Why can't we treat $\text{d}y/\text{d}x$ as a fraction?
Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
How to modify the page at admin/structure/types? Can wizards really cast spells in armor? I am given that $V$ is n-dimensional vector space over $\mathbb{C}$ and $T \in L(V)$. And $T$ has least $m$ distinct nonzero eigenvalues. How do I show that $\text{null}(T^{n-m}) = \text{null}(T^{n-m+1})$?  I'm really not sure how to start here so just the first couple steps would be very helpful. Thanks!! Distance function is continuous in topology induced by the metric The question is (from Topology without tears) that: Let $(X,d)$ be a metric space and $\tau$ the corresponding topology on $X$. Fix $a \in X$. Prove that the map $f:(X,\tau) \rightarrow \mathbb{R}$ defined by $f(x) = d(a,x)$ is continuous.  My first attempt was that let an open ball, $B_{\epsilon}(a)\subset \mathbb{R}$ and show that $f^{-1}(B_{\epsilon}(a)) \subset \tau$. Since $f(x) = d(a,x)$, $f^{-1}(B_{\epsilon}(a))=B_{\epsilon}(a) \in \tau$.   I am pretty sure the last sentence is wrong. I am not sure if every open ball is an open set in topology induced by metric space.  Please give me some hint and direction. Thanks Merging/Joining GeoJSON and JSON? How can we communicate short messages long-distance? In our 5e game, we stole a boat. And a horse carriage. And a lot of other stuff for moving things between cities.   Our DM meant for this to be a way to skip road encounters. We decided to fund a shipping company and hire managers (Knights retainers, etc.) to turn a profit. The DM ruled that these would cover lifestyle expenses, provide us with easy smuggling, etc.   However, we want to keep tabs on the treasure we're moving back and forth.   What can we use for communicating with our managers from anywhere in the world? What about from say, across the city?  We don't need to communicate often or for long - a single round will work. All we need is for the manager to say "we need you back" How to determine equality for two JavaScript objects? A strict equality operator will tell you if two object types are equal. However, is there a way to tell if two objects are equal, much like the hash code value in Java?  Stack Overflow question  is similar to this question, but requires a more academic answer. The scenario above demonstrates why it would be necessary to have one, and I'm wondering if there is any equivalent solution. I can't figure out how to line up the symbols of an itemize environment in beamer with the left part of the main text. In other words, I would like to supress the left margin in beamer itemize lists.  It would be nice if the solution worked with any itemize label defined with  \setbeamertemplate{itemize item}[]   In order to make myself clearer, what beamer produces by default is something like:  Main text. Main text. Main text...    * Item 1    * Item 2    * Item 3    ....   and the desired result is   Main text. Main text. Main text... * Item 1 * Item 2 * Item 3 .... My parents are Indian Citizens. They hold a valid B2 Tourist Visa to USA. I'm planning to book a flight with Hyderabad (India) - Abu Dhabi (UAE) - Dublin (Ireland) - USA. The leg from Hyderabad to Dublin is operated by Etihad and I know there is no problem hopping at Abu Dhabi. The leg from Dublin to US is operated by Aer Lingus. I called Aer Lingus customer care agent told me a transit visa is required to land in Dublin. She did not care to ask for the citizenship of traveller or about the USA visa. I went through Irish immigration website - (), India is not in list of countries that require transit visa. I'm now confused. Can some one confirm if they traveled with the same itinerary recently  Update: I called Aer Lingus again. Another agent told as long as I don't exit the airport, a transit visa is not required. I think these people don't really understand trouble we go through when boarding is denied. I put this question because I read a person was denied boarding earlier - . His case mentions about denied because of different day. But I see his transit time is 12 hours only. I have an Ubuntu machine that I'm using as my home Internet router.  It uses a USB mobile broadband modem as its Internet connection, and shares this with another router (via the router's "Internet" port) which I use as my LAN.  How do I redirect requests from within my LAN for a given URL to a custom IP address (ex have google.com redirect to x.x.x.x)? Remove "Set as desktop background" from Windows context menu Does flying to Panama from the US reset the ESTA time counter? Why does Oracle 9i treat an empty string as NULL? I know that it does consider ' ' as NULL, but that doesn't do much to tell me why this is the case.  As I understand the SQL specifications, ' ' is not the same as NULL -- one is a valid datum, and the other is indicating the absence of that same information.  Feel free to speculate, but please indicate if that's the case.  If there's anyone from Oracle who can comment on it, that'd be fantastic! Can not switch Node.js to a default version of my choice How to interpret a QQ plot I am working with a small dataset (21 observations) and have the following normal QQ plot in R:     Seeing that the plot does not support normality, what could I infer about the underlying distribution? It seems to me that a distribution more skewed to the right would be a better fit, is that right? Also, what other conclusions can we draw from the data? What voltage is a 3-LED light from a LED-TV? I have some "NDV rev1.1 4248 back lights" from a television.   There is a print that sais "94V" on the strip, and on the wire supplying the strips it said "96V".   Every strip has 9x buttons which have 3 LED's in them. So i devided 94 by 9 and figured that every button should have 10.4V roughly, which makes sense, because a white LED is normally 3.5 volts.  I have a 12v Lithium battery which measured 11.1V so i tested one of the LED's with it and it lasted less than one second.   Are the LED's are rated for 10.4V roughly and not more? how to play wav file in python? I am trying to convince my friend that the integral of $0$ is $C$, where $C$ is an arbitrary constant. He can't seem to grasp this concept. Can you guys help me out here? He keeps saying it is $0$. Select first occurring element after another element What command should I use to rotate wood to S,N,W,E,D and U?  I read the entire world edit guide and tried some things but all the results are not satisfactory.