Calculations using Android
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How is missing data calculated on Likert Scale? Quadratic Formula in Complex Variables Let $a$, $b$, and $c$ be complex numbers with $a\neq0$. Show that the solutions of $az^2+bz+c=0$ are $z_1,z_2=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$, just as they are in the case when $a$, $b$, and $c$ are real numbers. Can hypercomputation compute the impossible? There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be inconsistent and illogical/logically impossible.   There are other types of logic systems apart from classical logic, like paraconsistent logics or even trivialism, that allow these contradictions to occur, prove them as right and work with them.   We can make a paraconsistent or trivialist system and work with it. For example, with trivialism, in theory, we would be able to derive and state everything we would want (since literally everything, even including illogical/logically impossible inconsistencies and contradictions), but we as humans (or as brains), are limited and can't conceive everything we want (at least to what I know). Therefore, no matter how many trivialist models we create and how much time we would work with them, we would never find or conceive many illogical/logically things because they are just that: impossible. There are impossible things to describe and conceive. For example, Russel's set is the set of all sets that do not contain themselves. If Russel's set contains itself, then it cannot contain itself, since it only contains sets that don't contain themselves. But if Russel's set does not contain itself, then it must contain itself, since it contains all sets that don't contain themselves.  There are quite a few logic bombs like this. You cannot ever compute the contents of Russel's set, and there are more formal, mathematical ways to present it. All of them have in common that you can't actually compute what the set is, whether you do it by hand, in your head, or on a computer. It's just a statement that cannot be fully logically processed.  If you take every possible state the human brain can be in, none of them include the computation of Russel's Set's contents. That is, not only can the contents not be computed, they cannot even be represented. No stimulus can cause us to comprehend Russel's Set, since such comprehension is not possible to begin with. It does not have a solution. Even if we try to solve it using trivialism, we would just be able to write a solution that does not make sense and prove it has sense and it is the real solution, but we could not be able to have a solution that would make sense "outside" the realm of trivialism (for example in classical logic), even though, using trivialism, we could prove that such solution would have sense in whatever context and logic system.   But what about hypercomputational machines (for example oracle-like machines)? I've read about some models of hypercomputation which are compatible with paraconsistent or trivialism logics. I've also read there are some models of hypercomputation (particularly those oracle-like models which use a black box) where, essentially, the hypercomputer is an algorithm that cannot exist. It might be because such an algorithm is fundamentally forbidden by logic itself (which is hided in a black box). Would any of these be capable of computing/"conceiving" these impossible things I wrote before? Do you know of anything that would help? Complex number isomorphic to certain $2\times 2$ matrices? I have been trying to prove this, but I am having trouble understanding how to prove the following mapping I found is injective and surjective. Just as a side note, I am trying to show the complex ring is isomorphic to special $2\times2$ matrices in regard to matrix multiplication and addition. Showing these hold is simple enough.  $$\phi:a+bi \rightarrow \begin{pmatrix} a &amp; -b \\ b &amp; a \end{pmatrix}$$  This is what I have so far:  Injective: I am also confused over the fact that there are two operations, and in turn two neutral elements (1 and 0). Showing that the kernel is trivial is usually the way I go about proving whether a mapping is injective, but I just can't grasp this.  $$ \phi(z_1) = \phi(z_2) \implies \phi(z_1)\phi(z_2)^{-1} = I = \phi(z_1)\phi(z_2^{-1}) = \phi(z_2)\phi(z_2^{-1}).$$  So if we can just show that the kernel of $\phi$ is trivial, then it also shows that $z_1 = z_2$. The only complex number that maps to the identity matrix is one where $a = 1$ and $b = 0$, $a + bi = 1 + 0i = 1$.  Using a similar argument for addition we can just say that the only complex number $z$ such that $\phi(z) = 0\text{-matrix}$, is one where $a=0$ and $b=0$, $a+bi=0+0i=0$.   Surjective:  I forgot to add this before I posted, but I honestly don't really understand how to prove this because it just seems so obvious. All possible $2\times2$ matrices of that form have a complex representation because the complex number can always be identified by its real parts and since the elements of the $2\times2$ matrix are real then the mapping is obviously onto.  I have always had trouble understanding when I can say that I have "rigorously" proved something, so any help would be appreciated! How to list all installed packages I'd like to output a list of all installed packages into a text file so that I can review it and bulk-install on another system.  How would I do this? Falsely accused witch befriends transforming dragon she was to be sacrificed to Story is in a medievalish setting and starts with a woman who has been falsely accused of being a witch being taken by 2 men to be sacrificed to a dragon.  She ends up befriending the (male) dragon, who is able to transform into various forms, including human, and can speak only the language of whatever form he is in. e.g. can speak English in human form, but can't in dragon form.  He needs to return to his dragon form every day at sunrise or he dies.  Contact with iron or steel causes him pain and prevents him from transforming.  Near the end of the book, he's been put in handcuffs by one of the two men from the start and the woman has to get the assistance of the other one (village blacksmith?) to remove them before sunrise, which they manage to do just in time.  