Is there a bijection from $[0,1)$ to $\mathbb R ?$
How to define a bijection between $(0,1)$ and $(0,1]$?
Changing a Part of a variable within ParallelDo Finding determinant of matrix without expanding show that determinant $$\left|\matrix{ x^2+L  &amp;  xy   &amp;   xz \\ xy   &amp;    y^2+L &amp;   yz \\ xz   &amp;    yz   &amp;   z^2+L \\ }\right| =  L^2(x^2+y^2+z^2+L)$$  without expanding by using the appropriate properties of determinant.  All i can do is LHS  $$x^2y^2z^2\left|\matrix{ 1+L/x^2  &amp; 1  &amp;   1 \\ 1   &amp;   1+L/y^2 &amp;   1 \\ 1  &amp;    1   &amp;   1+L/z^2 \\ }\right|$$ Semigroup analogue to the classification of finite simple groups? Is there a semigroup analogue to the classification of finite simple groups?  If so what are some of the major results?  --Edit, reference links--- call function declared below Is it possible to call a function which is declared below in bash?  Example  if [ "$input" = "yes" ]; then     YES_FUNCTION elif [ "$input" = "no" ]; then     NO_FUNCTION else     exit 0; fi  YES_FUNCTION() {   .....   ..... }  NO_FUNCTION() {   .....   ..... } Which is correct?     Everyone were convinced that he would go to the game.   Everyone was convinced that he would go to the game.   I think it's "was", because "everyone" is singular, but I just wanted to check. A map is continuous if and only if for every set, the image of closure is contained in the closure of image As a part of self study, I am trying to prove the following statement:  Suppose $X$ and $Y$ are topological spaces and $f: X \rightarrow Y$ is a map. Then $f$ is continuous if and only if $f(\overline{A})\subseteq \overline{f(A)}$, where $\overline{A}$ denotes the closure of an arbitrary set $A$.   Assuming $f$ is continuous, the result is almost immediate. Perhaps I am missing something obvious, but I have not been able to make progress on the other direction. Could anyone give me a hint which might illuminate the problem for me? Why does a RegExp with global flag give wrong results? I am running linear regression models and wondering what the conditions are for removing the intercept term.   In comparing results from two different regressions where one has the intercept and the other does not, I notice that the $R^2$ of the function without the intercept is much higher. Are there certain conditions or assumptions I should be following to make sure the removal of the intercept term is valid? Fire Adaptive Domain rendering like a solid cube When I render I see a solid cube which is Adaptive domain. But it shouldn't show up. I feel like I missed something. It is my first time simulating fire.  Candle with a solid domain blocking the fire    The material seems to be plugged in to the volume already :/  Node setup Book recommendation on the history of PDE/ODE? I have several files with the same base filename. I'd like to remove all but one  foo.org #keep foo.tex #delete foo.fls #delete foo.bib #delete etc   If I didn't need to keep one, I know I could use rm foo.*.    demonstrates ^ to negate a match. Through trial and error, I was able to find that  rm foo.*[^org]   does what I need, but I don't really understand the syntax.   Also, while not a limitation in my use case, I think this pattern also ignores foo.o and foo.or. How does this pattern work, and what would a glob that ignores only foo.org look like? Suppose $R$ is a ring and every prime ideal of $R$ is also a maximal ideal of $R$. Then what can we say about the ring $R$? Capturing Blue Screen of Death (BSOD) screen Possible Duplicate:          Sometimes I get a BSOD screen for a split second and I have no chance to see the cause of it. It also happens when I am not at the computer. The event log doesn't have enough information. Is there a way or tool that captures the screen when it happens so I can look at the cause later.  I already did a memory diagnostics test so that's not the problem. I would like to align the view straight on to a face, perpendicular to the normal. How do I align the 3D viewport to the face of a mesh? Are there rules about using "that" to join two clauses? He will understand that I was not joking.   He will understand I was not joking.  Which of the sentences is correct? Are there any specific rules about the use of &quot;that&quot; in the sentences I reported as example? svmono template and `\mathcal` Why, with Springer's  svmono template, do the letters written with the \mathcal font change? It seems that \mathcal becomes \mathscr.  Edit: Look at this image:    With the svmono template \mathcal returns the first alphabet and not the (classical) latter.  Here the packages I use in my document:  \documentclass[envcountsame,envcountchap]{svmono}  \usepackage{subfiles} \usepackage[utf8]{inputenc}  \usepackage{mathptmx} \usepackage[bottom]{footmisc} \usepackage{microtype} \usepackage{stmaryrd}    \usepackage{amsmath} \usepackage{courier} \usepackage{mathrsfs}  \usepackage{amssymb}  \usepackage[all,cmtip]{xy} \usepackage{faktor} \usepackage{graphicx} \usepackage{mathdots} \usepackage[colorlinks={true},linkcolor={blue},citecolor={blue}]{hyperref} \usepackage[frame,width=15truecm,height=23.5truecm,center]{crop}   With this settings I have the above strange behavior of \mathcal. Suppose that $a_1,a_2, \cdots, a_n$ are $n$ different integers. Then $[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$.   I've no idea why it is true. Thanks very much. Why do birds sitting on electric wires not get shocked? When we touch electric wires, we get shocked. Why don't birds sitting on electric wires not get shocked? Individual Phase shift provided by Op-Amp in Closed loop configuration I have a framed picture about two feet by three feet in size that weighs about one pound (not a sheet of paper). I want to hang it onto a wall that is of full-blown hard concrete and covered with paper wallpaper (not vinyl - just paper).  The default way would be to drill the concrete and insert an anchor but that would damage the wall surface.  Is there a way to hang such picture onto such wall without damaging the wall?