Java NullPointerError
What is a NullPointerException, and how do I fix it?
Do virtual particles actually physically exist? Einstein's first postulate implies the second? Does "FN" stand for or mean anything? I have not used Evolution for long time now and I would like to reset all the settings and start from scratch. How would I be able to do this? Does the Great Old One warlock's telepathy from the Awakened Mind feature take an action? Does the Great Old One warlock's telepathy from the Awakened Mind feature take an action?  It doesn't seem too clear to our group and we have basically ruled it as equivalent to talking. How to terminate a script? I am aware of the die() command in PHP which exits a script early.  How can I do this in Python? Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups? Isomorphism of a product $C_n \times C_m$ of cyclic groups with the cyclic group $C_{mn}$ Given that $C_n$ is a cyclic group of order $n$, what conditions must integers $n$ and $m$ satisfy such that the group $C_n \times C_m$ is isomorphic to C$_{mn}$?   So I attempted to investigate a few lower-order cyclic groups to find a pattern. In particular, I looked at $C_2 \times C_3$ and compared it to $C_6$. Here are a couple of diagrams:  $C_2 \times C_3$ -   $C_6$ -   They Cayley tables look pretty different (identity elements are all over the place for $C_2 \times C_3$) so I concluded that they are not isomorphic.  I did the same for $C_2 \times C_4$ and $C_8$:  $C_2 \times C_4$ -   $C_8$ -   Again, I arrived at the conclusion that the 2 groups are not isomorphic due to their Cayley table structure.  It seems I'm stuck now. Are my conclusions wrong for the examples I examined? If so, how do I find the conditions for the general case of comparing $C_m \times C_n$ with $C_{mn}$? Countable axiom of choice: why you can't prove it from just ZF This is a follow-up question to the discussion about the finite axiom of choice .  Suppose we have a countable collection of non-empty sets $\{A_1, A_2, A_3,\cdots\}$ Reasoning as indicated in that discussion, we can prove the existence of a choice function $c_n$ such that $c_n(i)$ belongs to $A_i$ for $i = 1,\cdots,n$  Again reasoning as suggested and using induction, we can prove the existence of a function $C$ defined over $\{1, 2, \cdots\}$ such that $C(n)$ is a choice function defined for $i=1,\cdots,n$ with $C(n)(i)$ an element of A_i. We can require in addition that $C(n)(i)$ and $C(n-1)(i)$ are equal for $i=1,\cdots,n-1$.  Now it would it seem that we can prove the countable axiom of choice by taking the union of $C(1)$, $C(2)$, $\cdots$  The question is as follows: why is that proof wrong? I suspect the answer may have something to do with the axiom of union. I don't understand this..maybe there is something wrong with my understanding of battery or electricity.  I am learning about electricity more deeply this time. So please bear with me.  So lets begin with what I know:   follow of current occurs when there is voltage drop. voltage drop happens when there is imbalance in charge. a battery is basically two separated chemicals. One side with electrons to spare and other side that needs electron to balance itself. which is imbalance in charge. When both sides are connected + side snatches electrons from - side. (And if there is a medium, conductor, then first electrons are taken from conductor that in turn snatches from - side, which not being able to keep electrons lose them and give up those electrons, we label it as excessive.)   The analogy i was taught with used marbles in pipe... When one side has excessive marbles And this pipe is connected to other side that has no marbles the marbles will instantaneously start falling out so even though marbles from container with excessive marbles haven't traveled there yet, they still start falling because filled side marbles are pushing marbles in pipe and which in turn push the last marbles in pipe out.   1st, Aren't electrons pulled by atoms that can use more electrons, and not move because one side is overfilled with electrons so they can't wait to push some out.  Questions:    if I connect a conductor to positive side of a battery, shouldn't it make all electrons/marbles fall into empty container as empty container will pull marbles as atoms need electrons? if I connect two batteries' only opposite sides to each other shouldn't they drain (balance the each other out, cancelling all - &amp; + charges)? I have often read that using RSA for encrypting bigger size plaintext is not good solution.  What I understand is that using RSA encrytion is best for small plaintext and most effective if it is smaller than 'bit size' of RSA. For instance, if I use RSA with a 2048 bit size then the plaintext that I can encrypt must be smaller than 256 bytes.  Is this true? What happens if the plaintext is bigger than 256 bytes? Why is there a problem with larger plaintext when performing RSA encryption? Finding the asymptotic of an integral I came across the following exercise on asymptotic behavior of integrals: $$I(a) = \int_0^\infty\frac{\cos x}{x^a} \, dx, \text{ where } a\to0^+.$$ I have tried integrating by parts or replacing $\cos x$ with the first summands of its Taylor series, but I end up with something equal to infinity (independent of $a$ and that is not what we want).  I just thought about the substitution $x \leftrightarrow\frac{1}{1+x^2}$ and I get the  following result:  $$I(a) = \frac{\cos(1/2)}{2^{2-a}} + \int_0^1\frac{2x^3 \cos\left(\frac{1}{1+x^2}\right)}{(1+x^2)^{3-a}} \, dx - \int_0^1 \frac{2x^3\sin\left(\frac{1}{1+x^2}\right)}{(1+x^2)^{2-2a}}\,dx$$ If I could prove that the last summands are $o(I(a))$ then it would be OK, but I think, in general my strategy won't work. Apparently this is supposed to be an easy exercise, but I can't come up with anything right now. Local BLAST Copy Number per Hit I generated a series of local BLAST databases using makeblastdb of metagenomic data and am searching for the presence of a particular gene. While I can do the normal BLAST analysis looking at e-values, % identity, etc. I haven't been able to figure out how to determine how many times a given sequence exists in the database.  So: given a BLAST database of metagenomic data where a particular gene may exist multiple times, how do I determine the copy number of a given BLAST hit?  Thanks in advance. Text in an equation This is best explained by example. Suppose I have the following:  \[     \begin{align*}     C_3 \rightarrow 6 automorphisms\\     C_4 \rightarrow 8 automorphisms\\     C_5 \rightarrow 10 automorphisms     \end{align*} \]   How can I get the word "automorphisms" to display as if it were not enclosed by the brackets? Anomalous community user activity 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. How can I get a more traditional drop-down like menu for Unity? I've always wondered how to write the "A ? B : C" syntax in a C++ compatible language.  I think it works something like: (Pseudo code)  If A &gt; B    C = A Else    C = B   Will any veteran C++ programmer please help me out? Auto-fit TextView for Android For ridiculously small hard drives (8GB), what Ubuntu Based (although not necessarily official) distribution offers the smallest installed size?  Let me clarify: I still want a certain amount of personal file space, preferably a few gig. I also don't have a problem with performance, while it is mediocre, a 2.6GHz single-core and 1GB of ram suffice to run ubuntu fine, but i find that it  uses 6-7GB of space. I am aiming for closer to 4GB. If angular velocity & angular acceleration are vectors, why not angular displacement? Are angular quantities vector?   ... It is not easy to get used to representing angular quantities as vectors. We instinctively expect that something should be moving along the direction of a vector. That is not the case here. Instead, something(the rigid body) is rotating around the direction of the vector. In the world of pure rotation,a vector defines an axis of rotation, not a direction in which something moves.   This is what my book (authored by Halliday, Walker, Resnick) says. But they mentioned with a caution that      Angular displacements cannot be treated as vectors. ....to be represented as a vector, a quantity must also obey the rules of vector addition..... Angular displacements fail this test.   Why do they fail in this test? What is the reason?