Apply all possible permutations into a function
Using sets of arguments from a list
"Goose"–"geese" vs. "moose"–"moose" Why is it that the plural of goose is geese but the plural of moose is moose? The same goes for mouse and house. Mouse becomes mice, yet house becomes houses. How do you show that $e^{-1/x^2}$ is differentiable at $0$? Define the real valued function $f(x)$ by $f(x) = e^{-1/x^2}$ if $x \ne 0$ and $0$ if $x = 0$.    How do you show that $e^{-1/x^2}$ is differentiable at $0$? How do you show that this function is infinitely differentiable? I am starting to see a lot of people claiming that convential current is 'wrong' because Franklin made an error when he first started investigating electrostatics, and that later scientists didn't bother correcting the mistake, but preferred to keep the 'convention' (here is a classic example: )  I always thought he didn't get it wrong. He said that current is positive in the direction that positive charge flows, and vice-versa. He of course had no way to know which side of two sticks behind rubbed actually gained or lost mass. So he wasn't wrong. What were you taught?  P.S. I can't help but feel we are lucky that he got it 'backwards', because clearly many people are confused about electrostastics (including the author of that text book!) and believe electricity has to involve electrons (an unfortunate name... why couldn't they have been named negatrons...) Money transfer from India to USA My daughter is a US Citizen. We (parents)are also planning to permanently settle in US. We will go their as Permanent Resident,as per US Law. We have a house here in India worth Rs.2 Crores.  We want to sell it and take money with us. We have ordinary savings Bank account here in India.  My US Citizen Daughter is a Income Tax payer.  Now your advises are required as under:   What are the routes to take money from India to US and our tax liabilities Can I gift this whole amount to my US Citizen Daughter or what is the maximum limit of Gift amount.  What will be the tax liability on me and on my Daughter in case of Gift   Whether I have to show it in my Income Tax Return or in my Daughter's Tax Return. What US Income Tax Laws says. What will be the procedure to send money as Gift to my Daughter. Will the money will go directly from my Bank Act.to my Daughter's Bank Account. Will there will be wire transfer from bank to bank Can I send money through other money sender Certified Companies also.    Please advise. If there is something more on the subject to make me understand, please advise. Thanks, Find generator of multiplicative group of $\mathbb{F}_{27}$ I have a finite field $\mathbb{F}_{27}$. I need to find an element of order 13. I know that multiplicative group of this field is cyclic with order 26. So I want to find a generator $g$ of this cyclic group, then $g^2$ will have order 13. Also I know that all elements of this field can be represented by polynomials from $\mathbb{F}_3[t]$, where t is root of irreducible polynom $x^3-x-1$.  Probably we can find generator of $\mathbb{Z}_{26}$ and than build an isomorphism to $\mathbb{F}_{27}\setminus 0$.  Anyway I don't know were to start.  Thanks! What is a one-word synonym for "science lover"? I'm searching for a one-word synonym for "science lover". In my case, I love science and I self study it, but I never got a degree in Physics or Chemistry or any of these related subjects (except computer-science). But I enjoy experimenting stuff and see what's going on.  So, what would be a one-word good alternative for "science lover"?  The best one I found is learner, but that's more general I guess. Scientist is probably too much in my case. I saw sciencophile in another post, but I don't really like it–it sounds too complicated. The PHB is a bit unclear when it comes to readied spells in combat. If I lose my concentration do I lose the spell slot? What about if the trigger never occurs, do I get the spell slot back? Show that G is a group, if G is finite, the operation is associative, and cancellation law holds Let $G$ be a non-empty finite set with an associative binary operation so that cancellation law holds, i.e. $ab=ac$ or $ba=ca$ implies $b=c$, for any choices of $a,b,c$ in $G$. Assume that there is an identity element $e$ in $G$. Show that $G$ is a group.  Proof: To show $G$ is a group, conditions must hold. Suppose that $ab=ac$, then $b=eb=(a^{-1}a)b =a^{-1}(ab)=a^{-1}(ac) =(a^{-1}a)c=ec=c$. So left cancellation holds in $G$.  2) Suppose $ba=ca$, then $b=be=b(aa^{-1}) =(ba)a^{-1}=(ca)a^{-1} =c(aa^{-1})=ce=c$. So right cancellation holds in $G$.  3) If $a$ exists in $G$ then $aa^{-1}=a^{-1}a=e$, where $a$ is an inverse of $a^{-1}$. Since inverses are unique, $(a^{-1})^{-1}=a$.  4) Let $x$ be the inverse of $ab$. Then $(ab)x=e$. By associativity we have $a(bx)=aa^{-1}$. Through left cancellation we have  $bx=a^{-1}bx=ea^{-1}=b(b^{-1}a^{-1})$ and $x=b^{-1}a^{-1}$.  Thus $(ab)^{-1}=b^{-1}a^{-1}$. So all conditions hold, $G$ is a group.  