I don't need anything to be blurred. I need everything to be focused
How can I take a photo with everything in focus with my DSLR?
What's the C++ way of parsing a string (given as char *) into an int? Robust and clear error handling is a plus (instead of ). Given $S \hookrightarrow T$ construct $U ≈ T$ disjoint from $S$ in Z set theory? Analytic continuation of function continuous on boundary Suppose one has a function $f$ in the disc algebra ie: $f$ is continuous on $|z|\leq1$ and holomorphic in $|z|&lt;1$. I wondered, can $f$ always be extended to a holomorphic function on some region containing the boundary (ie: $T$ the unit circle). If not can you give me an example? Thank you, Calculating extent of custom tiles? Problem  The picture is just an example of my case, but I am left with blank space on the left when I load all the tiles and I get error message in the console:   Failed to load resource: the server responded with a status of 404 (Not Found) http://path/to/the/tile//base/8/6/53.png  etc.     I could guess and limit the extent of the layer, but I would really like to know is there any way to calculate it and also be able to get rid of the error message.  What I know about the tiles?   Originally they are served as TMS They represent png images 256*256 They are in projection: EPSG:3857 In OpenLayers2 they were called like TMS layer In OpenLayers3 (v.3.8.2) they are called like XYZ layer (that includes -y):     var baseLayer = new ol.layer.Tile({   source: new ol.source.XYZ({     url: 'http://path/to/the/tiles/base/{z}/{x}/{-y}.png'   }) });   Thoughts and questions   How can I calculate extent of the tiles? Or in another words how can I find out zmin zmax xmin ymin xmax ymax or whole range of x/y?  What does x/y really represent? Are they coordinates of the left bottom corner or center of the tile? In which direction does x/y increase? How can I figure out x/y of at least one of the tile, for example left bottom one?    (I have modified the question for better understanding of the problem) Does transparency work in eevee I have been trying to create a transparent lens using the eevee rendering engine in 2.8 but the transparency slider has no effect. Has this feature not been implemented yet? I've looked all over the Web for an answer with no luck. I'm a noobee so am probably doing something wrong. Deriving even odd function expressions What is the logic/thinking process behind deriving an expression for even and odd functions in terms of $f(x)$ and $f(-x)$?  I've been pondering about it for a few hours now, and I'm still not sure how one proceeds from the properties of even and odd functions to derive: $$\begin{align*} E(x) &amp;= \frac{f(x) + f(-x)}{2}\\ O(x) &amp;= \frac{f(x) - f(-x)}{2} \end{align*}$$ What is the logic and thought process from using the respective even and odd properties, $$\begin{align*} f(-x) &amp;= f(x)\\    f(-x) &amp;= -f(x) \end{align*}$$   to derive $E(x)$ and $O(x)$?    The best I get to is: For even: $f(x)-f(-x)=0$ and for odd: $f(x)+f(-x)=0$  Given the definition of $E(x)$ and $O(x)$, it makes a lot of sense (hindsight usually is) but starting from just the properties. Wow, I feel I'm missing something crucial. Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$ Let $G$ be a finite abelian group and let $\phi: G \rightarrow G$ be a group homomorphism. I am trying to show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$.  I know that since $G$ is abelian we have that $\ker(\phi^{k})$ and $\phi^{k}(G)$ are normal subgroups of $G$ for any $k$  I also suspect we have the following towers which stabilize at $m$ and $m'$  $$\phi(G) \unrhd \phi^{2}(G) \unrhd \cdots \unrhd \phi^{m}(G)=\phi^{m+1}(G)=\cdots$$  $$\ker(\phi) \unlhd \ker^{2}(\phi) \unlhd \cdots \unlhd \ker^{m'}(\phi)=\ker^{m'+1}(\phi)=\cdots$$  I know that if given a group of the form $HK$ where $H$ and $K$ are normal subgroups of $HK$ and $H\cap K=1$ then $H \times K \cong HK$. I want to apply this to this situation but I am unable to show how write $G$ as a product $HK$  Resolution One of the comments directed me to the following article:  The last part of which answers the question. Below is what is says:  Choose $n=\max(m,m')$, then we have for $x \in \ker^{n}(\phi) \cap \phi^{n}(x)$, this means that $x=\phi^{n}(y)$ for some $y \in G$. This gives:  $0=\phi^{n}(x)=\phi^{2n}(y)$ which means that $y \in \ker^{2n}\phi=\ker^{n}{\phi}$. and then we have that $0=x=\phi^{n}(y)$.  