I paid my CC bill last Friday morning. The payment appeared in my CC account that same day. But now, 3 days later, the money still hasn't left my checking account (which is in a different bank).  I did verify that I used that checking account for payment. I also checked that the transaction is not marked as "pending". Should I call the bank, or should I wait? Both banks mentioned are in the U.S.
Based on , I figured that there might be multiple questions for distinct locales. Why do the most common transactions to or from bank accounts in the US require waiting one or more days before they are completed? In the information age, it seems like we should be able to transfer money instantly (or nearly so).
If $x_1 = 3$, $x_{n+1} = \frac{1}{4-x_n}$ for $n \geq 1$, prove the sequence is bounded below by $0$, above by $4$. If $x_1 = 3$, $x_{n+1} = \dfrac{1}{4-x_n}$ for $n \geq 1$, prove the sequence is decreasing and bounded below by $0$, above by $4$.  Want to show: $0 &lt; x_{n+1} &lt; x_n &lt; 4$  I decided to do the bounded part first.    Base Case, $n=1$  $0 &lt; 3 &lt; 4$ [works]  IH  Suppose $0 &lt; x_k &lt; 4$, for some $k\in\mathbb{N}$  IS  Show $0 &lt; x_{k+1} &lt; 4$  We know $x_{k+1} = \dfrac{1}{4-x_k}$  We also know that $0 &lt; x_k &lt; 4$, by IH.  So we have:  $$\dfrac{1}{4} &lt; x_{k+1} &lt; \infty$$  But this doesn't show the boundness. Where have I went wrong? Proving that a Hölder space is a Banach space I am trying to show that the Hölder space $C^{k,\gamma}(\bar{U})$ is a Banach space. To do this, I successfully proved that the mapping $\| \quad \| : C^{k,\gamma}(\bar{U}) \to [0,\infty)$ is a norm, by proving its properties.   But how do I show that the sequence $\{u_k\}_{k=1}^\infty \subset C^{k,\gamma}(\bar{U})$ converges to $u \in C^{k,\gamma}(\bar{U})$, that is, how do I show that $$\lim_{k \to \infty}\|u_k-u\|=0,$$ which would mean the normed linear space is complete, and hence a Banach space?  Here are the following taken from PDE Evans, 2nd edition, page 255:     Definition. The Hölder space $$C^{k,\gamma}(\bar{U})$$ consists of all functions $u \in C^k(\bar{U})$ for which the norm $$\|u\|_{C^{k,y}(\bar{U})}:= \sum_{|\alpha|\le k} \|D^\alpha u \|_{C(\bar{U})}+\sum_{|\alpha|=k} [D^\alpha u]_{C^{0,\gamma}(\bar{U})}$$ is finite.   Also from page 254,     Definitions. (i) If $u : U \to \mathbb{R}$ is bounded and continuous, we write $$\|u\|_{C(\bar{U})}:=\sup_{x\in U}|u(x)|.$$      (ii) The $\gamma$th-Hölder seminorm of $u : U \to \mathbb{R}$ is $$[u]_{C^{0,\gamma}(\bar{U})}:=\sup_{\substack{x,y\in U \\ x \neq y}} \left\{\frac{|u(x)-u(y)|}{|x-y|^\gamma} \right\},$$ and the $\gamma$th-Hölder norm is $$\|u\|_{C^{0,\gamma}(\bar{U})}:=\|u\|_{C(\bar{U})}+[u]_{C^{0,\gamma}(\bar{U})}.$$   This is all I got so far: \begin{align} \|u_k-u\|_{C^{k,\gamma}(\bar{U})}&amp;=\sum_{|\alpha|\le k} \|D^\alpha u \|_{C(\bar{U})}+\sum_{|\alpha|=k} [D^\alpha u]_{C^{0,\gamma}(\bar{U})} \\ &amp;= \sum_{|\alpha|\le k} \sup_{x\in U} |u_k(x)-u(x)|+ \sum_{|\alpha|=k} \sup_{\substack{x,y\in U \\ x \neq y}} \left\{\frac{|[u_k(x)-u(x)]-[u_k(y)-u(y)]|}{|x-y|^\gamma} \right\}. \end{align} Now, where can I go from here, to show that $\lim_{k \to \infty}\|u_k-u\|_{C^{k,\gamma}(\bar{U})}=0$? The sequence is Cauchy, and I have to use that fact somehow. List comprehension with expensive computation Does the everywhere differentiability of $f$ imply it is absolutely continuous on a compact interval? Suppose $f$ is differentiable everywhere on $[0,1]$. Must $f$ be absolutely continuous on $[0,1]$? I know this is true if $f'$ is integrable but I'm not sure in this more general case. Does any particle ever reach any singularity inside the black hole? Showing that every field is an integral domain. Points disappear when zooming past certain scale in ArcMap? My points are disappearing when I zoom in past 300,000 in ArcMap.  I tried to repair geometry, but it doesn't fix anything?    I also checked the scale extents and those are turned off.  I can export the points to a new shapefile/feature class, but I'd like to not have to do that.    I'm using 10.1 on Windows 7 x64. Derive equation for a cantilever in SHM After Upgrade to Ubuntu 20.04: "Oh no! Something went wrong" Error When Create Drupal Commerce Product Display The outlet for my range hood was misplaced. It needs to be 4 inches to the side. I can make the junction and move the wiring to the new location but I really don't want to have the empty plate exposed.   The wire is not long enough to reach the required location, so I will make a junction in the existing box, and add a new box at the correct location.  Is there any acceptable circumstance where I could tile over the "old" in-wall junction box?  I'm guessing not, but I figured I'd ask.  EDIT: I should clarify, based on the answers below... I know for a fact that this outlet is the only line on this entire circuit, all the way back to the panel. I am asking explicitly if there is any way to acceptably splice the wiring without exposing a junction box. Updating a field programmatically, hook_node_update Currently trying to update a field every time a node is created or updated. However the value is not being populated within the node, do I have access to the node object with this particular hook? What could I be missing?    