Multiple Bank statement While applying for a UK Visa in Nigeria with my wife and kid, can we submit 4 bank statements? One of the statements is our joint business account, the second is my salary account from my part-time job, the 3rd statement is my personal and other contract job and the 4th is my wife's personal account. I hope it's okay if I submit them all since we receive money from all of them.
Should I submit bank statements when applying for a UK Visa? What do they say about me? 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?
Find the supremum of the following set Find the supremum of the following set:  $$A:=\left\{{(n-1)\over(2n+3)} : n \in\mathbb{N}\right\}$$  So I have as my answer that $\sup(A) = \frac12$ but need to justify. We were taught to justify in two steps, first show our answer is an upper bound for the set then show it is a least upper bound.   For step $1$: if $a$ is a member of $A$ then $a = (n-1)/(2n+3)$ for some natural number $n$ and $\frac{n-1}{2n+3} \leq \frac{n}{2n} = \frac12$ so $\frac12$ is an upper bound for the set  Step 2 is where I am uncertain. I think I need to show that for any $y&lt;\frac12$ there exists a member of the set between $y$ and $\frac12$ but not sure how to do this. Thanks for all the answers so far! I'm studying measure theory and two question came to my mind:        If $f:\mathbb{R}\to\mathbb{R}$ is monotone and $B\subseteq\mathbb{R}$ is borel, is the image $f(B)$ borel?   If $f:\mathbb{R}\to\mathbb{R}$ is a monotone function (say, non-decreasing), does there exist a sequence of continuous functions $f_n:\mathbb{R}\to\mathbb{R}$ converging pointwise to $f$?      Here's the motivation for those questions: Let $(X,M)$ and $(Y,N)$ be measure spaces.   It's known that if $\mu$ is a measure on $(X,M)$ and $f:X\to Y$ is measure, then we have the pushforward measure $f_*\mu(A)=\mu(f^{-1}(A))$ on $(Y,N)$. What if we were to define a "pullback measure"? Given a function $f:X\to Y$ such that $f(M)\subseteq N$ (i.e. $f$ maps measurable sets to measurable sets) and a measure $\nu$ on $N$, the natural formula would be $f^*\nu(A)=\nu(f(A))$. So we ask if is there a good amount of functions which map measurable sets to measurable sets in $\mathbb{R}$, and monotone functions seem like good candidates (for strictly monotone, continuous functions, the result is valid and there are several answers on the web). If this were true, maybe we could use some convergence argument to solve the problem above. Ubuntu 20.04 interface font too small after restart, even with high scaling factor What security systems and processes are in place to prevent malicious third parties from hacking/compromising the security of code in the Debian mirrors, or to verify that the packages we get are in fact the ones the maintainers think they are? where does lspci gather its information from? In  I found "[The   latest   version    of   this   document   ". There I says: "… lspci is a synonym for cat /proc/pci".  Which isn't the case here, on a Crunchbang 10 system (Debian based). No such directory. I do get the basic idea and, as far as I  know, the content of proc is (mainly) created during runtime. (Wrong?). This made me curious:  Question: Where does lspci gather it's information from? And where is this documented? (Where did I miss something?)  &nbsp; Another difference I found: In kernel.org's documentation, under "Table 1-5: Kernel info in /proc"      pci &nbsp;&nbsp;&nbsp; Deprecated info of PCI bus (new way -> /proc/bus/pci/, decoupled by `lspci) Do Skyrim mods work with the Special Edition? I typically play Skyrim with a number of mods installed, and while I'm excited to try the Special Edition, there are a few mods that I'd much rather not play without.  Can I install mods built for the normal Skyrim game with the Special Edition, or do I have to wait until mod authors write new versions before I can play with those mods? When you pick up items in Skyrim it tells you the value of each item. However when I go and sell the items the merchants are only paying 30% of this value, at best.  Discounting any perks or other effects, how high does Speechcraft have to be before merchants start paying full value for items? Literal &#39; appears in flag panel instead of being escaped Two homologous but not homotopic loops on a closed surface of genus greater than one Suppose $S$ is a closed surface with genus greater than $1$. Give an example of two loops on $S$ which are not homotopic, but are homologous to each other.   I need help solving this question. I have read the Wikipedia page on it and I realize that it does not contain the necessary knowledge to visualize this problem.  And I was also wondering the relation between the fundamental group $\pi_1(S)$ and the first homology group $H_1(S)$? Some restrictions is that $S$ is a closed surface and the genus is greater than $1$. Let $A$ be an $n \times n$ matrix with real enteries. Define $\langle x,y\rangle_A = \langle Ax,Ay\rangle, \quad x,y \in \mathbb R^n$ , where $\langle,\rangle$ is a standard inner product on $\mathbb R^n$. Then  $\langle x,y\rangle_A$ is an inner product iff  1)  $\ker A = \{0\}$.  