I’m a student, my parents and other relatives send me money, but I also have an online clothing store I started this year. Because it’s online and upcoming I haven’t registered it. Should I explain this in my cover letter, incase they notice a deposit that is not in my parents name?
The UK Visas and Immigration Directorate publishes  that provides helpful tips that can result in successful visa applications. Section 2 of this guidance opens is entitled &quot;other documents you may want to provide&quot; (emphasis mine).  Section 2: other documents you may want to provide – all visitors This section provides guidance on the types of documents that you may want to provide to help us consider your application against the Immigration Rules. Previous travel documents/passports, which show previous travel. Financial documents showing that you have sufficient funds available.  These must clearly show that you have access to the funds, such as:  bank statements building society book proof of earnings such as a letter from employer confirming employment details (start date of employment, salary, role, company contact details) where a third party (who is either in the UK or will be legally in the UK at the time of your visit) is providing financial support to you e.g. a business, a friend or a relative, documents to show that they have sufficient resources to support you in addition to themselves and any dependant family should be provided   The first item is &quot;bank statements&quot; and this ties in with the , which says...  evidence that you can support yourself during your trip, eg bank statements or payslips from the last 6 months  (Note 'eg' is a Latin abbreviation meaning &quot;for example&quot;; this appears to be optional rather than a fixed requirement.) Question: How should someone interpret this such that the chances of success are maximized? How many statements should I submit? What are they looking for and what do my bank statements tell about me?
Number of Pairs of Subsets Find the number of Pairs $(A,B)$ of subsets of $[n]$ such that $A ⊆ B$? I just need clarification in my thought process. My professor's wording at times can through me off. I just want to know if I am on the right track. We will have $3$ regions: 1.Outside $B$ 2.Inside $A$ 3. Inside $B$, Outside $A$ I believe the number of pairs is $3^n$ but I am not sure. Any help would be appreciated. Let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove $r \mid \phi(n)$. Let $a \in \mathbb {Z}$, $n &gt; 1$ a natural number with $\gcd(a, n) = 1$, and let $r$ be the smallest positive integer such that $a^r \equiv 1 \bmod{n}$. Prove that $r \mid \phi(n)$.  Euler's generalization of Fermat's Little Theorem: If $n \in \mathbb {N}$ and $m \in \mathbb{Z}$ such that $\gcd(m, n) = 1$, then $m^{\phi(n)} \equiv 1\bmod(n)$.  By Euler's generalization I would have $a^{\phi(n)} \equiv 1\bmod{n}$.  Then I could say $a^r \equiv a^{\phi(n)} \equiv 1 \bmod{n}$. At this point I can see that $r$ clearly must be some multiple of $\phi(n)$.  If I want to show that $r \mid \phi(n)$, then I can show that $\phi(n) = rk$, for some $k \in \mathbb {Z}$.  However, I am a bit stuck about how to make this last step showing that  $\phi(n) = rk$, where $k \in \mathbb {Z}$. How to add a PPA on a server? We want to encrypt / encode URL parameters on our pages. I tried to encrypt a parameter using  with AES algorithm as explained in the   %%[SET @encData=EncryptSymmetric("test", "AES", @null, "1111", @null, "0000000000000000", @null, "00000000000000000000000000000000") ]%% AES: %%=v(@encData)=%%   The result of this function is      AT1r0irnzM+Ax1j8zN+zAw==   Then I tried to decrypt the value using an , but I always received an error message.  I suppose there is a difference between AES algorithm in Marketing Cloud and AES used in the online tool. Indeed if I encrypt the same word with an online tool (128-bit), I received this result      l4Yo3sFofFD1EMmtoh397w==   Do you have any deep information regarding this function? What could be the difference? Adapt BibTeX style to give all initials I'm using a modification of the plainyr BibTeX style. Although my bib-file contains all initials for some authors (e.g. B.D. McKay), I end up with just the first initial in my document (e.g. B. McKay). I thought about editing the BibTeX style myself, but after seeing the code, I decided against it. Maybe there are some people who are more knowledgeable in this area of expertise.  I want my final document to include the initials for all the names, and not just those of the first name.  This is the relevant code of the BibTeX style, or at least, I think it is the relevant code.  FUNCTION {format.names} { 's :=   #1 'nameptr :=   s num.names$ 'numnames :=   numnames 'namesleft :=     { namesleft #0 &gt; }     { s nameptr "{f.~}{vv~}{ll}{, jj}" format.name$ 't :=       nameptr #1 &gt;         { namesleft #1 &gt;             { ", " * t * }             { numnames #2 &gt;                 { "," * }                 'skip$               if$               t "others" =                 { " et~al." * }                 { " and " * t * }               if$             }           if$         }         't       if$       nameptr #1 + 'nameptr :=       namesleft #1 - 'namesleft :=     }   while$ } How to Connect & Share your Internet Connection (Wired & Wireless) I have Ubuntu 12.04 on a HP 430 notebook and this has a single wired internet connection and I would like to share this with a LG Optimus One with Android 2.3.3. I followed  instructions and created a hotspot as shown below, but UbuntuHost is not visible on the LG Optimus One when I enable the Wifi on it.  To summarize, I want my Laptop with an internet connection to act as a WiFi router and access the internet from other devices (LG Optimus One with Android in this case).  