continuous rational value function in R Can there be a continuous non-constant function with only rational values defined on an interval in R?           Or is the whole property meaningless?
Is a rational-valued continuous function $f\colon[0,1]\to\mathbb{R}$ constant? Let $f\colon[0,1]\to\mathbb{R}$ be continuous such that $f(x)\in\mathbb{Q}$ for any $x\in[0,1]$. Intuitively I feel that $f$ is constant, since $\mathbb{Q}$ is dense in $\mathbb{R}$.  How can I formally write this down?
Ideal column width for paragraphs online There is nothing worse than coming across a website with paragraphs that span the width of your screen resolution. They are usually so hard to read, I don't even bother.  A lot of web designers use generic grid and column systems, but I don't feel these have been optimised for readability, they are more of design guide on general aesthetics.  I guess it comes down to words per line. Are the rules that apply to print media the same for screen media?  Are there any type of guidelines to help me size the width of paragraphs on the screen?  I want to take into consideration:   Major web font faces (i.e. Arial, Verdana, Georgia, Times) A range font sizes (i.e. 8px-24px) Space between columns Profile page "activity" tab is broken How to fix very slow Ubuntu booting? How to know if something is a primitive concept, a law, a definition or a theorem Some basic Physics books are often misguiding in the sense that they don't make clear whether something is a primitive concept, a law, a definition or a theorem. This is often a little confusing. I've asked here some moments ago if there's a definition of force, and I've been redirected to a question about whether Newton's Laws are laws or definitions of mass and force.  This is just an example, but there are many others, like for instance, the conservation of energy, which some books present as a theorem, and some places says that this is a law of Physics. Time on the other hand, is something that according to Feynman's lectures on Physics, cannot be defined, so we just say how to measure it and leave it as a primitive concept.  In this context: how in general can we identify whether something is a primitive concept, a fundamental law of Physics, a definition or a theorem? When editing a post and using the image uploader, any unused link references are completely removed.  For example, this post has three image references, only one of which is used ([3]) in the body of the post:        After uploading a fourth image, references [1] and [2] are completely removed (and the remaining references are renumbered to become [1] and [2]):        I sometimes write link references before using them in the body of the post and sometimes remove images temporarily before reinserting them elsewhere in the post so this is inconvenient.  (Note: this also applies for the iOS app, having the same behavior) I get it after updating in Synaptic Manager  I recently did a clean install of Ubuntu 17.04 from 16.10.  error message:-  W: Download is performed unsandboxed as root as file '/var/cache/apt/archives/partial/samba-libs_2%3a4.5.8+dfsg-0ubuntu0.17.04.1_i386.deb' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) Difficulty in creating macro '\newcommand' for the beginning and end of frames in Beamer Do the non-zero eigenvalues of AB and BA have the same algebraic multiplicity (for AB and BA not square)? I know that if A and B are square nxn matrices, then AB and BA have the same characteristic polynomial and thus the same eigenvalues (and same algebraïc multiplicity).   I'm wondering though if this can be generalized: if A is a nxm matrix and B a mxn matrix, then AB is a nxn matrix and BA a mxm matrix.  So my question is: will the eigenvalues of AB and BA, that differ from zero, have the same algebraïc multiplicity? Apache2 restart failed in Ubuntu 16.04 I read this story in the early 2000s, but it was a Chinese translation so the English version could be older.  The beginning is a bit like the Passengers movie: on a spaceship, a man woke up from stasis too early and found that he could not go back to sleep. So he has to spend his whole life on the spaceship, alone.  For some reason (technical or ethical), instead of waking other people up, he created a fantasy adventure story featuring a brave prince as a pastime. He did stories, and drawings all over the inside of the ship. Then he died, not knowing how people are going to respond to his work. How can I make an object follow a path exactly Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$ Why doesn't Neo teleport at random? How can I get my external IP address in a shell script? Working in an enterprise system. We need to determine if everyone needs to update to 10.6 at the same time for mxd cross-compatibility or can we update from 10.5 as needed. Does "apropos" take a preposition? How do you use this word, anyway? Which is more correct:     Apropos of your earlier comment, I decided to....   or      Apropos your earlier comment, I decided to...   Actually, apropos is so fancy a word, even I, a word maven if I do say so myself, am not entirely sure when to use it.  If I may add to my preposition question, are there any constructions where it would be appropriate to use something like with regard to and not apropos? Expanding an event group shows more events than labeled when there are new events A sci-fi book or TV show about a tribesman discovering he or she actually lives in a huge spaceship The story starts with a tribesman going on a exploratory voyage around the land, meeting other progressively more and more distant tribes, learning about the world. Gradually he or she discovers that the "world" is actually a giant spaceship flying through space.  The story climaxes by the hero ascending to the commanding deck and learning who actually pilots the ship and to what purpose. NULL in MySQL (Performance & Storage) What exactly does null do performance and storage (space) wise in MySQL?  For example:  TINYINT: 1 Byte TINYINT w/NULL 1 byte + somehow stores NULL? What is the correct way to pluralize an initialism in which the final word is not pluralized by adding the letter "s"?