MySQL ALL Combinations from Two Tables
MySQL cartesian product between two SELECT statements
"All our X" vs. "all of our X" Is the word "of" optional in this instance? Is either of these considered preferable to the other?        Taste all our delicious treats.   Taste all of our delicious treats. NSArray becomes NSCFArray when passed How do you prevent oatmeal from overflowing? Whenever I cook oatmeal (whether steel cut oats in a rice cooker or pan, or rolled oats in the microwave), it always overflows. How do you prevent this?   Do you just use a bigger container? Do you just take the pan off the heat or bowl off the microwave when it's about to overflow? I've also heard that if you put dried fruit or something like that along with the oatmeal while cooking, that helps prevent it from overflowing -- is this true? How do I add VBA in MS Office? I've seen posts showing answers which use VBA () code/macros, however, I've also noted additional comments afterwards about how to use the VBA (how to implement and execute it). I'm hoping this will help just to get the code executed.   So, my question is:  I have some VBA code. How do I add VBA to my MS Excel or Word or Outlook project? In a preadditive category, products are coproducts $\renewcommand{\phi}{\varphi}$ $\require{AMScd}$ My question is different from .  I want to see how in a preadditive category $\mathcal{C}$ a product is a coproduct, following . I'll write the proof up to the point where I get stuck.  Let $A=A_1,B=A_2$ be objects and suppose their product $P$ does exist, with projections $\pi_i:P\rightarrow A_i$. By considering a wedge  $$\begin{CD}A @&lt;{id_A}&lt;&lt;  A @&gt;{0_{AB}}&gt;&gt;  B\end{CD}$$  and the obvious analogous one with $A$ and $B$ exchanged, where $0_{A,B}$ is the zero morphism, we see that the product property implies the existence of two unique morphisms $k_i\in\mathcal{C}[A_i,P]$ s.t.  \begin{align*} \pi_j\circ k_i=\begin{cases} \mathrm{id}_i &amp;\text{if }i=j\\ 0_{A_i, A_j} &amp;\text{if }i\neq j \end{cases}. \end{align*} Using these equations and the definition of zero morphism, it's easy to see that the morphism $m\equiv k_1\circ \pi_1+ k_2\circ \pi_2$ satisfies $\pi_i\circ m=\pi_i$.   This is where I get stuck: In the linked proof, they now state that this implies $m=\mathrm{id}_P.$ But I don't see why this should be true.   Specifically, if $\phi\in\mathcal{C}[S,P]$ for some arbitrary object $S$, it is not apparent why $m\circ\phi=\phi$. All that we know is that there are some morphisms $x_i\in\mathcal{C}[S,A_i]$ that factor through $P$ via the universal property, but these are not necessarily unique.  And we learn even less about $m$ by looking at morphisms in $\mathcal{C}[P,S]$.  What am I missing here? What do I set the 'Opens with...' property to in order to get the system to run .bat files again (when they are double-clicked)?  Somehow my boss convinced his workstation that the handler for .bat files was supposed to be Word. Now, when double-clicking .bat files, they're opened up in Word. I am trying to get an intuitive idea of how the  affects Quantum computation. My understanding is that given a qubit $Q$ in superposition $Q_0 \left| 0 \right&gt; + Q_1 \left| 1 \right&gt;$, NCT states another Qubit $S$ cannot be designed such that $S$ is equivalent to the state of $Q$.   Now the catch is, what does Equivalent mean? It could mean either that:   $S = S_0 \left| 0 \right&gt; + S_1 \left| 1 \right&gt;$ such that $S_0 = Q_0, S_1 = Q_1$. Or it could mean that $S = Q$, meaning that if $S$ is observed to be some value ( for example 0) then $Q$ MUST be that same value, and vice versa.    So it seems that point 2, occurs anyways in entangled systems (particularly cat-states), so I can eliminate that option and conclude that that No Cloning states, given a qubit $Q$, it's impossible to make another qubit $S$ such that:  $S = S_0 \left| 0 \right&gt; + S_1 \left| 1 \right&gt;$ such that $S_0 = Q_0, S_1 = Q_1$.  Is this correct? So i have this $3\times 3$ matrix  $$     \begin{pmatrix}     -2 &amp; 0 &amp; 0 \\     3 &amp; 1 &amp; -6 \\     0 &amp; 0 &amp; -2 \\     \end{pmatrix} $$  I want to check if the matrix is diagonizable. First thing i do is find the roots : namely $\lambda_1 = −2$ of multiplicity $2,$ and $\lambda_2 = 1$ of multiplicity $1.$  In order to ensure that the matrix is diagonalizable we need to find a basis of $\mathbb{R}^3$ whose elements are eigenvectors for $A.$ In particular, since we have the eigenvalue $\lambda_1=-2$ having multiplicity $2$ we need to check that the dimension of the eigenspace $E(\lambda_1)$ is equal to $2.$ We compute the eigenspaces of $A.$  $\DeclareMathOperator\Nul{Nul}$On the answer sheet is says that we need to find $\Nul(A+2Id)$... but why $2Id?$ Isn't is supposed to be $-2,$ so $\Nul(-2Id-A)$??   I do not understand this $\Nul(A+2Id).$ I always thought that we should compute $\Nul(-2Id-A),$ so what do i need to do ?   $\Nul(-2Id-A)$ gives me a different result from $\Nul(A+2Id).