What's the difference between them, and I know that their meanings or the same but I don't know how they both are grammatical.      I have no car.   I don't have a car.
Would you please tell me which of the following terms is correct? If both are correct, are they equal?     I have no [...] I don't have any [...]
A question from Kunen's book: chapter VII (H9), about diamond principle I have a Godox X2Tc and a Godox X1Rc. I want to control my Canon Speedlite 430 EXII. (I also have a Godox V1, which is a beautiful thing!) I have the Canon Speedlite attached to the Godox receiver, so it should fire. It just wont! How do I set it up correctly so the receiver makes the Canon Speedlite fire?  Update: Michael C answered this question. I had the ID numbers set differently on the transmitter and receiver. I made them the same and now it all works. Perfect! Thanks Michael!! Better HTTPS support for Stack Exchange sites "Scaled $L^p$ norm" and geometric mean Find an example where Markov's inequality is tight in the following sense: For each positive integer $a$, find a non-negative random variable $X$ such that $P(X\ge a)=E(X)/a$.   How to do this problem, I am really confused. Also, what is the definition of Markov's inequality? How do I time a method's execution in Java? solving diophantine equations using congruences So, a question in Elementary Number Theory by David M. Burton:     Problems 4.4      2(a) Using congruences, solve the diophantine equation 4x + 51y = 9       Hint: $4x \equiv 9(mod \ 51) $ gives $ x = 15 +51t$, whereas $ \ 51y \equiv 9 (mod \ 4)$ gives $y = 3+4s $. Find the relation between $s$ and $t$ From this hint, I substitute $ x = 15 +51t$ and $y = 3+4s$ in the given equation $4x + 51y = 9$ to get the relation $s = -t-1$ and using which I can get the solutions $ x = 15 + 51t, \ y =-1-4t$ But we know that the solutions of $ax \equiv b (mod \ n)$ is equivatent to the solutions of the diophantine equation $ax -ny = b$, so, solutions of $4x \equiv 9(mod \ 51) $ is equivalent to solutions of the equation $4x-51y=9$ whereas, solutions of $51y \equiv 9(mod \ 4) $ is equivalent to solutions of the equation $-4x+51y=9$ Now, my question is: as, the above equations $4x-51y=9$ and $-4x+51y=9$ are different, then what is the point of substituting $ x = 15 +51t$ (solution of $4x-51y=9$) and $y = 3+4s $ (solution of $-4x+51y=9$) in the given equation $4x+51y=9$ to find a relation between $t$ and $s$ ? Isn't it absurd as $ x = 15 +51t$ and $y = 3+4s $ are solutions of two different equations? Can anyone please explain this? PS: I did it like this $4x \equiv 9(mod \ 51) $ gives $ x = 15 +51t$ and by substituting it in $4x+51y=9$ we get $y=-1-4t$ I have the below list of files  aro_tty-mIF-45875564pmo_opt aro_tty-mIF-45875664pmo_opt aro_tty-mIF-45875964pmo_opt aro_tty-mIF-45875514pmo_opt aro_tty-mIF-45875524pmo_opt   that I need to rename to  aro_tty-mImpFRA-45875564pmo_opt aro_tty-mImpFRA-45875664pmo_opt aro_tty-mImpFRA-45875964pmo_opt aro_tty-mImpFRA-45875514pmo_opt aro_tty-mImpFRA-45875524pmo_opt Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$ I have trouble on this question: "Characterize the groups G for which the map $$\iota: G \to G$$ sending $$x \mapsto x^{-1}$$ for all $x \in G$, is an automorphism of $G$." From  post I have seen that $G$ must be abelian. Can anyone propose another characteristic of $G$ that I can derive from the given conditions besides abelian? Thank you so much!! What makes Stealing Signs wrong? Ubuntu 12.04 (Wubi) not starting - root.disk corrupted I have Ubuntu 12.04 installed through Wubi on my laptop. For some reason when i click on Ubuntu on start up (when you have to either select windows or Ubuntu) I get the following screen, the grub cursor keeps flashing.  Gnu grub version 1.99-21 Ubuntu 3.4   Minimal bash-like line editing is supported. For the first word, tab lists possible command completions. Anywhere else tab lists possible device or file completions.   grub&gt;   Could you tell me what I can do to fix this problem and to start Ubuntu normally? Apt "could not find a distribution template" error When I attempt to install anything using apt-get I get the following error:  Traceback (most recent call last):   File "/usr/bin/add-apt-repository", line 60, in &lt;module&gt;     sp = SoftwareProperties()      File "/usr/lib/python2.6/dist-packages/softwareproperties/SoftwareProperties.py", line 90, in __init__     self.reload_sourceslist()   File "/usr/lib/python2.6/dist-packages/softwareproperties/SoftwareProperties.py", line 538, in reload_sourceslist     self.distro.get_sources(self.sourceslist)       File "/usr/lib/python2.6/dist-packages/aptsources/distro.py", line 90, in get_sources     raise NoDistroTemplateException("Error: could not find a " aptsources.distro.NoDistroTemplateException: Error: could not find a distribution template   Any idea what this means and how to resolve it? How to show the full path of a file or directory in the terminal? I need to know how the directory name in order to type it out in the terminal. How do I access the names of directories?   