Is this proof correct? I know to show $G$ is a group these conditions have to be met. This is all I have to show right? Why the CMB has not been dispersed so far? Imagine you have a box of black body radiation. What happens if you open the box for a long time? It becomes dispersed and no radiation remains in the box.   Now, apply this example to the Cosmic Microwave Background radiation. The CMB has been produced about 380,000 years after the Big Bang. Giving that the space is flat as many observations suggest, that radiation has been produced in a universe with no boundaries.   Now, my question is this: in these conditions, why that radiation has not been dispersed completely so far? It is true that the radiation has been produced everywhere in the space but giving that the space is infinite, why has not it been dispersed do far?   Calculations in the standard textbooks are done in such a way as if the CMB has been within a physical box, however expanding with the universal expansion. But, this is not the actual situation. The CMB has not been and is not enclosed by walls of a box, so it must have completely dispersed so far. What has prevented this to happen? $$\displaystyle\int \:\sin^n\left(x\right)\cos^m\left(x\right)\mathrm  dx=\frac{\sin^{n+1}x\cos^{m-1}x}{m+n}+\frac{m-1}{m+n}\int \:\sin^nx\cos^{m-2}x\,\mathrm dx$$  I have been trying to solve for over a week now can someone please help me. I know it's possible to match a word and then reverse the matches using other tools (e.g. grep -v). However, is it possible to match lines that do not contain a specific word, e.g. hede, using a regular expression?   Input:  hoho hihi haha hede   Code:  grep "&lt;Regex for 'doesn't contain hede'&gt;" input   Desired output:  hoho hihi haha Do I have to move swap partition to the right side? According to  I just expand my sda4 to include unallocated space, my question is after create 2 new partitions sda7, sda8, do I need to move the swap partition to the most right of the disk? (I really don't know this, I saw  which moving the swap partition to the right side)  Thanks. How to prove the divisibility rule for $3\, $ [casting out threes] The divisibility rule for $3$ is well-known: if you add up the digits of $n$ and the sum is divisible by $3$, then $n$ is divisible by three.  This is quite helpful for determining if really large numbers are multiples of three, because we can recursively apply this rule:  $$1212582439 \rightarrow 37 \rightarrow 10\rightarrow 1 \implies 3\not\mid 1212582439$$ $$124524 \rightarrow 18 \rightarrow 9 \implies 3\mid 124524$$  This works for as many numbers as I've tried.  However, I'm not sure how this may be proven.  Thus, my question is:     Given a positive integer $n$ and that $3\mid\text{(the sum of the digits of $n$)}$, how may we prove that $3\mid n$? Change pivot or local origin of an object How does tangzhong (water roux) make bread softer? As I understand it, tangzhong in relation to bread making is an Asian technique in which a portion of the flour in the recipe is pre-cooked with water to make a roux, before being cooled and added to the rest of the ingredients. It is supposed to make the resulting bread very soft, often for days longer than non-tangzhong breads. I thought maybe it works by binding the proteins so gluten development is restricted, but I'd have thought that would inhibit rise, which seems not to be an issue.  Disclaimer: I have not yet made a tangzhong bread, but I believe I have eaten a few... My first attempt is currently doing a bulk rise.  How does tangzhong work exactly? How does it actually change the dough to achieve the distinct softness for which it is so famous? How do you teleport a certain player to spawn after they win a 1v1 I managed a KitPvP server in Minecraft and everything works fine except when players wants to duel each other. They get sent to a room where they will be dueling. The main problem is when the winner wins, I have no idea how to teleport them back to spawn. Why should users never use normal sudo to start graphical applications? Foreign key referring to primary keys across multiple tables? I have to two tables namely employees_ce and employees_sn under the database employees.   They both have their respective unique primary key columns.   I have another table called deductions, whose foreign key column I want to reference to primary keys of employees_ce as well as employees_sn. Is this possible?  for example  employees_ce -------------- empid   name khce1   prince  employees_sn ---------------- empid   name khsn1   princess   so is this possible?  deductions -------------- id      name khce1   gold khsn1   silver Multiple Image in Canvas ItemsControl What does the "bugs" section of /proc/cpuinfo actually show? On a Debian Stretch and testing/Buster system with a current kernel and installed microcode I still see meltdown and spectre listed as bugs in /proc/cpuinfo.  However, running the spectre-meltdown-checker shows not vulnerable.   So I'm wondering what /proc/cpuinfo does show. Are these just the vulnerabilities for this cpu and will those always be listed despite having a patched system?