I’m new to this Linux stuff... I may have a fundamental misunderstanding, but I need some clarification on why getting the Ubuntu app on windows and using that terminal is so inferior (according to other Linux developers) than actually dual booting or solely using the Ubuntu distribution.  Thanks.
As most of you know, in the Microsoft Store, there are . This means that on Windows I can emulate Ubuntu and have the Ubuntu command line directly on Windows.  The question is very easy: what can’t I do from the Ubuntu command line emulated in Windows that I can do on a proper Linux-based Ubuntu? Is it useful to download this Ubuntu application, install it, and work just with it instead of the real OS? Is it possible to install all the development libraries? Can I write (or not) device drivers? In other words: what are the limits?  What features of Ubuntu Linux-based are missing from Ubuntu-on-Windows?  New answers are welcome: I know that every software is always changing by improving characteristics and features!
If $x_1,...,x_n$ are positive real numbers and if $y_k=1/x_k$, prove that $$\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2.$$   I've been learning induction, and I've come across this problem that I really can't even break down and begin to think about. I've been told it has something to do with Cauchy-Schwarz, but I cannot figure out how to apply it. I would appreciate help figuring out how to go about and formulate this proof. Thanks! Unable to solve equation for a variable by any method CAST and IsNumeric Why would the following query return "Error converting data type varchar to bigint"?  Doesn't IsNumeric make the CAST safe?  I've tried every numeric datatype in the cast and get the same "Error converting..." error.  I don't believe the size of the resulting number is a problem because overflow is a different error.  The interesting thing is, in management studio, the results actually show up in the results pane for a split second before the error comes back.  SELECT CAST(myVarcharColumn AS bigint)   FROM myTable   WHERE IsNumeric(myVarcharColumn) = 1 AND myVarcharColumn IS NOT NULL   GROUP BY myVarcharColumn   Any thoughts? The age of the universe Many times I have read statements like, "the age of the universe is 14 billion years" . For example this wikipedia page .   Now, my question is, which observers' are these time intervals? According to whom 14 billion years? find and echo file names only with pattern found Prove that free modules are projective Where do I ask a question about copyright? Evaluate $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n})$ I'm struggling to find the limit at infinity of : $$\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n}), n\in\Bbb N$$ I know it is $1$ but I don't understand why this is wrong :  $\sin^2(\pi\sqrt{n^2 + n}) = \sin^2(\pi*n\sqrt{1 + \frac{1}{n}})$.  So $\lim \limits_{n\rightarrow\infty}\sin^2(\pi\sqrt{n^2 + n}) = \lim \limits_{n\rightarrow\infty}\sin^2(\pi*n\sqrt{1 + \frac{1}{n}}) =  \lim \limits_{n\rightarrow\infty} \sin^2(\pi*n) = 0$.  Thanks. iSight cable for mid 2009 macbook pro 13" help If my iSight camera no longer works and neither does my bluetooth, should my wifi still technically be working? Aren't they all co-dependent(if that makes sense) or can the fact that my wifi is still functional mean that the iSight camera still works and it's a software problem. I've noticed that in comments, when you create `code region` with backticks, the backslash will still work as an escape character within that region (but it should not, IMHO).  To clarify:   In comments, `\\` will be rendered as \, but it should be rendered as \\ In the post body itself, `\\` will be rendered as \\ (i.e., correctly)   This is especially confusing when you enter regular expressions into a comment, since backslash-escaping is very common there, and confusion increases if you are dealing with a regex that is double-escaped for representation in a string.   At some point you lose track how many backslashes you must make so the comment renders correctly, or you don't notice fast enough (or at all) and the comment contains wrong code where the same markup in a question or answer would come out as perfectly correct.   It's just that comments can't be corrected anymore after the grace period, leaving you with the choice of either deleting the comment, thus crippling the conversation, or engaging in a trial-and-error game of writing another comment with even more backslashes to explain the issue.  