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How do I compare strings in Java?
Are the WotC archives of d20 Character Optimization forum forever lost? I was looking for the Wizard Handbook but all the links were broken.  Somewhere on the handbooks of other classes (on other forums) I saw a      This was archived by WotC, here's the link   But the link leads to the welcome page of WotC (since it's broken).  Is there a way to get all that info back? Do you know where to get it from? The Wayback Machine did not archive the forums. I need to find limit points of the set $\{  \frac{1}{n} +\frac{1}{m} \mid n, m = 1,2,3,\dots \}$.  My try :   If both $m$ and $n$ tend to very large values say $\infty$ then the value of $\{ \frac{1}{n} +\frac{1}{m} \}$ tends to $0$, and if only one of $m$ or $n$ tends to very large values, then the set $\{ \frac{1}{n} \mid n=1,2,3,\dots\} $ acts as limit points.   So is it true that a set of limit points is $\{0\}$ $\cup$  $\{\frac{1}{k} \mid k=1,2,3,\dots \}$?  How should I write this proof rigorously? Creating polygon feature class from area in one not covered by another using ArcGIS Desktop? I am working on a project doing spatial analysis at a statewide level. I am looking at a form of transportation coverage in a state, and part of my analysis involves buffers and drive time polygons. I am using a geodatabase (therefore ArcGIS) for all my work, so new features will be exported as feature classes in feature datasets. To visualize: I have said state border, and some dissolved buffer rings around some points, and they cover parts of the state. I want to create a feature class for the parts of the state these buffer rings don't cover, AKA gap areas. Is there a tool I can use or create to do this? I know I could draw them in manually in editor, but I am unsure if that's the most precise way to generate these feature classes. To me, I am thinking this operation would be like an inverted &quot;Clip&quot; in that I take the two layers, and instead of pulling out the clipped area, it would take everything not in the clipped area. I am using a Desktop Basic license. Proof that $n\Bbb Z \leq \Bbb Z$ and are the only subgroups of $\Bbb Z$ My challenge is      Prove that if $n = 0,1,2,\ldots$ and $n\Bbb Z = \lbrace nk: k \in \Bbb Z \rbrace$, show that $n\Bbb Z$ is a subgroup of $\Bbb Z$ and are the only subgroups.   I handled the first point by saying that  i) Identity is 0, and $0\in n\Bbb Z$ and $0 \in \Bbb Z$  ii) For any $a,b \in n\Bbb Z$ $a+b = na_2 + nb_2 = n(a_2+b_2) \in n \Bbb Z$  iii) For any $na \in n\Bbb Z$, its inverse $n(-a) \in n\Bbb Z$.  For the second point, I said that all of the subgroups should be infinite, because for any finite group the largest element $a+a \notin H$, where $H$ is the potential subgroup, which is a contradiction. So $H$ must be of infinite order. For any $a \in H, -a$ should also be in $H$. The difference between any $a,b \in H$ should also be in $H$, i.e. $(a-b) \in H$. This leaves only the whole group or any group of the form $n\Bbb Z$.  Is my proof complete? I have to show that the ring $\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$.    I know that $(\mathbb{Z}\times\mathbb{Z})^*=\{(\pm1,\pm1)\}$, so I thought I should be looking for elements which have inverses in $\mathbb{Z}[X]/(X^2-1)$ and hopefully find more or less than 4. But I didnt succeed, so I need hints. Thanks. Limits involving factorials $\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$ I am trying to calculate the following limit  $$\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}$$ where $k$ can be any number between $0$ and $N$.  I thought of the following:  If I take the logarithm of the expression then I get:  $$\lim_{N\to\infty} \left(\log(N!)-\log((N-k)!)-k\log N\right)$$    Using the Stirling formula this can be approximated as:  $$\lim_{N\to\infty} \left(N\log(N)-(N-k)\log(N-k)-k\log N\right)$$  Now there are two cases: If $k$ is $N$, then the second term vanishes and the remaining terms cancel. If $k$ is smaller than $N$, then I can drop the $k$ inside the second logarithm and all the terms cancel. So the limit $$\lim_{N\to\infty} \log\left(\frac{N!}{(N-k)!N^{k}}\right)=0$$ Which means that: $$\lim_{N\to\infty} \frac{N!}{(N-k)!N^{k}}=1$$ I don't know if this is mathematically rigorous. Would like some help. Thanks What is a terminal and how do I open and use it? What is a terminal? How do I open a terminal window? How do I use the terminal? Why is the year NOT displayed in the questions and comments dates? Why is it that the year is never displayed in the questions or comments? Is it because it is the current year? I, and maybe others, wonder. Windows 10 non-persistent installation (live ISO) We've got a Windows 10 installation running in an environment where it can occasionally lose power and restart. However, this sometimes leads to corruption of files.  I've had a look at Windows "To-Go" but this seems to be persistent. And I've also checked out virtualisation, but that would require us to run a non-persistent Windows 10, in another Windows 10 environment.  Is it possible to install Windows 10 as a "non-persistent live CD"? So that a user will have a seemingly fresh Windows 10, but doesn't require to re-install it at each startup? Was there any reason why Dr Soong chose for Data's eyes to be yellow?  I can understand that he wasn't going for a completely human-looking android based on his skin color, but why yellow eyes? Is there a *simple* example showing that uncorrelated random variables need not be independent? Shape of confidence interval for predicted values in linear regression I have noticed that the confidence interval for predicted values in an linear regression tends to be narrow around the mean of the predictor and fat around the minimum and maximum values of the predictor. This can be seen in plots of these 4 linear regressions:    I initially thought this was because most values of the predictors were concentrated around the mean of the predictor. However, I then noticed that the narrow middle of the confidence interval would occur even if many values of were concentrated around the extremes of the predictor, as in the bottom left linear regression, which lots of values of the predictor are concentrated around the minimum of the predictor.  