The vowels &quot;æ&quot; and &quot;a&quot; sound the same to me. For example: &quot;æ&quot; is used in words like &quot;cat&quot; or &quot;hat&quot; &quot;a&quot; is used in words like &quot;now&quot; or &quot;round&quot; It looks like &quot;a&quot; is only used in diphthongs. However, in American English they sound to me exactly the same to me. Does anyone know the difference?
I don't quite understand the difference between /a/ and /æ/. Google gives the transcription for 'add' as /ad/, while Wiktionary returns /æd/.  Are these sounds actually distinct or is this just two different ways of writing the same one?
Why was "An Update to our Community and an Apology" deleted? Recently, Sara Chipps posted her message . After reading it, I wanted to compare it with . It turns out that she deleted it. Does anyone know why? It looks strange since (as far as remember) it was a sort of official position of SE. Why would such a statement be deleted? Algebraic Property inherited by a "lift"? Suppose $K$ is a field, and $K\subset E$ is an algebraic extension, and $K\subset F$ is any extension.  Suppose that $L$ is some field which contains both $F$ and $E$ as subfields.  I want to show that $FE$ (the smallest subfield of $L$ containing both $F$ and $E$) is algebraic over $F$.  Lang mentions that the result is true because an element remains algebraic under lifting, but I can't prove the claim with this.  I interpret his comment to mean that if $x\in E$ is algebraic over $K$, then $x\in FE$ is algebraic over $F$.  This is certainly true.    But this doesn't seem enough if I start with any element of $FE$. Low-RAM Linux Distro Specifically for serving static sites I'm looking for a near-zero-configuration linux distro that is designed specifically for serving static web sites and nothing else on a low-RAM machine (I'm planning on 128MB, but the option of less would be nice).  Any ideas of a linux distro specifically tuned for serving static sites in a small footprint? Set the maximum character length of a UITextField How can I set the maximum amount of characters in a UITextField on the iPhone SDK when I load up a UIView? Is Thomae's function Riemann integrable? Let $\displaystyle f: [0,1] \rightarrow \mathbb{R}$ given by   $$f(x) = \begin{cases} 0 &amp; x \notin \mathbb{Q} \\ \\ 0 &amp; x = 0 \\ \\ \frac{1}{q_x} &amp; x = \frac{p_x}{q_x} \in \mathbb{Q} \backslash \{0\}, \ p_x \in \mathbb{Z}, \  q_x \in \mathbb{N}, \ \text{gcd}(|p_x|, q_x) = 1 \end{cases}$$  Is $\displaystyle f$ Riemann integrable?  I am trying to use the equivalent statements $\displaystyle g:[a,b] \rightarrow \mathbb{R}$ is Riemann integrable and $\displaystyle \forall \epsilon &gt;0 \ \exists$ step functions $\displaystyle \rho, \psi$ with $\displaystyle \rho \leq g \leq \psi$ such that $\displaystyle \int_a^b (\psi - \rho) \leq \epsilon$.  I guess that means I would have to somehow show that given $\displaystyle \epsilon$, there exists only a finite amount of $\displaystyle x \in [0,1]$ with $\displaystyle f(x) \geq \epsilon$?   Is it recommended that I consider something else instead? If not, how should I do this? Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic I'm reading a book about abstract algebra, but I'm having trouble solving this excercise: "Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic"  Where $(\mathbb{Q}^*,\cdot)$ is the group of nonzero rational numbers under multiplication and $(\mathbb{R}^*,\cdot)$ is the group of nonzero real numbers under multiplication.    Here is my attempt for the first.  Suppose $(\mathbb{Q}^*,\cdot)$ is cyclic, then $\mathbb{Q}^*=\langle\frac{p}{q}\rangle=\{(\frac{p}{q})^n,n\in\mathbb{Z}\}$, where $p$ and $q$ are coprime.  $\frac{2p}{q}$ is also in $\mathbb{Q}^*$ so it must be equal to $(\frac{p}{q})^n$ for some $n\in\mathbb{Z}$.  