Tried running sudo apt-get update and it can't find the release files
How can I fix a 404 Error when using a PPA or updating my package lists?
Is AncestryDNA match of 1,655 cM a half sibling? Shared DNA: 1,655 cM across 46 segments.   Can someone that shows this as one of my matches on AncestryDNA be a half sibling? Show that if $\sup\big\{\sum\lvert\, f(a)\rvert\big\}  0\}$ is countable. Let $f:A \to \mathbb R$ and suppose that $$ \sup\Big\{\sum_{a\in F}\lvert\, f(a)\rvert :  F\text{ is finite subset of }A\Big\} &lt; \infty $$ then the set $\{ a \in A : f(a) &gt; 0\}$ is countable.  My try: Define these element of ${ a ∈ A : f(a) &gt; 0}$, then $∑_{n=1}^\infty\lvert\, f(a_n)\rvert$ is determined, regardless of the method of arrangement. Floating Objects and Weight The Situation:  A ball is placed in a beaker filled with water and floats. It is also attached to the bottom of the beaker via a string.   The Question:  The ball is attached to the beaker, thus making the ball and beaker (and string included) a system. However, it is floating. Does the ball add to the weight of the beaker? How to launch terminal on login How could I get the terminal to be launched once I have logged in, so that typing commands is much simpler? What TV movie had lost space cadets who piloted yellow tripod robots, and a squid bad guy? I'm trying to find a movie I watched on TV, probably in the 90s. I think it was a made-for-TV movie.  It was about a ship with an AI. The ship was crewed by young adults. I think they were cadets?   There was an accident (like a warp drive malfunction) and they end up in another part of space where they meet a female alien whose ship had been shot down.  I remember they had manned robots they would pilot and they took them to a planet to get upgraded and they are attacked by more manned robots. They had three legs and they were yellow, I think.  I also remember the baddie had a holo-projector or something like that which allowed him to change his appearance. He commanded a massive fleet and he worked for someone he spoke to in a video chat that looked like a squid. What is the Taylor series of $$\ln \frac{1-x^2}{1+x^2}$$   ?   I started by evaluating the first derivatives but the more I go, the more complicated they are and I can't identify a pattern. When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes? I've been considering the rings $R_1=\mathbb{F}_p[x]/(x^2-2)$ and $R_2=\mathbb{F}_p[x]/(x^2-3)$, where $\mathbb{F}_p=\mathbb{Z}/(p)$.   I'm trying to figure out if they're isomorphic (as rings I suppose) or not for primes $p=2,5,11$.   I don't think they are for $p=11$, since $x^2-2$ is irreducible over $\mathbb{F}_{11}$, so $R_1$ is a field. But $x^2-3$ has $x=5,6$ as solution in $\mathbb{F}_{11}$, so $R_2$ is not even a domain.  For $p=5$, both polynomials are irreducible, so both rings are fields with $25$ elements.  I know from my previous studies that any two finite fields of the same order are isomorphic, but I'm curious if there is a simpler way to show the isomorphism in this case, without resorting to that theorem.  For $p=2$, neither ring is even a domain as $x=0$ is a solution of $x^2-2$ and $x=1$ is a solution for $x^2-3$, but I'm not sure how to proceed after that. Thank you for any help. Limit involving the exponential of an expression plus a small-o I'm trying to formalize the following limit:  $$\lim_{x \to \infty} \left[1+\frac{a}{x}+o\left(\frac{1}{x}\right) \right]^x= e^a$$ however I can't see how to rigorously show this identity.  Any suggestions? Add a new repository to software sources align vs equation How do I add newlines between lines printed on the command line? Mail logs are incredibly difficult to read. How could I output a blank line between each line printed on the command line? For example, say I'm grep-ing the log. That way, multiple wrapped lines aren't being confused. Create a local texmf tree in MiKTeX If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$? Confidence bands in case of fitting ARIMA in R? Are there any keyboard shortcuts for Windows 10 developer preview's virtual desktops ("Task View")? Why is the triangle inequality property important for metric spaces? There is a property in the axiomatization of metric space: $d(x,z)\le d(x,y)+d(y,z)$. I understand that property applies well when it come to the measure of distances among points. However, that property seems to be irrelevant in the definitions of continuity, open set and some other key concepts.  My topology book says that it is asserting "the transitivity of closeness", a vague term that loses me. So why is that property important? Why did the founders (if any) of topology consider it at the first place? And what if that property is missed? How to favorite a question from Android app? Equation of the locus of the foot of perpendicular from any focus upon any tangent to the ellipse ${x^2\over a^2}+{y^2\over b^2}=1$ Find the equation of the locus of the foot of perpendicular from any focus upon any tangent to the ellipse ${x^2\over a^2}+{y^2\over b^2}=1$. will it also be an ellipse? I've just had to write a string reverse function in C# 2.0 (i.e. LINQ not available) and came up with this:  public string Reverse(string text) {     char[] cArray = text.ToCharArray();     string reverse = String.Empty;     for (int i = cArray.Length - 1; i &gt; -1; i--)     {         reverse += cArray[i];     }     return reverse; }   Personally I'm not crazy about the function and am convinced that there's a better way to do it. Is there? What does the word "SARGable" really mean?