Can the act of having certain thoughts be unethical?
Evil thoughts without actions?
Gel circular polarising filter I am contemplating buying a lens that only takes rear gel filters. Is it possible to buy a circular polarising filter in gel format? If so, who can supply them (preferably UK based)? Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$ Consider the space $C^1([0,1])$ and the function $d:C([0,1])\times C([0,1]) \to \mathbb R$ defined as $d(f,g)=|f(0)-g(0)|+sup_{x \in [0,1]}|f'(x)-g'(x)|$. Decide whether the metrics $d$ and $d_{\infty}$ are topologically equivalent in $C^1([0,1])$ (where $d_{\infty}=sup_{x \in [0,1]}|f(x)-g(x)|)$  My attempt at a solution:  If two metrics are topologically equivalent, then they have the same convergent sequences. Honestly, I couldn't do anything. I am trying to define a sequence of functions $\{f_n\}_{n \in \mathbb N}$ such that $f_n \to f$ in, for instance, $(C^1([0,1]),d)$ but $f_n \not \to f$ in $(C^1([0,1]),d_{\infty})$. Could it be this two metrics are topologically equivalent? If this is the case, how could I prove it? If not, I would appreciate any hint to find an adequate sequence of functions that works for what I am trying to prove. I just learned that some Lenovo laptops include a utility that offers to limit battery charging capacity to within 0–80% in order to slow the attenuation of the battery lifespan:    How can I do this in Ubuntu? Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$ For an odd prime $p$, prove that any primitive root $r$ of $p^n$ is also a primitive root of  $p$   So I have assumed $r$ have order $k$ modulo $p$ , So $k|p-1$.Then if I am able to show that $p-1|k$ then I am done .But I haven't been able to show that.Can anybody help me this method?Any other type of prove is also welcomed. Counting invertible $0$-$1$ matrices that remain invertible under negating the diagonal There is an invertible $n×n$ matrix with each entry $0$ or $1$. Now we negate ($x\to 1-x$) the diagonal of the matrix, and it is still invertible. How many such matrices exist for a given $n$?  Can we derive a general formula? If $n=2$ there are $2$ such matrices, if $n=3$ there are $48$. But I have no idea whether a formula exists for higher $n$. I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and Minkowski tensors, instead of the more traditional "beginners" approach. Would anyone have a recommendation for such a textbook ?  I already have decent knowledge of the physics and maths of both SR and GR ( including vector and tensor calculus ), but would like to take a step back and expand and broaden my intuition of the geometry underlying SR, as described by 4-vectors and tensors. What I do not need is another "and here is the formula for time dilation..." type of text, of which there are thousands out there, but something much more geometric and in-depth.  Thanks in advance. I'm rewiring a a small part of a wall and I'm confused about a combination of the NEC and the products that I'm able to find.  I'm working on a 20 amp circuit (with 12g wire of course).  I'm connecting 4 receptacles each in their own box, 15 amp receptacles for normalcy.  But the terminals don't seem to accept 12g wire, even on the screws.  My first reaction was to make pigtails 14g pigtails, so that the 14g tap goes directly to the receptacle and is not used to feed the rest of the circuit.  12g in the box, 12g out of the box, and 14g inside the box only.    Is that type of splice allowed, or should I look harder for a 15 amp outlet that can more easily accept 12g wire? I'm currently doing a couple of exercises on logarithmic expressions, and I was a bit confused when presented with the following: $5^{\log_5 17}$.  The answer is $17$, which is the argument of the logarithm in the exponent, but I don't understand the reason why.  A previous question in the exercise was $12^{\log_{12} 144}$, which is pretty straight forward since $\log_{12} 144=2$ and $12^2=144$ but since $\log_5 17$ is an irrational number, I couldn't calculate it the same way.  So my question is, why is $x^{\log_x n}=n$?  [Update]  I've now managed to reason this out and realized how simple it is.  Basically, if $y=\log_x n$, then $y$ is the number that  $x$ must be raised to to become $n$; therefore, if I raise $x$ to that power $y$, I will naturally get $n$.  I guess my problem was that I tried to work out the question mechanically instead of intelligently and that's why I failed, because once I realized that I can't calculate $\log_5 17$, I was stumped.  Now that I reasoned it out, as explained in the previous paragraph, I understand it. This week I've read two news stories about two different camera lenses that can magnify things that are very far away.  The first is the , which is a point-and-shoot camera that costs $600, has an 83x optical superzoom lens ("the same field of view as a 2,000mm lens on a full-frame camera"), and lets you see the craters of the moon.  The second is the , which weighs 36 pounds, costs $180,000, and can take portraits of people a half mile away.  A non-photographer might ask, "Why would somebody spend their life savings on a gigantic telescope of a lens when you could take far away pictures with a handheld camera for 1/300th the price?"  