Escaping backtick How can I escape a backtick?  I've tried whatever is written in the "How to Format" rubric that's on the right of the page, but it didn't work: like _so_  I want the backtick to be written in a comment (This is why a code block isn't a solution)  Thank you.  Edit #1 (12:04 UTC):  By using CodeCaster's answer, I've managed to escape a backtick. But a funny thing happens when using the following two examples:  First example:  Code:  `like _so_\``   Result: `like so``  Second Example:  Code:  ``like _so_\`   Result: ``like so`
Backslash escaping in code regions in comments I've noticed that in comments, when you create `code region` with backticks, the backslash will still work as an escape character within that region (but it should not, IMHO).  To clarify:   In comments, `\\` will be rendered as \, but it should be rendered as \\ In the post body itself, `\\` will be rendered as \\ (i.e., correctly)   This is especially confusing when you enter regular expressions into a comment, since backslash-escaping is very common there, and confusion increases if you are dealing with a regex that is double-escaped for representation in a string.   At some point you lose track how many backslashes you must make so the comment renders correctly, or you don't notice fast enough (or at all) and the comment contains wrong code where the same markup in a question or answer would come out as perfectly correct.   It's just that comments can't be corrected anymore after the grace period, leaving you with the choice of either deleting the comment, thus crippling the conversation, or engaging in a trial-and-error game of writing another comment with even more backslashes to explain the issue.  My question is two-fold:   Will this error be corrected? If yes, existing comments should probably be searched and "fixed" by a routine that tries to do the right thing (this is probably somewhere between hard and impossible) Or, can I rest assured that never ever the behavior of the backslash in comments is going to be changed, so I can start working around this issue by hand, knowing that they won't start displaying incorrectly at some point in the future?
How could it possible to factorise $x^8-1$ in product of irreducibles in the rings $(\mathbb{Z}/2\mathbb{Z})[x]$ and $(\mathbb{Z}/3\mathbb{Z})[x]$? How could it possible to factorize $x^8-1$ in product of irreducibles in the rings $(\mathbb{Z}/2\mathbb{Z})[x]$ and $(\mathbb{Z}/3\mathbb{Z})[x]$?  I'm having a hard time starting the problem. Could anyone help me at this point? What does "bad girls go backstage" mean? (sorry for my poor English)  I saw this phrase somewhere but I don't know what this means..     Good girls go to heaven, bad girls go backstage   What means 'bad girls go backstage'?   Maybe.. it's when good girls try to be good, but bad girls become famous?  Am I right? How to install Android Studio on Ubuntu? Tweak showlabels/showkeys - wrap the label Anybody kindly help me to find how to calculate pressure in bar from flow rate. I have a pipe and from that I am transferring water at a constant flow rate of 5ml/min. At this flow rate, with a 0.5 cm diameter pipe, what will be the pressure generated by water? What is the square root of complex number i? Good text on Clinical Trials? I'm an undergraduate statistics student looking for a good treatment of clinical trials analysis. The text should cover the fundamentals of experimental design, blocking, power analysis, latin squares design, and cluster randomization designs, among other topics.   I have an undergraduate knowledge of mathematical statistics and real analysis, but if there's a fantastic text that requires a bit higher level of statistics or analysis, I can work up to it. When I log in with LightDM on my laptop running Debian Unstable, it recently started to hang for around 2 minutes until journalctl shows the message kernel: random: crng init done. When I press random keys on my keyboard while it hangs, it logs in faster (around 10 seconds). Before I didn't have this issue, is there any way I can fix it?  