Does there exist any monotone function $f : \Bbb R \longrightarrow \Bbb R$ which takes connected sets to connected sets without being continuous? If the answer is &quot;no&quot; then can we extend this result to arbitrary topological space?
Let $f:\mathbb{R}\to\mathbb{R}$ be a map sending closed intervals to closed intervals. Prove that $f$ is continuous or find a counter example.  WLOG we just have to prove continuity at $0$ and we can also assume that $f(0)=0$ and $f(1)=1$ (by considering $x\mapsto (f(x)-f(0))/(f(1)-f(0))$ ).  I build up this question while thinking of the question .
Can I wield just a shield and use magic? I play a wizard and while I am rarely hit due to being in the back I'm still paranoid I will get hit. So I was wondering if, after getting a feat to wield a shield, I can use that with one hand and use magic with the other? How to use unicode characters in Windows command line? We have a project in Team Foundation Server (TFS) that has a non-English character (š) in it. When trying to script a few build-related things we've stumbled upon a problem - we can't pass the š letter to the command-line tools. The command prompt or what not else messes it up, and the tf.exe utility can't find the specified project.  I've tried different formats for the .bat file (ANSI, UTF-8 with and without ) as well as scripting it in JavaScript (which is Unicode inherently) - but no luck. How do I execute a program and pass it a Unicode command line? My 13 year old daughter says she wants to be a boy. This is out of character for her. Is this a phase? My daughter, 13, has said she wants to be a boy. A little background: we moved to a new state a year and a half ago. In her new school, she felt isolated among her peers until she met a girl in art, and became good friends. She joined the drama club, and made  friends with some 8th graders. They joined “the diversity club”. This club is a LGBT club. The kids put on a play they wrote and starred in, which had homosexual connotations. “Romeo and Juliet”, but script  rewritten to include  2 females as the couple, for instance.   My daughter got so wrapped up in it, that her life was as if she was copying the play. She’s no longer friends with the friend from art, but remains close with the 8th grade crowd. They all labeled themselves. One week, my daughter said she was gay, then, changed to bi, then onto pan. (I had to google that one). Now she is emphatic about being disgusted with her body and wants to be a boy. She wants to donate all the “girly” clothes she picked out last year, and tossed out all the makeup she bought a few months ago.   All her life, she was the classic girly girl. She had crushes on boys, and she and this boy were inseparable since first grade. She was sad when it came time to move away. When we settled here, she became sullen and angry, putting herself down. She now sees a therapist who she really likes. We’ve been working on her self esteem issues. She’s wanting us to call her “he” and by a male name. I can’t do that. She’s my daughter. She is female. Had we seen this coming, maybe I could come to accepting. But it happened out of the blue.  Sometimes the old her comes back-I got a makeup sample and she was interested in trying it, looked at me, then quickly put it down and said “ewww, makeup”—just a few months ago, she bought a bunch. She’s now wanting to wear boys clothes and talks of wearing a suit to her prom. She is very impressionable, and seems affected by viral YouTube videos about kids coming coming out to their mothers, and the mothers gleefully embrace with happy tears. She has told me when she’s 18, she’s having her breasts removed.    Nothing seems normal to me anymore-in terms of how she always was-this new situation just doesn’t fit.  My gut tells me this is a phase.  I’m hoping it’s a phase. But with all I’m seeing in the media about this, I’m not sure. I love her; this is too much for me to process. I’m a stay at home mom; we were inseparable. I knew her. Until now.:(  She cut off all her beautiful hair, and wears boys shorts, baggy tee shirts, and bought this awful men’s deodorant spray. Please help me sort this out. I’m at my wits end.  Do you think this is a phase? Is this common? What does it mean that a package is "set to manually installed?" When packages are already installed and I run an apt-get install &lt;package-name&gt;, sometimes it will print a line &lt;package-name&gt; is set to manually installed.  