is anyone able to explain why confidence intervals for the predicted values in an linear regression tend to be narrow in the middle and fat at the extremes? How often should I remove the charger from my rMBP? I want my battery to remain healthy. I used to charge it full then remove the charger after it's done, then put it back on when it goes down to 10% .. However this is becoming hectic and I was wondering if I can keep it plugged in the whole day and probably remove just an hour or so before going to sleep.  What is the best way to charge and discharge my Retina Macbook Pro while keeping the battery healthy ? This question is here so we can offer users who are looking for information on how to make one or more common or basic redirects in Apache using the htaccess file. All future questions pertaining to finding information that is that is covered by the question should be closed as a duplication of this question. .  Whats the point in this question? The idea while not perfect is catch the most commonly asked questions regarding redirects using the  htaccess on the Apache platform either on  some type of lamp or a live server. The type of answers should be generally those that you could imagine are used by 100,000’s of sites world-wide and are constantly asked here at Pro Webmasters repeatedly over and over in various forms.  A few examples of the type of answers we are looking for:   How can I redirect non-www to www? How can I redirect a sub domain to the main domain? How can I redirect a sub folder from domain to a root or a subdomain?  How can I redirect an old URL to a new URL?   A few examples of the types of answers that we are not looking for:   Answers that do not involve a redirect. Any answers relating to NGinx, IIS or any other non-Apache platform. Answers that involve custom and complex string or query removals.   Resources for Advanced to Complex Mod_Rewrite Rules:      Please note: that this question is still in construction and may need some refining either by myself or a real moderator of Pro Webmasters, if you have any concerns or questions . From a previous question, we have that $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[4]{3})$, and I am assuming that we would need to use this to justify the answer to the question.   Would it be right to use some idea of a splitting field here? Or is it something to do with $\mathbb{Q}(\sqrt[3]{3}, \sqrt[4]{3})$ not containing a primitive 3rd root of unity?   This is a past exam paper question worth 8 marks, so it doesn't seem like it's a few lined answer, but I am a little stuck on where to go. Convert list of ints to one number? Can I visit the USA as a VWP tourist immediately prior to entry on non-tourist visa? Here's my situation: I'm a UK citizen. I have an H-1B visa to work in the US as of 1 August. I also have a valid ESTA.  I would like to go to the US in July for a holiday, immediately prior to beginning my work. The holiday would be at the other end of the country from my work.  I can't enter with the H-1B as I can only enter the US on that visa 10 days prior to starting work.  Specific question: Would it be possible to visit the US in early July on the VWP, visit Canada/Mexico for a few days in late July, and re-enter the US with my H-1B visa?  General question: Is it possible to visit the US on the VWP, leave briefly, and re-enter on a different status (e.g. H, F, J, K, etc), without ever returning to one's home country?  I have posted this in Travel rather than Expatriates because, although in my specific case I have an H-1B visa, my question is more generally about VWP and travel, and I believe that it is applicable to travellers with non-immigrant visas.  There's a similar question , although that's about going to the US and before having the H-1B visa. Average length of the longest segment This post is related to a previous SE post  concerning average length of a smallest segment.  A rope of 1m is divided into three pieces by two random points. Find the average length of the largest segment. My answer is 11/18.  Here is how I do it:  Here we have two independent random variables $X,Y$, both uniform on $[0,1]$. Let  $A=\min (X,Y), B=\max (X,Y)$ and $C=\max (A, 1-B, B-A)$. First we want to find the probability density function $f_C(a)$ of $C$. Let $F_C(a)$ be the cumulative distribution function. Then $$ F_C(a) = P(C\le a)=P(A\le a, 1-B\le a, B-A\le a).$$  By rewriting this probability as area in the unit square, I get $$F_C(a)=\left\{\begin{array}{ll} (3a-1)^2 &amp; \frac{1}{3}\le a\le \frac{1}{2}\\ 1-3(1-a)^2 &amp; \frac{1}{2}\le a\le 1\end{array}\right.$$ from which it follows that  $$f_C(a)=\left\{\begin{array}{ll} 6(3a-1) &amp; \frac{1}{3}\le a\le \frac{1}{2}\\ 6(1-a) &amp; \frac{1}{2}\le a\le 1\end{array}\right.$$ Therefore the expected value of $C$ is $$\int_{1/3} ^{1/2}6a(3a-1) da+\int_{1/2} ^{1}6a(1-a) da= \frac{11}{18}.$$  My questions are:  (A) Is there a "clever" way to figure out this number 11/18?  (B) What is the answer if the rope is divided into $n&gt;3$ segments? User deleting code after question has been answered If a user keeps  (thus making the answer meaningless), what should we do? Rollback the edit (what if the user just deletes the code again)? Delete the question?  More examples (same user): ,  (see also edit histories). How do Stack Overflow questions appear in Google search results in seconds?