How to I get to my linux partition?
How can I repair grub? (How to get Ubuntu back after installing Windows?)
How long do seasons last? In the Kittens Game, how long (in real life minutes) do seasons last? I want to do something like String.Format("[{0}, {1}, {2}]", 1, 2, 3) which returns:  [1, 2, 3]   How do I do this in Python? I have put a bounty on , however I don't see it appear in the  (also not when I'm not logged in).  Why is this. Aren't all bounty questions supposed to be visible there? ubuntu 18.04 LTS bluetooth [0cf3:3004] discovery not working With the new  and the upcoming release of  film, JK Rowling has been awesome and given us new writing on the .  In the introduction it is stated that there are eleven established/registered schools. There are writings for six of them. I don't think we need a new writing for Hogwarts... so that means seven have been located and defined.   Hogwarts School of Witchcraft and Wizardry - Great Britain  - France  - Northern Europe (possibly Estonia, Latvia, or Belarus)  - Japan  - Africa (possibly Congo/DRC)  - Brazil  - United States   Do we know anything of possible location or names of the other four schools? I know Koldovstoretz was mentioned as school in Russia, but is that still canon?   Koldovstoretz - Russia (maybe depending on current canon)   The final three are my guesses based on the population and geography on the world.   Name Unknown - China (based on population) Name Unknown - India (based on population) Name Unknown - Australia (based on geography)   Related: What is an observer in quantum mechanics? My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.  What is an observer? What are the conditions required to be qualified of observer, both mathematically and experimentally? In a linear program, I have a variable $y$ that must obey $y=\max(x-a,0)$ where $x$ is a linear combination of the other variables and $a$ is a constant. $x$ and $y$ and $a$ are always non-negative. If the objective function decreases w.r.t. $y$, then adding the constraint $y\geq x-a$ makes it work. Are there any way to add dummy varibles and contraints such that $y=\max(x-a,0)$ when the objective function increases w.r.t. $y$? I can't say $y\leq x-a$ because if $x-a&lt;0$ it contradicts the non-negativity of $y$ whereby the solution might no longer be in the feasible region or the problem might even be infeasible. Firstly, I apologise that this question is specific to two polynomials. I understand that this post will not help a lot of people, and for that I am sorry. I will make it up to you all by anwsering lots more questions in the future! However, as my lecturers enjoy time off on the weekend, I am unable to ask this to anyone else who would know what the heck I'm talking about. Sorry if my notation is not widely used, I can elaborate more if required. Please excuse my poor Latex too.  Let:  $B = Y^2 - X^3 + X$, and   $F = (X^2 + Y^2)^3 - 4X^2Y^2$.  I wish to find the intersection number of $B$ and $F$ at $P = (0,0)$  i.e $I(P,F \cap B). $  However, I want to use the following proposition to do this:  If $P$ is simple on $B$ then $I(P,F \cap B) = ord_P^B(F) $.  I will omit proving that $P$ is simple on $B$ as I hope it is clear to see it is.  I know that $I(P,F \cap B) &gt; M_p(F) * M_p(B) = 1 * 4 $, where $M_P(G)$ is the multiplicity of $P$ on $G$.  Now, consider the Image of $X$ and $Y$:  $K[X,Y] \longrightarrow \frac{K[X,Y]}{Y^2 - X^3 + X} \longrightarrow O_P(Y^2 - X^3 + X)$  $X \longrightarrow x$  $Y \longrightarrow y$  Where lower case denotes the image.  