function vbtoken_node_update($node) {         entity_get_controller('node')-&gt;resetCache(array($node-&gt;nid));         $types = node_type_get_types(); //What are the current Node Content Types?       $yes = ($types['volunteer_project']-&gt;type);        if($node-&gt;type === $yes){           $hash = md5($node-&gt;title . $node-&gt;nid . $node-&gt;nid);         $hashed = substr($hash, 0, 6);         $node = node_load($node-&gt;nid);         $node-&gt;tcode[$node-&gt;language][0]['value'] = $hashed;         node_save($node);          watchdog('vbtoken', 'Added a new Token code to %nid', array('%nid' =&gt; $node-&gt;nid));          }         else          {           dpm('not working dude');         }      } is a one-by-one-matrix just a number (scalar)? I was wondering. Clearly, we cannot multiply a (1x1)-matrix with a (4x3)-matrix; However, we can multiply a scalar with a matrix. This suggests a difference.  On the other hand, I was, for example, in an econometrics lecture today, where we had for a (Tx1)-vector $\underline{û}=\left( \begin{array}{c} û_1\\ \vdots\\ û_T\end{array}\right)$:     $S_{ûû}:= \sum_{i=1}^T û_i^2$ shall be minimized. We see see that   $S_{ûû}=\underline{û}^T\underline{û}$.   Well, formally, shouldn't it be $(S_{ûû})=\underline{û}^T\underline{û}$ or $S_{ûû}=\det(\underline{û}^T\underline{û})$, to ensure that we stay in the space of matrices and not suddenly go to the space of scalars? So here, the professor (physicist) not only treats $\underline{û}^T\underline{û}$ like a scalar, but also calls it a scalar. Is this formally legit or a wrong simplification (though it does not seem to have any impact, and surely makes life easier)? What files should i put in a logo pack to give to clients? Should I put small, medium and large version of my logo as well as the vector file. What is the expected minimum euclidean distance between $N$ points uniformly and independently chosen on the shell(sphere) of 3-D ball of radius $R$?   Note that the expected minimum distance might be difficult to compute, so a good lower bound is also fine.   My approach  I take the approach similar to this   .   Suppose we put $N$ circles of radius $r$ uniformly on the surface of the ball. Therefore we could compute the expected minimum distance by the following expression \begin{align} E[D]=\int_0^\infty P(D&gt;t) dt. \end{align}  So, it remains to compute  $P(D&gt;t)$. Actually, since we are after a lower bound on  $E[D]$ it is enought to give a lower bound on $P(D&gt;t)$.  Let $S_i$ be the event that the pair of circles does not intersect which should be given by \begin{align} P(S_i) =  \frac{ Surf(R)-Surf(r)}{Surf(R)}= 1-\frac{  \pi r^2}{ 4\pi R^2}=1-\frac{ r^2}{ 4 R^2} \end{align}  Now the probability that euclidean minimum distance $D$ between $N$ balls is bigger than $t$ should be similar to  \begin{align} P[ D \ge t] \stackrel{?}{=}  P[ \cap S_i] \end{align} However, I think we somehow need to converte from the geodesic distance to euclidean distance but I am not very sure how to do that? Two sidebars in Beamer for two presentations in one tex file I love the game Terraria for PC and played it for ages. Now I saw Terraria on the PS3-Store and gave it a shot. After some wandering around I saw something like a snow-biome and realised later on, that I was on a floating Island. I haven't played much of Terraria the last months, but this stuff seems kind of new. In addition I haven't found the (current) differences between the PC and the Consoleversion. Is there just one (upcoming?) Patch missing on the PC? What's included or - like the title said - what are the current differences (besides the splitscreen-feature of course)? What are some good examples of a function  $f : \mathbb{R} \to \mathbb{R}$ where its derivative is equal to its inverse? I attempted to find a monomial that satisfied it by starting with $f(x) = ax^b$ and showing that $f^{-1}(x) = f'(x) \implies b-1=\frac{1}{b} \implies b=\phi$ and got $$f(x) = \frac{x^\phi}{\sqrt[\phi]{\phi}}$$ Which seems to work according to WolframAlpha, but I'm having trouble double-checking it. Any other ideas? What character / attack / stage combination can get me a combo of 100? For the first two challenge panels, I just used my golden hammers on the "get a combo of x," but now I'm seeing on challenge panel 3, the game expects you to get a combo of 100! I can barely get past a combo of 9 without the counter resetting. What character / stage combination can get you a combo of 100? Are there multiple, so I can more easily get the "get a total combo of 400 across all characters" challenge?  Additionally, what exactly constitutes a combo? Sometimes my combos are cut short and sometimes they're longer, so I must not understand how they're tracked. When can a (finite) group be written as the quotient of some other group by its center? So if I'm given $H$, when I can conclude there is a group $G$ such that $H\cong G/Z(G)$? It's easy to show that non-trivial cyclic groups are not of this form. More generally, any group with the property that all finitely generated subgroups are cyclic (e.g. $\mathbb{Q},\mathbb{Q}/\mathbb{Z}$) cannot be of this form. Are there are any others?