What additional steps have to be done? Completely synchronise multiple Macs Can you transit through the Schengen Area without a visa when traveling on separate tickets? I am planning to travel from US to Albania, and when I search on flight ticket websites such that US as origin and Tirana (TIA) as destination, then it costs me $1050 cheapest. However, it costs me $850 when I buy two separate round-trips through Barcelona (US to Barcelona round-trip, Barcelona to Tirana round-trip). I just checked Barcelona, but there might be other transfer airports in Schengen area which costs me even less. I don't need a visa for Albania but I need a visa to go into a Schengen country, so my question is 3-fold:   How can I learn which Europe airports have the international transfer area, so that I don't need a Schengen visa to transfer through the airport? I guess the airlines would take care of that when you buy the tickets together (I already have such an experience multiple times), but given that I will buy them separately, I need to have that information beforehand. The two separate flights I am planning to buy are through different airlines, and in my experience, the airlines check whether the traveler has a visa for the destination country before they let you into the airplane. So, would it be easy to convince the US to Barcelona trip airline that Barcelona is not my final destination, but I have a separate flight from Barcelona to Albania? Are there any Europe airports that have "international baggage claim" areas which are before the passport checkpoint? I mean, if I buy separate flights, do I have any chance to check-in a baggage for the US to Barcelona trip? How to stop creating .DS_Store on Mac? What is the difference between "What are you?" and "Who are you?"? I am often asked "Who are you?" and "What are you?", but I don't know the difference between these two questions.  Please explain it to me. Why do return flight costs vary depending on the country of origin? Local SEO Strategies What are your strategies for local SEO? For example, if you had a web design company in Lincoln, Nebraska, what would you do for your website from an SEO perspective? Finding value of $S-T$ in $2$ binomial sum. If $\displaystyle S=\sum^{n}_{k=0}(-1)^k\frac{1}{k+m+1}\binom{n}{k}$ and f $\displaystyle T=\sum^{m}_{k=0}(-1)^k\frac{1}{k+n+1}\binom{m}{k}$.Then $S-T$ is   Try:$$S=\sum^{n}_{k=0}(-1)^k\int^{1}_{0}x^{k+n}\binom{n}{k}dx=\int^{1}_{0}x^n\sum^{n}_{k=0}(-x)^k\binom{n}{k}dx$$  Could some help me, thanks Can the Force be used to fly? Allow linking to specific revision of revision history showing diff Currently, the only way to link to a revision (clicking "link"), you just get  which shows what the post looked like at that revision:        Personally, I rarely use this and haven't ever found myself in a scenario (as far as I remember) where I would prefer the way it currently works to what I'm suggesting here.  Could we:   Add another link, or Change the current link   Such that it:   Displays the diff on a separate page (I'd prefer this, since the highlight and scroll thing doesn't always work properly - although perhaps it has something to do with loading images, so it might not apply here, or, if it doesn't, we could fix that instead), or          Highlights and scrolls to a diff, like what is done when you link to an answer () $\bigcup \emptyset$ is defined but $\bigcap \emptyset$ is not. Why? Why does $\bigcup \emptyset = \emptyset$ but $\bigcap \emptyset$ is not defined?    If I had to guess, I'd say it's also equal to $\emptyset$. Why didn't the Order of the Phoenix assist with the trio (i.e.  Harry Potter, Ron Weasley and Hermione Granger) in the Horcrux hunt? Why does Ubuntu only support versions for a limited time (and what does it mean)? Matlab filter electical spikes in accelerometric data I attempted a proof of mathematical induction using an arbitrary base case, but was unsuccessful (and hence this question). Below is what I was trying to do and along with my thinking; if anyone can point me in the right direction I'd appreciate it.  The induction I am using: Let $P$ be a property about the natural numbers $\mathbb{N}$ with $0\in\mathbb{N}$, and let $P(n)$ denote the statement that the property $P$ holds for $n\in\mathbb{N}$. Suppose $P(0)$. Furthermore suppose that for each natural number $k$, $P(k)$ implies $P(k+1)$. Then $\forall nP(n)$.  What I am trying to prove: Let $P$ be a property about the natural numbers $\mathbb{N}$ with $0\in\mathbb{N}$, and let $P(n)$ denote the statement that the property $P$ holds for $n\in\mathbb{N}$. Suppose for $n_0\in\mathbb{N}$, $P(n_0)$. Furthermore suppose that for each natural number $k\geq n_0$, $P(k)$ implies $P(k+1)$. Then $\forall n\geq n_0 P(n)$.  My attempted proof: define $Q(n)$ to be $n\geq n_0 \to P(n)$. Then we wish to prove $\forall nQ(n)$. We induct on $n$.  Base case (for ordinary induction): $Q(0)$ is $0\geq n_0\to P(0)$. Since $n_0\in\mathbb{N}$, $0\geq n_0$ implies that $n_0=0$. Since $P(n_0)$, $P(0)$, which proves the base case.  Inductive step: we want to show $\forall n(Q(n)\to Q(n+1))$. To do this, we assume $k\geq n_0 \to P(k)$ and try to show $k+1\geq n_0 \to P(k+1)$.  Since $k\geq n_0 \to P(k)$, we first prove the case where $k\geq n_0$ and $P(k)$. By the hypothesis of the proof, we see that $P(k+1)$, which proves the case for $k+1$.  This is where I am having trouble: For $k&lt;n_0$, I am unable to show the implication for $k+1$.  So my questions would be: (1) is the overall approach for the proof correct? (2) If so, how might I go on to prove the case when $k&lt;n_0$?  Thanks in advance. (This is not homework, by the way.)