To solve $\frac{2p}{q}=(\frac{p}{q})^n$, I take a logarithm of both sides and end up with $1+\log_\frac{p}{q}(2)=n$, since $n$ is an integer $\log_\frac{p}{q}(2)$ must be an integer too, but it is possible only when $\frac{p}{q}=2^{\frac{1}{k}}, k\in\mathbb{N}$, (i.e. $\frac{p}{q}$ is a k-th root of $2$), but $k$ must be $1$ for $2^\frac{1}{k}$ to be rational so $\frac{p}{q}=2$ contradicting the hypothesis of $p$ and $q$ being coprime.    However I don't know whether this is a proper proof and the same reasoning cannot be applied to $\mathbb{R}^*$, I'd like you to just give me an hint towards a proof, without telling me the whole proof, if possible. grub2 wont load Ubuntu on dual boot Having an issue with a dual boot setup that is being run from Windows boot manager. I can successfully load into grub2 from Windows boot manager, however it seems that grub2 cannot locate to the Kernel or something, as it is dropping me right into a shell with the following output:  [ Minimal BASH-like line editing is suported. For the First word, TAB list the posible command completion. Anywhere else tab list the posible completions of a device/filename,]  grub&gt;   I have used Easybcd in the past and successfully loaded a Linux grub through Windows bootloader, but this was when both operating systems were on the same partition, but since my OS installationd are now on separate partitions it seems EasyBcd cant work its magic.   ONe encouragement is that I was able to get Easybcd to load a working Grub if I used the Neo grub bootloader and edit the confg with:  title Ubuntu 14.04 find --set-root /boot/vmlinuz-3.19.0-61-generic kernel /boot/vmlinuz-3.19.0-61-generic ro root=/dev/sdc initrd /boot/initrd.img-3.19.0-61-generic   however this loads in Grub4DOS which is very slow, and as of today this method stopped working See  for details).  Here is the output of EasyBcd Settings for all the different methods I have tried for the Ubuntu 14.04 installation:  Default: Windows 7 Timeout: 30 seconds Boot Drive: C:\  Entry #1 Name: Windows 7 BCD ID: {current} Drive: C:\ Bootloader Path: \Windows\system32\winload.exe  Entry #2 Name: Ubuntu 14.04 Legacy BCD ID: {a4f127cf-3150-11e6-8aaf-408d5cb9e442} Drive: C:\ Bootloader Path: \NST\nst_linux.mbr  Entry #3 Name: Ubuntu 14.04 Grub2 BCD ID: {a4f127d0-3150-11e6-8aaf-408d5cb9e442} Drive: C:\ Bootloader Path: \NST\AutoNeoGrub0.mbr  Entry #4 Name: Ubuntu Neo Grub BCD ID: {a4f127d1-3150-11e6-8aaf-408d5cb9e442} Drive: C:\ Bootloader Path: \NST\NeoGrub.mbr   *It seems that none of the paths seen above are pointing to my dev/sdc2/ partition which would be considered DISK1 on my Windows Volume manager.     EDIT - In the confusion of attempting to get a working bootmanager for Ubuntu/Windows, you will see that grub and Windows Boot manager have all been installed in numerous locations. Below are the present locations and contents of all bootmanager &amp; Grub installations:  dev/sdb Windows7 drive  /dev/sdb1 - 512 MB fat32 partition which is currently empty  /dev/sdb2 - 110 GB ntfs partition containing Windows7 installation. This partition contains a 'Boot' folder which contains BCD files and a whole wack of langauage folders. THIS IS The FOLDER THAT WINDOWS BOOTLOADER uses.  /dev/sdb4 - 121.53 ntfs partition containing storage for media    dev/sdd - Ubuntu Drive  dev/sdd1 - 512 MB partition containing a 'EFI' folder, inside of which are two folders 'grub' and 'Ubuntu', both of which contain the exact same files (grub.cfg, grubx64.efi, MokManager.efi, shium64.efi)  dev/sdd2 - 48.83 GB ext4 partition that contains the '/' folder and Ubuntu instalation.   dev/sdd3 - 69.91 GB ntfs partition containing storage for media  what do I need to do so that the Grub shell I am being dropped into will load up Ubuntu? HOw can I get this machine to dual boot out of Grub? How to justify the definition of summation $s_n=\sum_{i=1}^n a_i=a_1+\cdots+a_n$? I read  and found that they define summation via recursion, so I decided to formalize the proof that that this definition is actually valid. I've two questions:   Does my proof contain any error? Are there other simple ways to define summation?   