The answer below kindly points out that every element $x$ is contained in one of the cosets of $G/\ker^{n}(\phi)$, this means that $x=k+g$ for some $k \in \ker^{n}(\phi)$ and $g \in G$. We also have that $g=\phi^{n}(h)$ for some $h \in G$. Writing $x=k+\phi^{n}(h)$ essentially shows that $G=\ker(\phi^{n}) + \phi^{n}(G)$. Using the fact above, the claim follows. Why are two different concepts both called "heap"? I am trying to define the probability distribution of $Z$ such as $Z = X_1\cdot X_2$ where $X_1$ and $X_2$ are two independent and identically exponentially distributed variables.  $$P(X_1=x) = \lambda e^{-\lambda x}$$ $$P(X_2=x) = \lambda e^{-\lambda x}$$  I tried something like that….  $$P(Z=x) = P(X_1 = a) \cdot P(X_2 = x/a)$$  Is this first equation correct?  $$P(Z=x) = \lambda e^{-\lambda a} \cdot \lambda e^{-\lambda x/a} = \lambda^2 e^{-\lambda (a+x/a)}$$  I doesn't feel like I found the solution as the dummy variable $a$ remains in the final result. Can you please help me solving this problem? Sum of two closed sets in $\mathbb R$ is closed? Is there a counterexample for the claim in the question subject, that a sum of two closed sets in $\mathbb R$ is closed? If not, how can we prove it?  (By sum of sets $X+Y$ I mean the set of all sums $x+y$ where $x$ is in $X$ and $y$ is in $Y$)  Thanks! Layers with same coordinate system should align/overlap in ArcMap but do not? I put 4 different layers into my ArcMap document, but only one of them will show up on the map! I should be seeing the other 3 layers as well. When I do a Zoom to layer, I can see one layer, but I cannot figure out how to make the other 3 show up at once on top of each other.  Before I opened ArcMap, I used ArcCatalog where I right-clicked 3/4 of the shapefiles and  clicked Properties &rarr; Coordinate system &rarr; Import and then clicked on my Trees layer, which has the coordinate system I want the other 3 to have. But when I opened ArcMap the 4 layers did not overlap, nor could I move them above or below each other. Creating a single index from several principal components or factors retained from PCA/FA I am using Principal Component Analysis (PCA) to create an index required for my research. My question is how I should create a single index by using the retained principal components calculated through PCA.  For instance, I decided to retain 3 principal components after using PCA and I computed scores for these 3 principal components. What is the appropriate ways to create, for each respondent, a single index out of these 3 scores?   Is it relevant to add the 3 computed scores to have a composite value? Or to average the 3 scores to have such a value?  Or should I just keep the first principal component (the strongest) only and use its score as the index?   Alternatively, one could use Factor Analysis (FA) but the same question remains: how to create a single index based on several factor scores? How do I change a close vote to a duplicate? Voted to close a question based on "lack of minimal understanding".  Later realized the question was a duplicate.  How to I change vote to mark as duplicate instead? Difficulty in creating macro '\newcommand' for the beginning and end of frames in Beamer I would like to create a Latex macro for my beamer presentations. I use beamer frequently, and want to make macros for the \begin{frame} and \end{frame} to require fewer keystrokes. At the beginning of the document I have:  \newcommand{\bfrm}{\begin{frame}}%start new frame \newcommand{\efrm}{\end{frame}}%end new frame   Which compiles fine. I then test the first of the two macros for the beginning of the frame:  \bfrm{New frame testing}     blah blah \end{frame}   Which produces the result I am looking for. I then test the second of the macros:  \bfrm{New frame testing}     blah blah \efrm   Fails to compile, saying that there is a runaway argument. What is the reason for the failure? Use of "to lunch" vs."for lunch" Which is right?      I went to the (mall) to meet my parents for lunch / to lunch   This for a paper I am submitting for a writing assignment. I have heard "to lunch" is right, but is it right in this sentence please? Does tourist visa (90 days) apply after a long-term visa ends in Schengen countries? I am an Australian currently on a Netherlands working holiday visa that ends in May next year. I would like to know if when my visa ends I then get another 90 days just as a regular tourist visa as I would like to do some more travel within Europe when my visa ends before going home to Australia. Limit of the geometric sequence $\{r^n\}$, with $|r| < 1$, is $0$? Convert object string to JSON How to remove a partition on a hard disk? Let $K/F$ be a finite field extension and suppose that $F$ is infinite. Is it possible to have a nonzero polynomial $p \in K[x_1,...,x_n]$ that vanishes in $F^n$?