Finding Limit of n-th root sequence
Calculating $\lim_{n\to\infty}\sqrt[n]{2^n-n^2}$
How Do You Select Only Part Of a Timeline To Be Rendered? Let's say I only want a section of the timeline to be rendered, and I want the final output to be in RAW AVI format.  How would you do that? Thanks guys! Some things I know:  omega_1 is the first uncountable ordinal, made up of all of the countable ordinals f is not necessarily continuous    For this proof, I currently have x as a condensation point in my range, and I know that (x - (1/n) , x + (1/n) ) is uncountable and everything to the left and right of this interval is countable. I understand that I want to shrink this interval small enough just to x (which will be my constant), making everything around x eventually countable. I also understand that this will eventually make all of the elements in omega_1 go to x but I am having a hard time seeing where my contradiction comes in. I also am struggling with writing this proof in a presentable fashion.   Thank you! What is the difference between Parse() and TryParse()?  int number = int.Parse(textBoxNumber.Text);  // The Try-Parse Method int.TryParse(textBoxNumber.Text, out number);   Is there some form of error-checking like a Try-Catch Block? Refer to renamed columns in WHERE clause SELECT name, gdp/population as capita  FROM world w1  WHERE continent = 'Europe'       AND capita &gt;  (     SELECT gdp/population      FROM world      WHERE name = 'United Kingdom' );   How come I can't refer to capita in the WHERE clause? It returns this error:  Unknown column 'capita' in 'where clause'   I can however, run the query if I replace capita with gdp/population.  I don't want to do gdp/population &gt; .... How can I do capita &gt; ...? Or is this not possible? Effective way to find any file's Encoding Prove that $x^x+y^y=z^z$ doesn't have integer solutions Newton's third law of motion states that every action has an equal and opposite reaction. That is the reason we do not sink into the earth, because when our weight exerts a force on the earth it also exerts an equal and opposite force on us.  But when we stand on quicksand or on fluids we can sink in. How is this possible? Does it not exert an equal and opposite force on us? Or are Newton's laws different in the case of fluids and substances of low densities? There's an election going on. What's happening and how does it work? Fantasy novel: magic school, talking rabbit, character bites off another character's fingers The plotline as a whole is completely lost to me, but it was a big inspiration to my preteen self at the time and has shaped my creative development up to now. I'll list some of the big points that I can recall from it, if anyone has the vaguest idea what book I am referring to I would be so appreciative for any guess! I just want to reread it.   Main character is a delinquent of sorts, goes to a magic school. I don't remember there being any pictures in this book. There is a threesome between the main character and his two friends I believe it is a talking rabbit that says something along the lines of "My dear child, you are incensed", followed by one of the characters saying something like "Damn right I am!" A character that had been mentioned earlier but never made an appearance (he was banned for doing bad magic I think) shows up to fight and he bites off another character's fingers. Main character seeks out a magical white stag near the end of the novel because the stag can grant a wish if it's caught because he wishes to reset his timeline. The stag is able to speak. How many generator has a cyclic group of order n? If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative. Let $R$ be a ring, where $a^{3} = a$ for all $a\in R$. Prove that $R$ must be a commutative ring. Are there any disadvantages to using your companions for transporting Power Armor After I read that companions don't drain the fusion core of a Power Armor when wearing it, I decided to try giving my armor to Nick so I'll always have it close by if I need it.  But I was wondering if there are any other drawbacks to that. For example, does the Armor get damaged or destroyed when the companion is under fire? If I left food out of the refrigerator for some period of time, is it still safe? If I left it out too long, can I salvage it by cooking it more? Solvability of Poisson's equation for $p$-forms directly from Hodge decomposition If $M$ is a closed manifold, it's well known that $\Delta\phi=\alpha$, where $\alpha$ is a $p$-form, has a solution if and only if $\alpha$ is orthogonal to the space of harmonic $p$-forms. This is proved on page 224 of Warner, but the proof depends heavily on his approach to Hodge theory. There are other methods that avoid his main technical lemma 6.6. So, can one prove this fact using only the "standard" facts of the theory?  For functions it is easy, for one has $$\alpha=\delta \psi+h.$$ But $(\alpha,h)=0$, so $\alpha=\delta\psi$. Then decompose $\psi$ to get $\alpha=\delta d\zeta$ for some function $\zeta$. But on functions, $\Delta=\delta d$. But for $p$-forms in general one has $$\alpha=d\xi+\delta \psi+h,$$ since $\Omega^{p-1}$ is nontrivial. Using the decompositions again, one has $$\alpha=d\delta \rho+\delta d\sigma,$$ where $\rho,\sigma$ are $p$-forms. I don't see how $\rho$ and $\sigma$ are related, but it looks close. What's the difference between eq, eql, equal and equalp, in Common Lisp? What's the difference between eq, eql, equal and equalp, in Common Lisp?  I understand that some of them check types, some of them check across types an all that, but which is which?  When is one better to use than the others? Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$ Find the following sum : $\sum_{n=1}^{\infty} \frac{\ln n }{n(n- \ln n)}$  I couldn't find any way to solve.   I just want a hint, how to initiate? Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$ Show that $$\lim_{x \to \infty} \frac{\log(1 + e^x)}{x} = 1$$ How do I prove this? Or how do we get this result? Here $\log$ is the natural logarithm. Proving that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$. I am looking to prove that $GF(p^n)$ contains a unique subfield isomorphic to $GF(p^m)$ if and only if $m$ is a divisor of $n$. In the Wikipedia article:    They say that this statement has been proven by E. H. Moore in 1893.  How to go about proving the theorem? I know first I need to generate a subset, prove that it's a subfield, and then assume they are two and show it's unique.  But how to generate it in the first place? Consider the set of polynomials of the form $x^{p^m}-x=0$? Is there a way to show that it's a subfield without checking all the axioms? Migrate hard drive with Windows 7 to new laptop? I have a Dell D630 laptop that has Windows 7 Professional on it that was in dire need for replacement so I recently picked up an HP G62 laptop that comes with Windows 7 Home Premium. I don't need both laptops and I'd rather spare myself the time reinstalling all my programs and making sure I didn't forget to migrate any of my data over by simply swapping hard drives from the Dell to the HP.  Well, I tried just that and my HP laptop instantly BSOD'd on startup.  I'm currently running 'Startup Repair' but it's been sitting there for over 20 mins saying &quot;Attempting repairs...&quot; and nothing is really happening so I don't have much faith in this. The good news is that before I swapped the drives I made an Acronis image of the Dell drive and stored it on my NAS so I can pretty much try anything with this drive and still get back to where I was if need be. I find it hard to believe that what I want to do would be rather difficult, although it sure is looking that way.  I'd appreciate any advice in making this happen. Thanks Edit All the answers were great, so thank you.  I accepted djechelon's answer because the Win7 migration tool saved me quite a bit of time. $(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field. Where $a \oplus b = a + b +1$ I have this problem from the book Real Analysis of Miklos Laczkovich ():     Let $\oplus : \mathbb R \times \mathbb R\to \mathbb R $, where $(a,b) \mapsto a + b +1$. Then,  $(\mathbb R, \oplus)$ is a group. Define a multiplication with which we get a field.   But in the exercise there are no hints. Could anyone help me?