My question is two-fold:   Will this error be corrected? If yes, existing comments should probably be searched and "fixed" by a routine that tries to do the right thing (this is probably somewhere between hard and impossible) Or, can I rest assured that never ever the behavior of the backslash in comments is going to be changed, so I can start working around this issue by hand, knowing that they won't start displaying incorrectly at some point in the future? What is the default bibliography package and backend in LaTeX? According to , biblatex and natbib are packages while biber and bibtex are backends. If I don't specify either any package or any backend, it still compiles fine. Which package and backend combination is being used in this case?  demo.tex  \documentclass{article} \begin{document}  \nocite{*} \bibliographystyle{ieeetr} \bibliography{pub}  \end{document}   pub.bib  @article{janssen1996evaluation,     title={Evaluation of the DNA fingerprinting method AFLP as a new tool in bacterial taxonomy},     author={Janssen, Paul and Coopman, Renata and Huys, Geert and Swings, Jean and Bleeker, Marjo and Vos, Pieter and Zabeau, Marc and Kersters, Karel},     journal={Microbiology},     volume={142},     number={7},     pages={1881--1893},     year={1996},     publisher={Soc General Microbiol} }  @article{vos1995aflp,     title={AFLP: a new technique for DNA fingerprinting},     author={Vos, Pieter and Hogers, Rene and Bleeker, Marjo and Reijans, Martin and Van de Lee, Theo and Hornes, Miranda and Friters, Adrie and Pot, Jerina and Paleman, Johan and Kuiper, Martin and others},     journal={Nucleic acids research},     volume={23},     number={21},     pages={4407--4414},     year={1995},     publisher={Oxford Univ Press} } No longer earning rep for editing posts Differentiability implies continuity - A question about the proof I have a question, to aid my understanding, about the proof that differentiability implies continutity.$\mathstrut$    Differentiability Definition  When we say a function is differentiable at $x_0$, we mean that the limit:  $$‎f^{\prime} ‎(x) = \lim_{x\to x_0} \frac{f(x) - f(x_0)}{x-x_0}$$ exists.  Continuity Definition  When we say a function is continuous at $x_0$, we mean that: $$\lim_{x\to x_0} f(x) - f(x_0) = 0$$  Theorem: Differentiability implies Continuity: If $f$ is a differentiable function at $x_0$, then it is continuous at $x_0$.  Proof:  Let us suppose that $f$ is differentiable at $x_0$. Then $$ \lim_{x\to x_0} \frac{f(x) - f(x_0)}{x-x_0} =  ‎f^{\prime} ‎(x) $$  and hence  $$ \lim_{x\to x_0} f(x) - f(x_0) = \lim_{x\to x_0} \left[ \frac{f(x) - f(x_0)}{x-x_0} \right] \cdot \lim_{x\to x_0} (x-x_0) = 0$$  We have therefore shown that, using the definition of continuous, if the function is differentiable at $x_0$, it must also be continuous.  My Question  The proof seems to execute the following steps:   Assume the function is continuous at $x_0$ Show that, with little algebra, we can change this into an equivalent question about differentiability at $x_0$. With this little bit of algebra, we can show that if a function is differentiable at $x_0$ it is also continuous.   What I am slightly unsure about is the apparent circularity. In my mind it seems to say, if a function is continuous, we can show that if it is also differentiable, then it is continuous. Rather than what I was expecting, namely, if a function is differentiable, we can show it must be continuous.  Hopefully my confusion is clear. Any help will be greatly appreciated. What does 'Ign' , `Get` or 'Hit' mean when running an apt-get update? Controversy over verb choice in "neither you nor I {is/am/are} in control" Approximating $\arctan x$ for large $|x|$ "wait more than" vs. "wait FOR more than" If you make him wait (for) more than ten minutes, he'll just walk away.  I found both instances on Google Books:  and . So I'm a bid confused. Separate Network Traffic on Two Network Interfaces Is it fair to buy a return ticket I know I will never use just because it's cheaper? On a series involving harmonic numbers Finding $$\sum^{\infty}_{n=1}\bigg[\bigg(\frac{(-1)^{n+1}}{n+1}\bigg)\bigg(\sum^{n}_{r=1}\frac{1}{r}\bigg)\bigg]$$   Try: Let $\displaystyle H_{n} =\sum^{n}_{r=1}\frac{1}{r},$ then series $\displaystyle \sum^{\infty}_{n=1}\frac{(-1)^{n+1}}{n+1}\cdot H_{n}=\frac{H_{1}}{2}-\frac{H_{2}}{3}+\frac{H_{3}}{4}\cdots\cdots$  could some help me to solve it, thanks