Edit: using linux-image-4.15.0-3-amd64 instead of linux-image-4.16.0-1-amd64 works, but I don't want to use an older kernel. I was reading a textbook. I found that it was mentioned the speed of sound increases with increase in temperature. But sound is a mechanical wave, and it travels faster when molecules are closer.   But an increase in temperature will draw molecules away from each other, and then accordingly the speed of sound should be slower. How is it possible that the speed of sound increases if temperature increases? What is the relation of speed of sound and temperature? How can I automatically name files being exported based on input parameters Image of the set of natural numbers under any function is denumerable. Hi everyone I'd like to know if the following reasoning is correct, any suggestion would be great. Thanks.  Proposition: Let $Y$ be a set and let $f: \mathbb{N}\rightarrow Y$ be a function. Then $f[\mathbb{N}]$ is at most countable.   Proof: If $Y$ is finite the result follows, this is because$f[\mathbb{N}]\subset Y$ and any subset of a finite set  is finite and has at most the size of the set in which is contained.   We may assume  that the set $Y$ is infinite. We set $A:= \{\,n\in\mathbb{N}:f(i)\not=f(n) \,\,\text{ for  any }i&lt; n\, \}$. And we define the function $g:A \rightarrow f[\mathbb{N}]$ as the restriction of $f$ in $A$. We claim that the function $g$ is a bijective map. From the definition of $A$ we already know that the map is $1:1$. We will show that also is onto.   Let $y\in f[\mathbb{N}]$. Suppose for the sake of contradiction that there is no $n\in A$ such that $g(n)=y$. Since $y$ lies in the image of $f$, then there is some $j\in \mathbb{N}$ for which $y=f(j)$. Then either $f(j)\not= f(i)$ for any $i&lt;j$ or there exists some $i&lt;j$ such that $f(j)= f(i)$. For the former, $j$ lies in $A$ (by its definition). For the latter, the set $\{\, n\in \mathbb{N}: f(j)=f(n)\, \text{and }\,n\not=j \}$ is non empty, and hence has a minimum element. Let $m$ be its minimum element. Then $f(m)\not=f(n)$ for any $n&lt;m$ and thus $\,m\in A$ but $g(m)=f(m)= f(j)=y$. Thus any case leads to a contradiction. The result follows by reductio ad absurdum. Hence $f$ is surjective and injective, i.e., a bijective map.   Since there is a bijection between $A$ and the images of the natural numbers under $f$, both have the same cardinality. Also we already know that $A\subset \mathbb{N}$ and any set of the natural numbers is denumerable, thus $f[\mathbb{N}]$ is countable. $\Box$ Cards entering the battlefield simultaneously and "Enter the Battlefield" effects Question:  Show that $n^2 + 3n + 5$ is not divisible by $121$, where $n$ is an integer. multiple regression and multiple comparisons Say I fit a multiple regression of p explanatory variables. The t-test will allow me to check if any single one of those is significant ($H_0: \beta_i = 0$). I can do a partial F-test to check if some subset of them is significant ($H_0: \beta_i=\beta_j=...=\beta_k=0$).  What I often see though is that someone gets 5 p-values from 5 t-tests (assuming they had 5 covariates) and only keeps the ones with a p-value &lt; 0.05. That seems a bit incorrect as there really should be a multiple comparison check no? Is it really fair to say something like $\beta_1$ and $\beta_2$ are significant but $\beta_3$, $\beta_4$ and $\beta_5$ are not?   On a related note, say I run 2 regressions on 2 separate models (different outcome). Does there need to be a multiple comparison check for significant parameters between the two outcomes?  Edit: To differentiate from the similar question, is there any other interpretation to the p-values besides: "B_i is (in)significant, when adjusting for all the other covariates"? It doesn't seem that this interpretation allows me to look at every B_i and drop those less than 0.5 (which is similar to the other post).   