We all are used to think that the lowest base for numeral system is 10 2. But is it possible to do math in unary system?   I found the funny section in MS windows registry:  If you want to add monospace font to console font set, you must create entry wich name is filled with exact numbers of '0'. Is that example of unary numeral system?  But i have no idea how to write 'zero' or negaitve numbers in such a numeral system.
In the decimal system: $...-3, -2, -1, 0, 1, 2, 3...$ In the binary system: $...-11, -10, -1, 0, 1, 10, 11...$ In the unary system: $-111, -11, -1, \text{ ??? }, 1, 11, 111...$   I was only able to find a related question but none with an answer so far:
How can I use pathauto to generate URLs for deeply nested vocabularies? I am generating breadcrumbs from URL arguments as described .  I have a vocabulary that looks like this:  Arts-> Performing-> Dancing-> Ballet  I want my url to look like this: arts/performing/dancing/ballet  Using the pathauto module, I can do this for taxonomy terms:  [term:parent]/[term:name]   Which, on the Ballet page, gives me the following; not what I want:  dancing/ballet    If I use parents instead of parent,  ([term:parents]/[term:name]); this is close but not quite:  arts-performing-dancing/ballet   How can I get from arts-performing-dancing to arts/performing/dancing? Matryoshka words Can anyone tell me how to interpret the 'residuals vs fitted', 'normal q-q', 'scale-location', and  'residuals vs leverage' plots?  I am fitting a binomial GLM, saving it and then plotting it. $C(n,p)$: even or odd? How do I get a mesh data-block with modifiers and shape keys applied in Blender 2.8? I'm trying to update an exporter to work with Blender 2.8 but can't seem to get a mesh data-block modified by modifiers or shape keys. It always gives me the base mesh.  I'm currently using Object.to_mesh(). But reading Object.data or bmesh.from_mesh(obj) all returns only the base mesh. So what is the new function to call for getting a mesh data-block with the modifiers and shape keys applied? In a table of contents that has been generated with LaTeX's \tableofcontents command, I would like to add a vertical space before a Chapter item in the table of contents. One way that I have in my notes is to use  \addtocontents{toc}{\protect\vspace{10pt}}   at a desired location in the document so that this gets processed by \tableofcontents to include an appropriate vertical space in the table of contents. I have two questions:   Is the above the correct way to get a vertical space in a table of contents? Why is it necessary to use the \protect command here?   Thank you... I am a physics Master's student.  I have good grades, with CGPA above 9(/10)(However, all courses in my university are graded on a curve so the actual marks are significantly lower than 90%). This has been my marks throughout my undergraduate and graduate courses and I was happy because this was above average. Also, my summer projects in UG were usually computational and any difficulty I had in theoretical aspects I attributed it to my inexperience in advanced Physics.   However, recently I have started to work on pure theoretical project and while reading for the project I realized that I consistently miss some details from each topic. I understand the general idea, can re-derive most of the equations(with some effort) however when I discuss things with my professor or when I read further topics I realize that I have missed certain key-details. This is exactly similar to the case of me missing a few key questions in my exams and getting that 9 grade point instead of 10(or at-least I think so). I was not worried about this before but now I realize that there is some flaw in the way I study (but I do not know what).   Since I want to apply for Physics PhD I realized that I will need to have solid concepts and it would be best to correct my mistakes but I do not know how or even what could be the reason for my imperfect understanding.  Any direct suggestion would help or even certain general guidelines on what I can do.    Things I've tried recently -   1) I've started to written down almost everything I read. This is slightly laborious but is certainly helping. It also helps me to gloss over the things I read previously when I come back the next day.  2) I completely avoid smartphone when I'm library/study room so that I won't get distracted. Not sure if it helps me solve the above problem but certainly helps me study better in general.  3) I've tried to read the topics from several sources. The books I am reading is somewhat like a collection of research papers and hence does not have a exercises. So I though reading from various sources might help get better ideas but it's not really helping because most other sources are too high level as an introductory text. But this will probably help me in cases where it's practical to do this.  4) Somewhat similar to point (1)- I am trying reread, whenever I can, what I've done until that point. But not sure how much this will help me in filling the gaps. How to make a film in black and white and add color to some objects? How is a movie made to show selective colors. For instance, in  a sister and brother are transported to the universe of an old black and white TV show, and the movie switches to being B&amp;W. Then, as the protagonists cause the inhabitants to have 'real' emotions, like fright, anger, or love, things (people, places, etc.) start having color. In the middle of the movie, many objects are still B&amp;W, yet many more are now colorized.   also used this effect (the whole film was initially shot in full color, and was converted to black-and-white. Colorization is used on certain subjects in a scene), for example.  How is this effect achieved? Is it post-production editing? What techniques might a director employ to do this? How do I install OpenStack? How do I install ? Is there an easier way other than official installation instructions? At some point I accidentally ran off a cliff with my War Horse which resulted in a death. After respawning, I noticed my War Horse was gone and the default Tennessee Walker was my main horse.   How did the War Horse disappear and is it possible to retrieve it? Make window always on top? Some applications do not have the functionality like Task Manager's &quot;Always on top&quot; feature.  Is there a way around this? How do I find the particular solution of this second order inhomogenous differential equation? (Using undetermined coefficients).  $y''-4y'+5y = 4e^{2x} (\sin x)$  I can find the generel homogenous solutions but I need help for the particular. In bash, read after a pipe is not setting values At the end of this nice video (), she says that  is a chain reaction of electric and magnetic fields creating each other so the chain of wave moves forward.  I wonder where the  is in this explanation. What is the relation between electromagnetic wave and photon? Windows registry entries for default explorer view I was wondering if there is a simpler way to find the last to digits of a power such as $3^{45}$. I reduced it modulo 100 to get the answer, which is 43. But I was curious if there was a simpler, or more eloquent way to get this result.  Here's my method:  Using the fact that $3^4=81\equiv -19 \pmod{100}$ and $19^5=2,476,099\equiv -1 \pmod{100}$  $$ 3^{45}\equiv 3(3^4)^{11}\equiv 3(-19)^{11}\equiv 3(-19)(19^5)^2\equiv 3(-19)(-1)^2 \equiv -57 \equiv 43 \pmod {100} $$  I just felt like this was sort of a messy way to find out that the last two digits are 43. MWE for externalize + automatic recompilation after tikz figure modification I have no idea how to prove that the set $\{(x, |x|): x\in\mathbb{R}\}$ is not the image of an immersion of $\mathbb{R}$ into $\mathbb{R}^2$  For example   If $f(t)=(t^3, |t|^3)$ then $f'(0)=(0, 0)$. If $x\sqrt{1+y}+y\sqrt{1+x}=0$ find $y'$ Find $\frac{dy}{dx}$ if $x\sqrt{1+y}+y\sqrt{1+x}=0$ for $-1\leq x\leq 1$   My Attempt $$ x\sqrt{1+y}=-y\sqrt{1+x}\implies x^2(1+y)=y^2(1+x)\implies x^2+x^2y=y^2+xy^2\\ 2x+2xy+x^2\frac{dy}{dx}=2y\frac{dy}{dx}+y^2+2xy\frac{dy}{dx}\\ \frac{dy}{dx}\Big[ x^2-2y-2xy \Big]=y^2-2x-2xy\\ \frac{dy}{dx}=\frac{y^2-2x-2xy}{x^2-2y-2xy} $$ How do I proceed further and find the derivative ? Cannot find Background Images feature to add in a photo in Blender 2.8  Where is it?