Why won't this If statement work for the string?
How do I compare strings in Java?
Rootspaces are $\mathop{ad}$ nilpotent $\sum a_n$ be convergent but not absolutely convergent, $\sum_{n=1}^{\infty} a_n=0$ Let $\sum a_n$ be convergent but not absolutely convergent, $\sum_{n=1}^{\infty} a_n=0$,$s_k$ denotes the partial sum then could anyone tell me which of the following is/are correct?  $1.$ $s_k=0$ for infinitely many $k$  $2$. $s_k&gt;0$ and $&lt;0$ for infnitely many $k$  3.$s_k&gt;0$ for all $k$  4.$s_k&gt;0$ for all but finitely many $k$  if we take $a_n=(-1)^n{1\over n}$ then $\sum a_n$ is convergent but not absolutely convergent,but I don't know $\sum_{n=1}^{\infty} a_n=0$? so I am puzzled could any one tell me how to proceed? Angle Constructions Over the numerous math tests I've taken, I have yet to understand what angle can be constructed and what cannot. From my understanding, 30, 45, 60, and 90 degree angles can be constructed. You can then use these angles and subtract or add them to create other angles like 15 or 75. Also, any angle can be bisected. Are there any other basic angle measures that can be constructed like 30, 45, etc.? So 82.5° is an angle measure  that can be constructed because you can add 60+60+45 to get 165 and then bisect it. I've got this one file, favicon.ico. It's actually a large group of nested files, but purely for example, just this one.  If I do cp favicon.ico favicon2.ico, Apache can read the second one just fine.  If I do mv favicon.ico favicon3.ico, Apache throws a 403 on favicon3.ico.  If I su apache, I can read the file as apache.  stat says both files are identical, except for the inode number.  Is there some hidden flag somewhere or something that I'm missing? I've never seen anything like this.  error_log says (13)Permission denied: access to /favicon3.ico denied Opposite of caregiver I want to write a book about the unfair expectations of a caregiver. A caregiver refers to somebody to looks after somebody else.  What is the term for that 'somebody else'.  'Patient' doesn't seem all encompassing. jQuery - auto size text input (not textarea!) I am travelling from Singapore to San Francisco and the airline has a layover of 7.5 hours at Tokyo Airport (NRT). I am wondering if I would be allowed to go out to experience the city for a while in some form a visitor visa.  I know Singapore has such facilities, but does anyone know if I can do it in Tokyo? Any suggestions or pointers are welcome. Note - I do not have a visa for Japan yet, but I am hoping that 1 day visitor visa could be possible at airport. Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$ I can't figure out an algebraic proof for the following identity:  $$\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$$  Combinatorical solution:  We can see that as choosing some from $n$ and the rest of $k$ from $m$, thus $k$ in total.  Or we could just choose $k$ from the union. On the meta home page I noticed the  is listed as doing something, but cannot figure out what it is.  There is nothing on the  or its , but the recent activity is listed with the same timestamp. Do professors care about their rating on websites such as RateMyProfessor or Koofers? I am wondering if a professor is already an Associate Professor, do they still care about their reputation in the eyes of the department considering tenureship is already granted? Proof explanation $A\setminus B = A \setminus B \cap A$ $A\setminus B = A \setminus B \cap A$  Proof $A\setminus B \subseteq A \setminus B \cap A$:  $x\in A\setminus B \to x\in A \land x \notin B$  $x\in A \land (x \notin B \color{red}{\lor x\notin A})$  $x \in A \land (x\notin B \cap A)$  $x \in A\setminus B\cap A$  Proof $A \setminus B \cap A \subseteq A\setminus B$:  $x \in A \setminus B \cap A \to x\in A \land x\notin B \cap A$  $x \in A \land (x\notin B \color{red}{\lor x\notin A})$  $x \in A \land x \notin B$  $x \in A \setminus B $  Therefore $A\setminus B = A \setminus B \cap A$  I am confused how the stuff in the red is formed. Can we add an or statement to anything and ignore if its true or not if the first part of the or is true? How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that? Subgradients of non-convex functions In  (section 2.3), it is stated that:     A point $x^*$ is a minimizer of a function $f$ (not necessarily convex) if and only if $f$ is subdifferentiable at $x^*$ and $0 \in\partial f(x^*).$   Could anybody provide me with references for a proof of the above statement?   Is there a reference where we can learn more about subgradients of non-convex functions?  In Section 3. Calculus of subgradients of the above notes,many properties of subgradients are presented for convex functions. I would like to know which ones among these properties still hold for non-convex functions.  Thank you in advance! launchd plist format for running a command at a specific time on a weekday I've been trying to develop an intuition based understanding of Bayes' theorem in terms of the prior, posterior, likelihood and marginal probability. For that I use the following equation: $$P(B|A) = \frac{P(A|B)P(B)}{P(A)}$$ where $A$ represents a hypothesis or belief and $B$ represents data or evidence. I've understood the concept of the posterior - it's a unifying entity that combines the prior belief and the likelihood of an event. What I don't understand is what does the likelihood signify? And why is the marginal probability in the denominator? After reviewing a couple of resources I came across this quote:     The likelihood is the weight of event $B$ given by the occurrence of $A$ ... $P(B|A)$ is the posterior probability of event $B$ , given that event $A$ has occurred.   The above 2 statements seem identical to me, just written in different ways. Can anyone please explain the difference between the two? convergence to infinity of$ (2^n + 3^n)^{\frac{1}{n}}$ (as $n \to \infty$) Just checking. $2^n$ ($n \to \infty$) tends to $\infty$. + $3^n$ also ($n \to \infty$) tends to $\infty$  so the sum gets me $\infty$.  Now $(\infty)^{1/\infty}$ : $(\infty)^0 = 1$  I see no other way.  Theorem: $n^{\frac{1}{n}} = 1$ as $n \to \infty$.  Analogous:  $(2^n - 3^n)^\frac{1}{n}$ = $(\infty  - \infty)^0$ = 1 ???  Is it ok to suppose infinity on any integer $k^n$ as $n$ goes to infinity ? How can I copy location info from geotagged phone images to images taken with my other camera around the same time? So i did quite a big trip recently, and took lots of pictures with my DSLR and occasionally Android phone. Only after coming back did i read about the whole GPX file, tracklog options in Lightroom. meaning i don't have such a tracklog file.  The android phone did geotag most photos it took. (at least, when it got a gps fix i guess)  So my question is, is there some software or way that will automatically copy the geotag from the android's photos to photos taken on the same time with my DSLR?  Or alternatively, generate a tracklog from the geotagged data in the android pictures? @online bibliography biblatex Every Artinian ring is isomorphic to a direct product of Artinian local rings I registered my Stack Overflow account using the Stack Exchange OpenID provider. I later changed my e-mail, but I cannot change the e-mail address associated with my OpenID for some reason. Why is that, and how do I change it? I logged in to Stack Exchange and it lets me change my password, but never my e-mail.