What does that mean? Pass shell variable as a /pattern/ to awk Having the following in one of my shell functions:  function _process () {   awk -v l="$line" '   BEGIN {p=0}   /'"$1"'/ {p=1}   END{ if(p) print l &gt;&gt; "outfile.txt" }   ' }   , so when called as _process $arg, $arg gets passed as $1, and used as a search pattern. It works this way, because shell expands $1 in place of awk pattern! Also l can be used inside awk program, being declared with -v l="$line". All fine.  Is it possible in same manner give pattern to search as a variable?  Following will not work,  awk -v l="$line" -v search="$pattern" '   BEGIN {p=0}   /search/ {p=1}   END{ if(p) print l &gt;&gt; "outfile.txt" }   '   ,as awk will not interpret /search/ as a variable, but instead literally. When exactly does combat start and surprise take effect? So say I'm going to ambush an orc. I successfully sneak up on him and I attack. The DM determines that the orc is surprised. The orc happens to get an initiative roll of 19, while I get a 10. How would this work? I can only think of two reasonable resolutions to this.   The orc, having a higher initiative, goes first. Since he's surprised, he does nothing. Then it's my turn. If the orc survives my attack, it is now his turn, and being that the orc has already gone through his round of surprise, he can now attack me or whatever, and combat proceeds as normal. I, having started the combat, go first. If the orc survives my attack, but he is surprised, so he does nothing. It is now my turn again, I attack again. If the orc survives my second attack, it is now his turn, and being that the orc has already gone through his round of surprise, he can now attack me or whatever, and combat proceeds as normal.   Which one of these is correct? neither? Does starting combat secure me a turn/action at the start of initiative order like in option 2? If option 1 is correct, could I ready an action to shoot the orc, effectively granting me a similar first attack as in option 2?  Sorry if this makes no sense. Fitting an infinite collection of balls in an infinite dimensional unit ball Given an infinite dimensional normed linear space, how would one show that it is possible to fit an infinite collection of non-overlapping balls of radius $\frac{1}{4}$ in the unit ball?  I guess one can immediately reduce the problem to a normed linear space of countably infinite dimensions. The solution seems clear if the concept of orthogonality exists, but not every normed linear space has an inner product so it's not possible to apply something like Gram-Schmidt to produce an orthogonal basis. Is there any way around this, or there another approach that can be used? Who was the real "Master Code Breaker"? Why does this work: returning C string literal from std::string function and calling c_str() I am trying to copy multiple files named "F3.bam" two level of directories to up and then rename these files with the name of the sub-directory after copy.  For example:  /samples/mydata1/RUN1/ID_date/PCR2/TIME1/F3.bam /samples/mydata2/RUN1/ID2_date4/PCR2/TIME7/F3.bam /samples/mydataxxx/RUN1/IDxxx_datexxx/PCR2/TIMExxx/F3.bam   Expected results:  1. The files are first copied two directories level up:  /samples/mydata1/RUN1/ID_date/F3.bam /samples/mydata2/RUN1/ID2_date4/F3.bam /samples/mydataxxx/RUN1/IDxxx_datexxx/F3.bam   2. The files are renamed according to the name of the current sub-directory:  /samples/mydata1/RUN1/ID_date/ID_date_F3.bam /samples/mydata2/RUN1/ID2_date4/ID2_date4_F3.bam /samples/mydataxxx/RUN1/IDxxx_datexxx/IDxxx_datexxx_F3.bam   Ideally a bash loop would be great (working on a Mac). Cannot get to a new line by hitting Enter I am using a Mac machine.  I asked a question, and then, someone answered it.    I clicked "Edit" to add a comment, and I would like to press Enter to go to a new line, but doing so submitted my comment and ended the edit instead. Adapt Ubuntu to a high-DPI resolution screen How can I adapt Ubuntu to a high resolution display?  I have a display with 3200x1600px on only 11'' and everything looks really tiny. Firstly, I apologise that this question is specific to two polynomials. I understand that this post will not help a lot of people, and for that I am sorry. I will make it up to you all by anwsering lots more questions in the future! However, as my lecturers enjoy time off on the weekend, I am unable to ask this to anyone else who would know what the heck I'm talking about. Sorry if my notation is not widely used, I can elaborate more if required. Please excuse my poor Latex too.  Let:  $B = Y^2 - X^3 + X$, and   $F = (X^2 + Y^2)^3 - 4X^2Y^2$.  