I think I read it maybe 10 years ago.    I also remember it was a very short book, probably only about 100 pages. Does $\mathbb R^2$ remain connected when countably many points are removed? Does it remain path connected?  This is not homework but is in response to working several problems where countable or uncountable many points are removed and the pattern always holds.  Thank you. That's really embarrassing, however I need to ask it. I could not prove that the normed space    $\langle \mathscr{C} [0, 1], \| \cdot \|_1 \rangle $ is complete (as a metric space), where $\| f\|_1 = \int_0^1 |f(x)|dx$. I don't really know how to explicit a continuous functions as a limit of a Cauchy sequence. I tried to prove that the pointwise limit (of the Cauchy sequence) have just a finite number of discontinuities (I don't know if it's true) and then approximate it by a continuous function.  Thanks in advance. List all files in all subfolders I have a small question regarding using sudo with output redirect &gt;. To enable IP forwrding, someone can use the command:  echo 1 &gt; /proc/sys/net/ipv4/ip_forward   Executing this command will give permission denied as it requires root privileges. However, executing the same command with sudo gives also permission denied error! It seems that output redirect &gt; does not inherit the permissions of the preceding command echo. Is this right?  As a workaround I do:  echo 1 | sudo tee /proc/sys/net/ipv4/ip_forward   Is this the best way to do it? Am I missing something?  Please, note that this is an example and it applies to all commands that use output redirect. BJT as a switch: what am I doing wrong? This is result of who -uH:  NAME     LINE         TIME             IDLE          PID COMMENT me    :0           2013-08-29 01:29   ?          1686 (:0) me    pts/0        2013-08-29 01:42  old         2905 (:0) me    pts/1        2013-08-29 01:45  old         2905 (:0) me    pts/2        2013-08-29 01:52  old         2905 (:0) me    pts/3        2013-08-29 02:26  old         2905 (:0) me    pts/4        2013-08-30 18:37 00:07        2905 (:0) me    pts/5        2013-08-29 10:34  old         2905 (:0) me    pts/6        2013-08-29 11:05  old         2905 (:0) me    pts/7        2013-08-29 13:34  old         2905 (:0) me    pts/8        2013-08-30 15:56 02:45        2905 (:0) me    pts/9        2013-08-30 18:27 00:17        2905 (:0) me    pts/10       2013-08-30 17:34   .          2905 (:0) me    pts/11       2013-08-30 17:37 00:13        2905 (:0) me    pts/12       2013-08-30 18:28 00:17        2905 (:0) me    pts/13       2013-08-30 18:38 00:07        2905 (:0)   Why it lists my username in 15 lines? How do I know If someone has connected to my system remotely? Hosting multiple distinct folders for distinct domains Windows 10 high memory usage (unknown reason) A few days ago I updated my PC to Windows 10. However, after some use my PC started to slow down until it was impossible to use – it was due to high memory usage. After a restart, everything came back to normal (total usage around 25% of 8GB of RAM). However, during a few hours of usage the memory builds up again to 70%, and if not restarted it further goes to 100%, and later on even freezes. Task manager does not help very much as it does not show all the processes (added screenshots below). Also tried RAMMap but it gives an error: "error refreshing database". I tried Googling this question, yet without much success.  I do not know much about PCs, but maybe some of you know this issue, or could help to find out what is using my RAM. Start TOC from chapter 1 and also page numbering How can I access the "Open command window here" option in Windows without holding shift? Genetically modified humans study insectoid alien miners with super-intelligent hive-mind This is a short story that appeared in a collection. Two genetically-modified humans (corporate anthropologists, basically) travel to a planetoid inhabited by an insect race that is mining the planet in order to study the race. While there, they are practically ignored, as the individual members of the race lack consciousness. The humans determine a type of pheromone is used to control the worker caste, and co-opt several members to create a living area. They make plans to put the mining towards human ends, but before that can happen they are discovered. The presence of the artificial pheromones wakes up a hive-mind, super-intelligent bug, who then bargains with the surviving member of the team (the man) after killing and taking over the female member of the team.  The collection was read at some point between 2000-2005. What are turret connectors? While working on a project recently, I noticed that Digi-key has a product category . I've never seen connectors like this before, and they don't look like any kind of contact I've seen before. What does the mating connector look like? I can't envision any mating contact that makes any sense for these.  On top of that, they look like they have to be individually machined, which can't be a cost-effective process. How and why do you use an image histogram? I realize that an image histogram is a graphical display of an images tonal distribution (i.e. horizontal darks to lights, vertical pixel distribution), but how does one really use it and why? I mean, can't you determine everything you need just by looking at the image? Let $f \in L^1(\mathbb{R})$, for $a\in \mathbb{R}$ let $f_a(x)=f(x-a)$, prove that: $$\lim_{a\rightarrow 0}\|f_a -f \|_1=0$$  I know that there exists $g\in C(\mathbb{R})$ s.t $\|f-g\|_1 \leq \epsilon$, this is also true for $f_a$ and $g_a$.  Now I have the next estimation:  \begin{align*} \|f_a-f\|_1 &amp;= \int_{\mathbb{R}} |f(x)-f(x-a)| dx \\ &amp;= \int |f(x)-g(x)+g(x)-g(x-a)+g(x-a)-f(x-a)| \\ &amp;\leq \|f-g\|_1 + \|f_a-g_a\|_1 + \int |g(x)-g(x-a)| \end{align*} my question is: I can argue that $\lim_{a\to0} \int |g(x)-g(x-a)| = \lim_{a\to0} \lim_{T\to\infty} |g(x_0)-g(x_0-a)| 2T$, now I think that I can change the order of the limits here, but I am not sure why?  P.s $x_0$ is some point in $[-T,T]$, and the above is valid from the intermediate integral theorem for continuous functions, right?  Thanks.