Please give me a definition of . A textbook I have defines it to be - "A fundamental property of matter, which determines whether the matter will receive an electric flow or liberate one" I don't find this convincing enough. Any help would be appreciated.
Is there a definition of  and proper explanation of it?  It is said "Electric charge is the physical property of matter that causes it to experience a force when close to other electrically charged matter."  How is it though that matter can get charged?  Defining charge as the property of feeling a force with other charged matter seems circular.  What is charge?  Is there a non-circular definition / explanation?
The Time That 2 Masses Will Collide Due To Newtonian Gravity What is the rule of thumb for mixing doughs? Without delving too deeply into specialty doughs, but addressing more than just  and , what concerns can I evaluate when calculating the technique for approaching a dough?  For instance, some recipes say not to mix too much, others would imply that beating every bit of air out of the dough is the best thing for it. What I am looking for is a set of criteria, maybe a flowchart, that outlines how to deal with having a well-reasoned technique (as opposed to just following a recipe).  Crumble, cream, or melt the fat first? Paddle or hook? Beat, fold or whisk? Knead once and rest or knead three times and throw? I would assume that to some extent getting air in or out, activating and mixing ingredients, distributing fats more or less evenly, and so forth play a factor in any decision. However, I have no idea what those different things do, or the food science behind them. What general principles would help me understand what each factor does, so that I can have more confidence when staring down the ingredients, whether for some cookies or pizza crusts or muffins? I am trying to prove the summation formula using induction:  $$\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$$  So far I have...  Base case:   Let n=1 and test   $\frac{1}{k(k+1)} = 1-\frac{1}{n+1}$  $\frac{1}{1(1+1)} = 1-\frac{1}{1+1}$    $\frac{1}{2} = \frac{1}{2}$   True for n=1   Induction Hypothesis:   Assume the statement is true for the n-th case   $\sum_{k=1}^n  \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$  Inductive Step:   Prove, using the Inductive Hypothesis as a premise, that   $$\sum_{k=1}^{n+1}  \frac{1}{k(k+1)} = \sum_{k=1}^{n}  \frac{1}{k(k+1)} + \frac{1}{(n+1)(n+2)} = 1-\frac1{n+1} + \frac{1}{(n+1)(n+2)} = \frac{(n+1)(n+2)}{(n+1)(n+2)}+\frac{-2-n}{(n+1)(n+2)}+\frac{1}{(n+1)(n+2)} = \frac{(n+1)(n+2)-2-n+1)}{(n+1)(n+2)} = \frac{(n+1)(n+2)-n-1}{(n+1)(n+2)} = \frac{n^2+2n+1}{(n+1)(n+2)} = \frac{(n+1)(n+1)}{(n+1)(n+2)} = \frac{n+1}{n+2}$$  To prove $$ 1-\frac{1}{n+2} = \frac{n+1}{n+2} $$ Multiply both sides by $n+2$ to get an equivalent expression. $$ (1-\frac{1}{n+2}) * (n+2) = (\frac{n+1}{n+2}) * (n+2)  $$ $$ n+1=n+2−1 $$  Does this all make sense? How can this be improved upon? I have designed a VF page to create a new record in which I am trying to display the value of a pick-list field. I have set a default value for this pick-list field. When trying to create the record using the salesforce native page, the value with which pick-list loads is the one I set as default but when creating the same record using VF page, the pick-list loads with "--None--" as default value.  Can anyone suggest If this is salesforce related bug or Am I doing anything wrong ? Standard Visitor visa refusal (Deception, V3.6(b)) and procedure for reapplying My mother acquired a criminal record in UK in 2010 when she was given a conditional discharge for 12 months and charged £85. This time while applying the on-line applications for her, I accidentally missed the criminal records column and replied "NO". The visa was refused with appeal and administrative review not allowed.  Can someone please suggest my next course of action for reapplying for a visa  It is an extremely urgent family matter, and I want the visa as early as possible. While researching I found in a blog some mention of a forwarding letter while reapplying.  Can someone please enlighten me on the entire issue? I know that $\operatorname{Spec} \mathbb{C}[x]$ can be identified with the set $\mathbb{C}\cup *$, where $*$ is a generic point via the correspondence  $$ \prod_{i}(x-a_i) \leftrightarrow \{a_i\}_i , \ \ \ \ (0)\leftrightarrow *. $$ This correspondence holds for any $\operatorname{Spec} k[x]$ with algebraic closed field $k$.   When $k$ is not algebraic closed, how should one understand $\operatorname{Spec} k[x]$? (1, eval)('this') vs eval('this') in JavaScript? The definition of derivative of a function $f(x)$ is $$\lim_{h\to0} \frac{f(x+h)-f(x)}{h}$$  Using this definition, the derivative of $\sin\sqrt{x}$ will be:  $$\lim_{h\to0} \frac{\sin\sqrt{x+h}-\sin\sqrt{x}}{h}$$  $$\lim_{h\to 0} \frac{\cos\left(\frac{\sqrt{x+h}+\sqrt{x}}{2}\right)\sin\left(\frac{\sqrt{x+h}-\sqrt{x}}{2}\right)}{h}$$  Now i got stuck. How to find the limit or simplify this expression?  