I wish to find the intersection number of $B$ and $F$ at $P = (0,0)$  i.e $I(P,F \cap B). $  However, I want to use the following proposition to do this:  If $P$ is simple on $B$ then $I(P,F \cap B) = ord_P^B(F) $.  I will omit proving that $P$ is simple on $B$ as I hope it is clear to see it is.  I know that $I(P,F \cap B) &gt; M_p(F) * M_p(B) = 1 * 4 $, where $M_P(G)$ is the multiplicity of $P$ on $G$.  Now, consider the Image of $X$ and $Y$:  $K[X,Y] \longrightarrow \frac{K[X,Y]}{Y^2 - X^3 + X} \longrightarrow O_P(Y^2 - X^3 + X)$  $X \longrightarrow x$  $Y \longrightarrow y$  Where lower case denotes the image.  Then $ord_P^{Y^2 - X^3 + X}((X^2 + Y^2)^3 - 4X^2Y^2)$  Can be found by substituting $y^2 = x^3 - x$ into $(x^2 + y^2)^3 - 4x^2y^2$  Which gives:  $ord_P^{Y^2 - X^3 + X}(x^9+3x^8 -5x^6 -4x^5 +3x^4 +3x^3)=3$  i.e $I(P,F \cap B) = 3$, a contradiction to  $I(P,F \cap B) &gt; 4$ as above.  The correct answer I know is 6, so where have I gone wrong? Bachelor thesis or Bachelor's thesis Let $f_1 : [-1, 1] \rightarrow \mathbb{R};\: f_1(0) = 0 $ be a continuously differentiable function and $\lambda &gt; 1$. Consider the sequence of functions defined inductively by $f_k(x) := \lambda f_{k-1}\left(\dfrac{x}{\lambda}\right);\: k \geq 2;\: x\in [-1, 1]$. Find the pointwise limit of the sequence of functions $(f_n)$.   I figured out that $f_k(0)=0 \:\forall\: k\implies f_k\rightarrow 0 $ when $ x=0$. Also $f_k$ is continuously differentiable $\forall \:k$.   $\Bigg($Since $\quad\displaystyle\lim_{h\rightarrow0}\dfrac{f_2(x+h)-f_2(x)}{h}=\lambda\lim_{h\rightarrow0}\dfrac{f_1\left(\frac{x+h}{\lambda}\right)-f_1\left(\frac{x}{\lambda}\right)}{h}.\: $Since$ f_1 $is continuously differentiable we see $ f_2 $ is differentiable and its derivative is continuous and hence $f_k$. $\Bigg)$.  Further since $f_1(0)=0$. So I assumed $f_1(x)=x\cdot g(x)$, where $g(x)$ is continuously differentiable and $g(0)\neq0$. Assume $x\neq0,\:f_2(x)=\lambda\cdot\dfrac{x}{\lambda}g\left(\dfrac{x}{\lambda}\right)=x\cdot g\left(\dfrac{x}{\lambda}\right)\implies f_3(x)=x\cdot g\left(\dfrac{x}{\lambda^2}\right)$ $\implies f_k(x)=x\cdot g\left(\dfrac{x}{\lambda^{k-1}}\right)$.   So taking limit as $k\rightarrow \infty$, we get $\displaystyle \lim_{k\rightarrow\infty}f_k(x)=x\cdot g(0)$. Now I am not sure how to proceed or whether there is something wrong here. Please provide hints or suggestions.  $\rule{17cm}{1pt}$  To sum up (using the arguments made by $\textbf{zhw}$ and $\textbf{Paul Frost}$)  When $\displaystyle x\neq0, \lim_{n\rightarrow\infty}f_{n+1}(x) = \lim_{n\rightarrow\infty}x\,\frac{f_1(x/\lambda^n)}{x/\lambda^n} = \lim_{n\rightarrow\infty}x\,\frac{f_1(x/\lambda^n)-f_1(0)}{x/\lambda^n}=x\:f'(0).$ Thus  $$f_n\rightarrow\begin{cases}0&amp;x=0\\x\:f'_1(0) &amp;x\neq0\end{cases}=f $$ I have the amulet of Mara but when I go to talk to maramal about a wedding nothing shows up. WHY is that. I'm looking for the title of a short story by Ursula Le Guin about a scientist (?) who is given a drug that slows the timescale of his perception enormously, so that he can perceive that an alien (?) forest is actually behaving as a sentient being, reacting to current events, but at an enormously slow (from a normal human point of view) timescale. It might be in , but I don't remember the title (and it doesn't jump out at me from the list of titles) and don't have access to that collection right now. It is not &quot;The Word for World is Forest&quot;, nor &quot;Direction of the Road&quot; (from ), nor &quot;Vaster than Empires and More Slow&quot;, the latter two of which look at similar plant perception/time-scale issues. Update: it turns out that the description was right, but I had most of the details wrong: not Le Guin, not alien, not a scientist ... Documents required by Indian citizens wishing to travel to Nepal I'm a citizen of India and I'm travelling to Nepal by air. Is an Aadhaar Card a valid document used for travelling to Nepal by air? Word for a task which is flawed or doomed to failure but which you have to do anyway? How to process a multi column text file to get another multi column text file? I have a text file:  a   aa  aaa     b   bb  bbb     c   cc  ccc d   dd  ddd     e   ee  eee     f   ff  fff g   gg  ggg     h   hh  hhh     i   ii  iii j   jj  jjj   How can I process it and get a 2 column file like this:  a   aa aaa b bb  bbb c   cc ccc d dd  ddd e   ee eee f ff  fff g   gg ggg h hh  hhh i   ii iii j jj  jjj   Or a three column file like this:  a   aa  aaa b   bb  bbb c   cc  ccc d   dd  ddd e   ee  eee f   ff  fff g   gg  ggg h   hh  hhh i   ii  iii j   jj  jj   I prefer to get awk solution but other solutions are welcomed too.