or animation to starts closer to the player's view and later change to far away from player's view.  Is there any good way to do that?  I know the question is quite long and difficult to understand. Let me know if you think it's better to have some drawings to try to explain which one and I'll try to do that. How to populate options of h:selectOneMenu from database? What is the process for a moderator to request reinstatement or appeal a removal? Please leave any feedback or questions about this process on .   From time to time, moderators will step down or be removed from their positions — they may have expressed their wish to step down due to time constraints or they may have had behaviors unfitting of a moderator and have been forcefully removed, along with a number of other possibilities that fall somewhere between those two. What is the process for evaluating moderator reinstatement or removal appeal requests?  Note: Feedback on the original version of this post can still be found . $f$ a real, continuous function, is it measurable? Let $f: \mathbb{R} \to \mathbb{R} $ be a continuous function. I need to show that is a measurable function.   I tried working with the definition:  Let $f: X \to \mathbb{R}$ be a function. If $f^{-1}(O)$ is a measurable set for every open subset $O$ of $\mathbb{R}$, then $f$ is called a measurable function.  Since $f^{-1}(O)$ also lies in $\mathbb{R}$, I think it is sufficient to show that every subset of $\mathbb{R}$ is measurable. But is this possible?   So far I concluded that $\mathbb{R}$ itself is measurable, since $$\mu(A) = \mu(A \cap \mathbb{R}) + \mu(A \cap \mathbb{R}^c) = \mu(A) + \mu(\emptyset) = \mu(A).$$ How do I need to approach? What alternative notation of subscripts/superscripts that are also treated as SYMBOLS in Mathematica? 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.