Thank you so much!     Suppose that $(a_1,\cdots,a_n)$ is a finite sequence in $\mathbb N$. Show that there is a sequence $(s_1,\cdots,s_n)$ such that $s_1=a_1$ and $s_{i+1}=s_i+a_{i+1}$ for all $1\leq i&lt;n$.   My attempt:  We define mapping $f$ as follows: $f: \mathbb N\times\mathbb N\to\mathbb N\times\mathbb N: (i,a)\mapsto\begin{cases} (i+1,a+a_{i+1})&amp;\text{if }i&lt;n\\ (i+1,a)&amp;\text{if }i\geq n \end{cases}$  By recursion theorem, there is a unique sequence $(p_i\mid i\in\mathbb N)$ such that $p_0=(1,a_1)$ and $p_{i+1}=f(p_i)$. Let $\pi:\mathbb N\times\mathbb N\to\mathbb N$ be the projection to the second co-ordinate i.e. $\pi(i,a)=a$. Let $s_i=\pi(p_i)$ for all $1\leq i\leq n$, then $(s_i\mid 1\leq i\leq n)$ is the required sequence. It's clear from the definition of $s_i$ that $s_{i+1}=s_i+a_{i+1}$ for all $1\leq i&lt;n$. [Salutations]  (check one)  [ ] Well trained professional, [ ] Casual reader, [ ] Hapless wanderer,   I have a (check all that apply)  [ ] query [ ] stored procedure [ ] database thing maybe     that was running fine (if applicable)   [ ] yesterday [ ] in recent memory [ ] at some point    but is suddenly slower now.  I've already checked to make sure it's not being blocked, and that it's not the victim of some long running maintenance task, report, or other out of band process.  What is the problem, what should I do, and what information can I provide to get some help?  [*Insert appropriate closing remarks*] How to insert strings containing slashes with sed? How to stop the Facebook app from updating itself automatically? I have the Facebook app installed on my Android 7 phone.   Auto-update is disabled for all applications on my Play Store account I have disabled installation from unknown sources   For some reason, whenever there is an update of the Facebook app, it automatically updates itself even though I disabled auto-updates for all applications.  How to stop the Facebook app from updating itself automatically? What governor limits impact Apex Describe methods? Always wanting more , of anything, never has enough,never contented with what they have Invoking JavaScript code in an iframe from the parent page Undefined reference error for template method Why is $5^{n+1}+2\cdot 3^n+1$ a multiple of $8$ for every natural number $n$? Right place to ask a "discussion" question (I'm setting up a blog, what should....) When is the expected stable release date of Ubuntu Phone and Ubuntu Tablet? Is there an expected stable release date of Ubuntu Phone and Ubuntu Tablet?  If so, what are their dates? Grammatically, what is "It" in the following sentence? I'm currently working at a private academy in Korea, and my boss just asked me a real head-scratcher.   In the sentence:     It doesn't have to be hot and humid for players to lose too much water from their bodies.    I'm aware that "It" is a subject pronoun replacing "The weather." Besides that, however, I'm unsure.   Is it a false subject? I wouldn't think so since it's a pronoun. Is it some crazy kind of indirect object?  Anyway, thank you all for your help! i just finished updating my Macbook pro to macOS Catalina and after the installation finished i got this error message that keeps reappearing. i do not know or have a file named "qnmqkmkrqwfq" (i tried searching for it) and when i press show in finder or ok it disappears for a second and then pops up again for no reason and i am not trying to open any files or apps. i searched and the only solution i found was setting "Allow applications downloaded from: Anywhere" but it did not work. Please Help.