It seems to me that a sure fire way to test whether B_i and Y have an a relationship would be to get a correlation coefficient p-value  for each covariate and then do a multcomp (although that would definitely lose signal).  Finally, say I computed the correlation between B1/Y1, B2/Y1 and B3/Y1  (thus three p-values). Unrelatedly, I also did a correlation between T1/Y2, T2/Y2, T3/Y2. I'm assuming the correct Bonferroni adjustment would be 6 for all 6 tests together (rather than 3 for the first group and 3 for the second group - and thus getting 2 "semi"-adjusted p-values). This is a homework problem for my real analysis class. It is problem 13.1 from Mattuck's Introdution to Analysis. The question reads:       Suppose F(x) is continuous on some open interval I and c is a maximum point inside this interval. Is it true that f(x) must be increasing immediately to the left of c and decreasing immediately to the right of c? Proof or counterexample. (Note: A constant function is considered to be both increasing and decreasing.)      My friend and I have been attempting to find a counterexample. We figured a function that begins oscillating infinitely many times near c but converges to c would work. We're having difficulty constructing such a function out of elementary functions so we think we will have to define it in another way, piece-wise using receding intervals. I have no clue how this would look. Any advice would be greatly appreciated. How do I store binary data in ? Let $f: \mathbb R^2 \to \mathbb R$ defined as   $f(x,y)=(x^2+y^2)\sin(\dfrac{1}{\sqrt{x^2+y^2}})$ if $(x,y) \neq (0,0)$, $f(x,y)=(0,0)$ if $(x,y)=(0,0)$  Prove that $f$ is differentiable at $(0,0)$ but that the partial derivatives of $f$ are not continuous at the origin.  The attempt at a solution:  I had some problems at the first part of the exercise:  I've calculated $\dfrac{\partial f}{\partial x}(0,0)$ and $\dfrac{\partial f}{\partial y}(0,0)$, both exist and are equal to $1$.  So, to prove $f$ is differentiable at the origin, I have to show that   $\lim_{(x,y) \to (0,0)} \dfrac{|f(x,y)-(f(0,0)+&lt;\nabla f(0,0),(x,y)&gt;)|}{\|(x,y)\|}=0$ But $\lim_{(x,y) \to (0,0)} \dfrac{|f(x,y)-(f(0,0)+&lt;\nabla f(0,0),(x,y)&gt;)|}{\|(x,y)\|}$ equals  $\lim_{(x,y) \to (0,0)} \dfrac{|(x^2+y^2)\sin(\dfrac{1}{\sqrt{x^2+y^2}})-(x+y)|}{\|(x,y)\|}$. I don't know how to show this limit equals $0$.  For the second part (I've only analyzed $\dfrac{\partial f}{\partial x}$ since both cases are the same), what I did was try to show that $\lim_{(x,y) \to (0,0)} \dfrac{\partial f}{\partial x}(x,y) \neq \dfrac{\partial f}{\partial x}(0,0)$   I thought of considering the curve $\phi(t)=(t,0)$, so   $\lim_{t \to 0} (f\circ \phi)(t)=\lim_{t \to 0} 2t\sin(|t|^{-1})-\dfrac{t\cos(|t|^{-1})}{|t|^{-1}}$. But $\lim_{t \to 0^{+}} \dfrac{t\cos(|t|^{-1})}{|t|^{-1}}=\lim_{t \to 0^{+}} \cos(\dfrac{1}{t})$ and this limit doesn't exist, so the original limit doesn't exist. This shows the partial derivative with respect to $x$ at the point $(0,0)$ is not continuous.   I would appreciate if someone could help me to finish the first part and tell me if what I did in the second part of the problem is correct. Suppose that $f$ is holomorphic on $\mathbb C$ and that $\Re(f(z))\ge 0$ for all $z$. Show that $f$ is constant. [Hint: consider $e^{−f(z)}$.]   My thoughts: If $\Re(f(z))\ge 0 $ holds, then $e^{−f(z)}$ is a bounded holomorphic function (do I need to prove this or is it obvious?) So then by Liouville's Theorem $e^{−f(z)}$ is constant.   But then I'm not sure how to rigorously go from this $\exp(−f(z))$ back to $f(z)$.   Could anyone help me piece this together please?  Thanks Applying for a UK Tourist Visa from outside country of origin Book recommendation on the history of PDE/ODE?