$  Does that mean that since $-2$ has a multiplicity of $2,$ we need to work with $2$ and not $-2$?  Somebody please help with a clear and simple explanation ! Thanks! The English alphabet has a common pronunciation. For example, the letter b is pronounced like the word bee, the letter c like the word see, and the letter i like the word aye.  Is there a formal spelling for the letter names? What do you call a person who is your friend only because you benefit them? Looking for a word to describe a person who only makes friends to benefit themselves. Can future execution start before the synchronous execution is completed Is there a way for @future annotated method to start execution before the synchronous request which invokes it has completed.  In other words, do I have some guarantees that the timing will look like this:  -start sync---call future---end sync---execute future-&gt;   instead of like this:  -start sync---call future---execute future---end sync-&gt;   I couldn't find the execution order guarantees in the documentation, although  states:     The reason why sObjects can’t be passed as arguments to future methods   is because the sObject might change between the time you call the   method and the time it executes. In this case, the future method will   get the old sObject values and might overwrite them.  To work with   sObjects that already exist in the database, pass the sObject ID   instead (or collection of IDs) and use the ID to perform a query for   the most up-to-date record.   This can be read as saying that the future is not queued at the end of the transaction, otherwise Salesforce could guarantee that the sObject sent is the most recent version. And since it's queued during the transaction, it might imply that it also might execute and complete while the synchronous transaction is still running.  On the other hand,  implies that futures are only fired after the transaction completes:     Invoking Database.rollback not only rolls back inserts, but it goes   much, much further.   [...]   It also rolls back:      Calls to @future methods. Any methods called within the rolled back part of your script will not be invoked (also why @future doesn't start until your script completes). Repeated squaring method How do I use the repeated squaring method to calcualte 2^176 (mod 177)? I'm not sure, but is there something about the fact that 177 is 1 greater than 176 that makes this a problem? I am in the middle of a problem and having trouble integrating the following integral:  $$\int_{-1}^1\frac1{(1+x^2)^2}\mathrm dx$$  I tried doing partial fractions and got:  $$1=A(1+x^2)+B(1+x^2)$$  I have no clue how to solve this since it is obvious there is no way to cancel out either $A$ or $B$ to get the other variable. Please guide me.  Thank you. How can I prevent Google mistakenly offering to translate a page? Several of my site's pages are appearing in search results with [Translate this page] next to it. When I click that it takes me to Google Translate and translates my page "from Catalan to English".  The pages are in English but have a couple of foreign words (actually Japanese romanisations, not Catalan) that appear to be tripping Google up.  A few weeks ago I set the html tag to &lt;html lang="en"&gt; which from research appears to be the best method to specify the language of a document. Google has cached the pages with this attribute but it is still offering to translate.  More research led me to a "notranslate" attribute which prevents translation entirely: &lt;html lang="en" class="notranslate"&gt;. The problem now is users cannot translate from English to their desired language!  Are there any other solutions that force Google to parse my site as English only? Can a 64-bit OS run as a guest on a 64-bit VirtualBox host? Is it possible to run a 64-bit OS as a guest on a 64-bit machine with VirtualBox? I'm guessing it should be, but I'd like to make sure.  Do some virtualization technologies allow a single guest machine to use multiple cores? I guess it should be possible, but my VirtualBox open-source edition doesn't seem to do it. Prepend 0 to sublists Justify text inside itemize environment with beamer class In MLE for continuous rv, why is it ok to evaluate a pdf at a point? Why is pressure in a liquid the same in all directions? I'd like answers both in the more intuitive side an on the more precise side.   Thinking of water as "cubes" of water, for example, would allow pressure in the z axis to be independent of the y or x axis. Choosing other "shapes", like a  triangular prism, yield different results. Will this fact, then, be dependent on the format of the molecules of the liquid ?  I've heard of the rotational symmetry of liquids. What is its precise statement ? Why is it true ? What does each SPECIAL stat in Fallout Shelter do? Besides its workplace uses, like Charisma in Living Quarters, Strength in Power Generators, Agility in Diners.   Do we know if Endurance increases HP in the Dwellers, or that strength helps in melee damage / survivability in the wastelands? And Perception?