Well, I am basically a non-photographer, and I would like to ask that question. What does the big one give you that the little one doesn't provide? I understand that small changes in lenses can make a big difference in size and price, but this seems to be of a different scale entirely.   What is going on with the optics of the lenses that makes the small one able to be so small and the big one have to be so...big?   I'm trying to get a basic intuition for what makes lenses different, and I realize I don't understand enough about how lenses work to even know how to compare these apples and watermelons. How to prevent Round with hidden fractions Getting an error in W3C Markup Validation when trying to get a whole  element as a link in a page Why does the connection time out when connecting to a server? How to replace all occurrences of a string in JavaScript? Let $T$ be a self adjoint operator on a finite dimensional inner product space. And let $4$ and $5$ be the only eigenvalues of $T$. Show $T^2-9T + 20I = 0$ .  proof:Let $T$ be a self adjoint. And let $4 , 5$ be the only eigenvalues of $T$. Then $Tv = 4v, Tv = 5v$ for some $v \neq 0$. Then $Tv = 4v, Tv = 5v$ if and only if $(T-4I)v = 0, (T-5I)v=0$.  Then $ (T-4I) (T-5I)v=0$ implies $(T^2 -5T -4T + 20I^2)v = 0$, implies   $(T^2 -9T + 20I)v = 0$, so we have  $T^2 -9T + 20I = 0  $. Can someone please check this? if it's not correct, could I please have some help on it? Thank you System.Drawing in Windows or ASP.NET services According to , it is not a particularly good idea to use classes within the System.Drawing namespace in a Windows Service or ASP.NET Service. Now I am developing a class library which might need to access this particular namespace (for measuring fonts) but it cannot be guaranteed that the host process is not a service.  Now there is a less optimal method I can fall back to if System.Drawing is unavailable, but if it is possible, I would rather use classes in System.Drawing. So what I would like to do is to determine at runtume if System.Drawing is safe or not, and if it is, use it, otherwise fall back to the suboptimal option.  My problem is: How could I possibly detect if System.Drawing is safe to use?  I think I should either   Detect if the current process is a Windows Service or ASP.NET service Detect if GDI is available Or maybe there is a way to ask System.Drawing.dll itself if it is safe to use   Unfortunately, I cannot come up with a way to implement any of these approaches. Does anyone have any idea? How to convert Wubi install into regular install? How to execute two mysql queries as one in PHP/MYSQL? pgfplots and using axis cs to add points I am trying to mark two inflection points using a foreach loop in a pgfplot, but it isn't working.  \documentclass[tikz]{standalone} \usepackage{pgfplots} \pgfplotsset{compat = 1.10}  \begin{document} \begin{tikzpicture}   \pgfmathsetmacro{\infx}{1/sqrt(2)}   \pgfmathsetmacro{\infy}{exp(-.5)}   \begin{axis}[     xmin = -3,     xmax = 3,     ymin = -0.1,     ymax = 1.05,     domain = -4:4     ]     \addplot[blue, samples = 500, smooth] gnuplot {exp(-x^2)};      \foreach \x/\y in {\infx/\infy, -\infx/\infy}{       \draw[red] (axis cs: \x, \y) circle[radius = .025];     }   \end{axis} \end{tikzpicture} \end{document}   I am being told:  Undefined control sequence.^M &lt;argument&gt; axis cs: \x ^M                        , \y ^M l.34   \end{axis}^M I need help finding the set of continuous functions $f : \Bbb R \to \Bbb R$ such that for all $x \in \Bbb R$, the following integral converges:  $$\int_0^1 \frac {f(x+t) - f(x)} {t^2} \ \mathrm dt$$  I think it might be the set of constant functions but i havent been able to prove it :(   I was thinking that you can use the stone weiestrass theorem considering the set of continuous functions on a closed  interval(non trivial) ,and a subset which contains the set of continuous functions whose integral above diverges in some point in that interval along with  with the set of constant functions. So in order to solve the problem i need only to prove that if two functions do not meet the condition of the problem then their product does not as well .  I hope you can provide some insight and thank you . Should searching by default be AND or OR? On my website I have a search bar.  It's powered by Lucene.net.  I have a requirement to make search be a substring case insensitive search, with direct hits appearing before substrings.  What I don't know, however, is when a user searches for a multi-word item--say "Chocolate Milk"--should that be treated under the hood as an AND or OR search?  As an example:  *chocolate* AND *milk*   vs  *chocolate* OR *milk*   The requirement right now is to treat this as an AND, but I'm not sure if that's the right way to go about it.  What would be the best in terms of UX?  I would think the best thing to do would be an OR search, with items containing both keywords appearing before items containing only one of the keywords.  Thoughts?  EDIT: The types of items being searched are medical supplies, with very cryptic names.