Then $ord_P^{Y^2 - X^3 + X}((X^2 + Y^2)^3 - 4X^2Y^2)$  Can be found by substituting $y^2 = x^3 - x$ into $(x^2 + y^2)^3 - 4x^2y^2$  Which gives:  $ord_P^{Y^2 - X^3 + X}(x^9+3x^8 -5x^6 -4x^5 +3x^4 +3x^3)=3$  i.e $I(P,F \cap B) = 3$, a contradiction to  $I(P,F \cap B) &gt; 4$ as above.  The correct answer I know is 6, so where have I gone wrong? Where can I ask a question about finding general software that meets certain requirements? Incubated but not hatched egg I got the message "oh" and it showed my egg. Before I could do anything the server went down. When I got back on my egg was gone. Is there anything I can do to retrieve my incubated but not hatched egg? Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only I have found a proof using complex analysis techniques (contour integral, residue theorem, etc.) that shows $$\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$$ for $n\in \mathbb{N}^+\setminus\{1\}$   I wonder if it is possible by using only real analysis to demonstrate this "innocent" result?  Edit A more general result showing that  $$\int\limits_{0}^{\infty} \frac{x^{a-1}}{1+x^{b}} \ \text{dx} = \frac{\pi}{b \sin(\pi{a}/b)}, \qquad 0 &lt; a &lt;b$$ can be found in the cone is contractible Git SSH error: "Connect to host: Bad file number" How is it possible in Eclipse JDT to convert a multiline selection to String. Like the following  From:  xxxx yyyy zzz   To:  "xxxx " + "yyyy " + "zzz"   I tried the following template   "${line_selection}${cursor}"+   but that way I only get the whole block surrounded not each line separately. How can I achieve a multiline processing like commenting the selected block? How to store credit card info on iphone? If the universe is 3D, how is space-time like a "fabric"? Prove $n\mid \phi(2^n-1)$ If $2^p-1$ is a prime, (thus $p$ is a prime, too) then $p\mid 2^p-2=\phi(2^p-1).$  But I find $n\mid \phi(2^n-1)$ is always hold, no matter what $n$ is. Such as $4\mid \phi(2^4-1)=8.$  If we denote $a_n=\dfrac{\phi(2^n-1)}{n}$, then $a_n$ is , but how to prove it is always integer?  Thanks in advance! Identifying a resistor with a weird band combination proof that $f'$ is continuous at $a$ Let $f:I \rightarrow \mathbb{R}$ derivable in set I. if $\lim x_n = \lim y_n =a \in I$ with $x_n \neq y_n$ and $\lim \frac{f(y_n)-f(x_n)}{y_n - x_n} = f'(a)$ proof that $f'$ is continuous at $a$  my attempt $x_n \neq y_n$ so by MVT $\exists z_n \in I$ like $x_n \geq z_n \geq y_n$ with $\frac{f(y_n)-f(x_n)}{y_n - x_n}=f'(z_n)$ for each $x_n$ and  $y_n$ then $f'(a) = \lim\frac{f(y_n)-f(x_n)}{y_n - x_n}= \lim f'(z_n)$   Using $\lim x_n = \lim y_n = a$ and $x_n \geq z_n \geq y_n \Rightarrow z_n \rightarrow a$  if $ \lim_{x\rightarrow a} f'(x) \neq f'(a)$ then $\exists \epsilon &gt; 0$ such $\forall n\in \mathbb{N}$, $z_n \in [x_n,y_n]$ $0 &lt; |z_n - a| &lt; \frac{1}{n}$ and $|f'(z_n) - f'(a)| \geq \epsilon$. So $z_n \rightarrow a$ but will do not have $\lim f'(z_n) = f'(a)$  so $\lim f'(z_n) = f'(a) = \lim_{x\rightarrow a} f'(x)$ when $z_n \rightarrow a$  and thats implies $f'$ continuous at $a$  my question is, that's correct ? if not, can you help me? thanks In $Sets$, the initial object is $0 = \emptyset$. We have $C \times \emptyset = \emptyset$ for any set $C$. As there are no maps to the empty set, we don't get much of the universal property of the product.  I am now wondering what is special about arbitrary categories $\mathscr{C}$ with $C \times 0 \cong 0$ for all objects $C$ of $\mathscr{C}$, where $0$ is the initial object of $\mathscr{C}$.   From Sheaves in Geometry and Logic by MacLane (p.194), in any topos $\mathscr{C}$, any arrow $k:C \to 0$ is an isomorphism. The universal property of the product would then also not yield very much.   Are there any categories of higher interest?