Windows Explorer used to have a title bar with the full path. Can someone please help me figure out how to see the full path of a certain file? New install - no network devices available - Realtek Device b822 I just purchased a Lenovo Yoga 730 15" laptop, and installed Ubuntu 16.04 in place of Windows 10. Install seemingly worked fine, but now I have no wifi device available.  Tried a reinstall just to be sure, and the same issue is happening. I don't believe it to be a hardware issue, as wifi was working without issue on Windows before I wiped it out.  When I run rfkill list I see:  0: ideapad_wlan: Wireless LAN Soft blocked: no Hard blocked: no   But when I run lspci I only see one item in the list claiming to be a network device:  3a:00.0 Network controller: Realtek Semiconductor Co., Ltd. Device b822 (rev ff)   I have a USB wifi adapter and that gets me connected without issue, but obviously that is not the desired solution.  Does anyone have any insight on what might be causing the issue?  Output from modinfo -p rtl8822be:  fix_rate: (int) debug_level: (int) swenc:Set to 1 for software crypto (default 0) (bool) ips:Set to 0 to not use link power save (default 1) (bool) swlps:Set to 1 to use SW control power save (default 0) (bool) fwlps:Set to 1 to use FW control power save (default 1) (bool) msi:Set to 1 to use MSI interrupts mode (default 1) (bool) dma64:Set to 1 to use DMA 64 (default 0) (bool) aspm:Set to 1 to enable ASPM (default 1) (int) debug:Set debug level (0-5) (default 0) debug_mask:Set debug mask (default 0) (ullong) disable_watchdog:Set to 1 to disable the watchdog (default 0) (bool) Given a collection of sets $\mathcal{C}$ and $E$ an element in the $\sigma$-algebra generated by $\mathcal{C}$, how do I show that $\exists$ a countable subcollection $\mathcal{C_0} \subset \mathcal{C}$ such that $E$ is an element of the $\sigma$-algebra, $\mathcal{A}$ generated by $\mathcal{C_0}$?    The hint says to let $H$ be the union of all $\sigma$-algebras generated by countable subsets of $\mathcal{C}$....although I don't know why. Does “gay” still include the meaning “merry”? Dictionary.com lists , with “merry, lively” as the first entry.  Microsoft  for listing  (a real place) as his hometown:   Xbox Live considered the term gay absolutely inappropriate in any context.     As a non-native English speaker, my question is whether in contemporary English, does gay always mean homosexual? Are British and American English the same in this respect? I've had at least one question featured as a "hot network question" and during that time it got thousands of views in the course of a few days. But if you look at that question now you won't have any way of knowing that that's where the bulk of its view count came from.  Is there a way to find out if an arbitrary question has been a "hot network question" or not? How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$? I am trying to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$ but am not able to think something except induction,which is of-course not necessary (I think) here, so I am inquisitive to prove this in a more general way.  The left side of an identity occurs while solving another problem (concerning binomial theorem) so I am more interested in deriving the right side from the left side, else I have to remember it now onward.  EDIT: I am more interested in an algebraic proof rather than combinatorial argument or something involving calculus (however I liked  and  solution), hence I am removing the combinatorics tag. proof relating to limit definition of e I'm studying the book A Primer for the Mathematics of FinancialEngineering, along with it's solution guide. I've ran into trouble with the solution to question 7 in chapter 1.    The problem is:  Show that $(1+\frac{1}{x})^x &lt; e &lt; (1+\frac{1}{x})^{x+1}$ .   Specifically, I'm having trouble with one step in the solution.    It says that  $$x\ln\left(1+\frac{1}{x}\right)&lt;1&lt;(x+1)\ln\left(1+\frac{1}{x}\right)$$  can be written as   $$\frac{1}{x+1} &lt;\ln\left(1+\frac{1}{x}\right)&lt;\frac{1}{x}, \forall \ge 1.$$  How can the first equality (or is it inequality?) be written as the second? $f:\mathbb{R}^3\to\mathbb{R}, f(rx)=r^{\alpha}f(x)$ for some $\alpha&gt;0$, $\forall x\in\mathbb{R}$, for any $r\in\mathbb{R}$, could any one tell me which of the following is true?  $1.$ If $f(x)=f(y)$ whenever $||x||=||y||=\beta&gt;0$, then $f(x)=\beta ||x||^{\alpha}$  $2.$ If $f(x)=f(y)$ whenever $||x||=||y||=1$, then $f(x)= ||x||^{\alpha}$  $3.$ If $f(x)=f(y)$ whenever $||x||=||y||=1$, then $f(x)=c||x||^{\alpha}$ for some constant $c$  $4.$ If $f(x)=f(y)$ whenever $||x||=||y||$, then $f(x)$ must be a constant function. Thank you.