I get intuition that we have to use $$\lim_{x\to0}\frac{\sin x}{x} = 1$$  but that too is leading no where. I am unable to remove h from denominator.  NOTE  I know the derivative of $\sin\sqrt{x}$ is $\frac{\cos\sqrt{x}}{2\sqrt{x}}$ using chain rule, but this exercise was given to us for practice using division quotient. Can we create a subsection of the References Cited section with different reference numbering? I need to add some more publications. I do not want to change the previous reference numbers, so I need to create new citations with difference reference numbering like [p1], [p2], etc. Can LaTeX do that? When looking at a PDF document I often want to zoom-out to scroll quickly to its contents and get an overview.  However, when I zoom-out past a certain threshold (it seems to differ per PDF) Safari thinks I want to see the tab overview:    I have never found a use for this function, so it only causes annoyance.  Can I turn this tab overview off somehow? A solution that uncouples the pinch-to-zoom gesture from the functionality would also work.  I'm on Mountain Lion 10.8.5 with Safari 6.1.3. I am failing to add a heading for the appendix to the ToC with the correct page number:  \documentclass{scrbook} \begin{document} \tableofcontents \chapter{test} \appendix \addcontentsline{toc}{part}{\appendixname} \chapter{First Appendix} \end{document}     I also tried to use the \addappheadtotoc command from the  package, but that changes nothing (expect that it writes 'Appendices' instead).  I assume that the appendix package provides the solution, but I could not figure out how to use it. How to get client's IP address using JavaScript? Why does the humidifier make a stove's flame orange? Just like , the color of my stove's flames were affected by the humidifier as well.  Why does this happen? Is it a good thing or a bad thing ? Why do we let hostile users dictate the perception of Stack Overflow? I am currently running Ubuntu 11.10 off of a SanDisk 16GB USB. I installed it using a Live USB with the following partition configuration:  6GB Primary /dos   FAT32 5GB Logical /      ext4 5GB Logical /home  ext4   I don't have a hard disk, and don't see myself getting one anytime soon.   I rely solely on this 16GB, and two other 4GB USBs, one of which I used as the LiveUSB. I bring the USBs around, and even use the install at work.   I previously used an install that used a swap file. It functioned fine for the most part, save for a few slow moments, but I came across , and it got me thinking about my USB's life, so I reinstalled with the current config.   My problem now is that it is slower. Applications like Firefox would hang more often. In my previous setup (the automatically partitioned setup), Firefox would start hanging if I was running an unzip or install task on the same partition as /.   Now however, it would hang if I had another window open i.e. the system settings window. My guess is that it may have something to do with the swap file or the install being on a Logical partition rather than a Primary partition, but I don't know.   Any insight as to why it has slowed down? Showing that two definitions of $\limsup$ are equivalent How do you prove that $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$? I tried to identify the sum as a binomial series, but the $4$ and the $-1/2$ puzzle me. (This series arises in studying the first passage time of a simple random walk.) What is the justification for locking votes? Why am I not allowed to change my vote after some period of time? There are times when I go back to things I voted on, and decide they didn't deserve that specific vote. (I get wiser as I grow older) Uniform convergence of $\sum_{n=1}^{\infty}\frac{1}{n(1+(x-n)^2)}$ Is $$\sum_{n=1}^{\infty}\frac{1}{n(1+(x-n)^2)}$$ uniformly convergent on $(0,+\infty)$? Sadly, Weierstrass' criterion nor Cauchy's condition don't seem to work here and I just ran out of ideas. Comparing nullable column values using "IS NULL" versus "= NULL" I'm dealing with nullable values in a column of a table, i'm wondering why this:  with cte as (     select 'c1'::text as c1,null::text as c2     union     select 'c2'::text as c1,null::text as c2 ) select * from cte where c2 is null   returns a result set with the two "rows" having a null value in c2; comparting to this query:  with cte as (     select 'c1'::text as c1,null::text as c2     union     select 'c2'::text as c1,null::text as c2 ) select * from cte where c2 = null   that returns an empty result set!!  so it looks like that field is null is actually different from field = null? the question is... is there "null-compatible operator" to use? so i can write the comparision like: column_name = $1 and argument $1 can be a not null or null value. IF $1 is a null value then it will semantically equals to write as IS NULL, ELSE (if $1 is not a null value) then it would be semantically equals to = $1.  P.D: This question also applies to the case is NOT NULL versus &lt;&gt; NULL