2) $\operatorname{rank} A= n$.  3) all eigenvalues of $A$ are positive.  4) all eigen value of $A$ are non negative.  Clearly if $\ker A \neq \{0\}$, then there exist $x \neq 0$ such that $Ax =0$, then $\langle Ax, Ax\rangle_A = 0$, then $\langle ,\rangle_A$ is not inner product, so $\ker A = \{0\}$, thus rank of $A$ is $n$.  I am unable to check the 3) and 4) option. Please help to check the other option. Thank you Pre-1972 sci-fi short story or novel: alien(?) tunnel where people try new moves and get destroyed if they're not the correct ones How do I find out which paths my (La)TeX installation checks looking for packages (on a Linux system)? I know that I can check from where one particular package would be called, using  kpsewhich &lt;packagename&gt;.sty   and that if I want a custom package, I usually have to put it in the same folder as my document.   I assume that similar to a $PATH, LaTeX checks a list of paths in an attempt to find my package.   Which paths are those? In what order are they checked? If this is system-specific, how can I find out the configuration for my system?   Related questions:    , the answers to which contain some paths that  LaTeX apparently checks.  mentions    &gt;    /usr/local/texlive/2009/texmf &gt;    /usr/local/texlive/2009/texmf-dist &gt;    /usr/local/texlive/texmf-local &gt; &gt; as well as other directories.   (Neither of those lists is complete). How can I stand on the ground? EM or/and Pauli? There is this famous example about the order difference between gravitational force and EM force. All the gravitational force of Earth is just countered by the electromagnetic force between the electrons on the surface of my feet and the ground.  But also wave-function of electrons(fermions) do not overlap each other due to Pauli exclusion principle.  So which one is the true reason of me not flopping inside the earth forever? Is it only one of them(my guess is Pauli exclusion) or is it both? How do I install Java? How do I install Java, including in my browser, so websites with Java work? ShareLaTeX compilation flags Is it possible and if so how can you pass flags to the ShareLaTeX compiler which one would have passed as parameters to the LaTeX compiler?  I am using the minted package and need to pass the -shell-escape flag. How to compress entire drive C in Windows including locked files? Does an uncountable discrete subspace of the reals exist? Does an uncountable and discrete subspace of the reals exist? I have a failure to transfer my game from one HDD to another, and one PC to another. I copied the entire Skyrim folder from one HDD to another. And told where to find it also. Steam did a huge check of my HDD.  But it ended up downloading most of the files anyway. It took a week to download Dawnguard, Hearthfire, and Dragonborn files along with my Hi-Res textures.  I did ask about it in chat. But I feel this could help me or somebody else.  This is the screen I am looking at after transferring my entire hard drive to to new one. Steam downloaded my games, including Skyrim even though my Skyrim data folder had all the data files for Dawnguard, Hearthfire, Hi-Res and Dragonborn.  I have my copied files and have got rid of everything not steam related. I just have my DLCs and they include my hires files.  This is what it looks like.    But I still get this :     What could be causing this? How can I rectify? And in future when one is migrating to a new PC, how can this be avoided?  EDIT::::::::::::::::: Removed everything : Here is how it looks :  Still the prompt as before Steam Error 15  (Side Note : I transferred all my Origin games just by copy/pasting. This really is not nice.)    EDIT 2 :::::::::::::::::::::  And one more EDIT  I tried getting game cache up to speed, but this is prompt I am getting. But I played the game, it was working, I could pick out my character and all, and escape from Helgen.  EDITED 3 :::::::::::::::::  How does one transfer a Steam game? A game that is heavily modded, will the backup a Steam Game option suffice? Why does main method in Java always need arguments? I'm far from being a physics expert and figured this would be a good place to ask a beginner question that has been confusing me for some time.  According to Galileo, two bodies of different masses, dropped from the same height, will touch the floor at the same time in the absence of air resistance.  BUT Newton's second law states that $a = F/m$, with $a$ the acceleration of a particle, $m$ its mass and $F$ the sum of forces applied to it.  I understand that acceleration represents a variation of velocity and velocity represents a variation of position. I don't comprehend why the mass, which is seemingly affecting the acceleration, does not affect the "time of impact".  Can someone explain this to me? I feel pretty dumb right now :)