In a very famous tv show we talk about a firm and in other tv show we talk about company  I want to know the main difference between them.
A company is any form of business whether it is small or large. Generally the term &quot;company&quot; indicates a particular kind of business dealing in a specific product. An organisation is the larger form and generally comprises of a number of companies.  Simply, a company is an organization, but an organization is not just a company. An industry is the combination of companies in same line of business. Firm, corporation and business  are synonyms of &quot;company&quot;. An Agency is a particular kind of company, which serves as an intermediary between clients (other companies or individuals).  Is this correct?
Below, the  of second-order logic is used.    My question is about a second-order analogue of $ZFC$ other than the usual "second-order $ZFC$." Rather than define the latter, I'll just state that its (set-sized) models are exactly the $V_\kappa$s with $\kappa$ strongly inaccessible (or if you prefer, the uncountable Grothendieck universes).  Specifically, I'm interested in the second-order theory consisting of the usual (first-order) axioms of Pairing, Extensionality, Union, Choice, Infinity, and Powerset, and the Separation and Replacement schemes ranging over second-order formulas. I'll call this "$ZFC_2^{scheme}$."    Specifically, for each formula $\varphi(x, y_1,...,y_k)$ of second-order logic with only the displayed variables, each of which is first-order, we have a corresponding Separation and Replacement instance. We do not allow second-order parameters here, so formulas with second-order free variables don't yield Separation/Replacement instances.   The passage from $ZFC$ to $ZFC_2^{scheme}$ has a nice uniformity: it's an example of a more general operation $\mathcal{ZFC}$ which spits out a $ZFC$-analogue given a logic at least as strong as first-order logic.    This is the reason for the parameter restriction above: I want $ZFC_2^{scheme}$ to look just like $\mathcal{ZFC}(\mathcal{L})$ for any other logic $\mathcal{L}$, and not take into account the particular feature that we now have a new kind of variable at our disposal - and in particular, take as "syntax-free" an approach to logics as we can get away with. (This is a choice of arguable value, but it's the one I'm making for now.)   It's easy to show that every model of $ZFC_2^{scheme}$ is well-founded, so to understand its models we only need to look at transitive sets. A natural hope at this point is that $ZFC_2^{scheme}$ is just second-order $ZFC$ in disguise, that is, that for a transitive set $M$ we have $M\models ZFC_2^{scheme}$ iff $M=V_\kappa$ for some strongly inaccessible $\kappa$. However, this isn't at all obvious to me (although it is easy to show the right-to-left direction).     Question. What are the (set-sized) models of $ZFC_2^{scheme}$?   (Note by contrast that the "arithmetic analogues" $PA_2^{scheme}$ and second-order $PA$ are equivalent since each pins down $\mathbb{N}$ up to isomorphism - although that leads to .)  (I'm happy to drop Choice if that would help.)  EDIT: As Hanul Jeon pointed out below,  shows that consistently $ZFC_2^{scheme}$ (there called "$ZFC_2^{def}$") has countable models, so we have a partial answer. However, I don't see at the moment a way to get an outright $ZFC$ proof that $ZFC_2^{scheme}$ is strictly weaker than second-order $ZFC$. Unknown site on Android app When I select the unknown site (i.e. the meta sites) the app crashes.   I have a Samsung Note 5 and version 1.0.89 of the app. Destroying a Planewalker before its ability is used Say my opponent plays a planeswalker during their first main phase.  I have a  or some other effect that will kill it after it is already in play, but before they use any of its abilities.  I could respond to them using a +1 ability, but I want to kill it before that effect goes on the stack.  In most casual situations, it would basically come down to whether I say "Hero's Downfall" first, or they say "+1" first.  But I can't imagine that's how it's supposed to work.  Is there a time between when the planeswalker hits the battlefield and when they activate its abilities that they must let me respond? It seems to me that situations like this arise frequently, and they are resolved simply by who speaks up first, which is horrible for such a rules-oriented game. Ubuntu 12.04 boots to TTY1 Alrighty, I have perused the threads already in existence and am finding none of them seem to have the exact combination of variables I've got going.  I'm working on a computer using Ubuntu 12.04. Currently, it boots straight into tty1  Ubuntu 12.04.4 LTS [computer name] tty1  [computer name] login: Password:   Login leads to:  Last login: Wed Mar 19 13:47:11MDT 2014 on tty1  Welcome to Ubuntu 12.04.4 LTS (GNU/Linux 3.2.0-32generic-pae i686   The owner of the computer stated that this issue happened after a recent update, if that gives anyone a hint as to the specific location of the graphics failure.   I'm capable of booting into the GUI utilizing startx, but am frankly at a loss of where to go from here. Years of Windows has molded me into a GUI heavy kinda person, so, if possible, work off the assumption that I've no idea what you're talking about and break it down to the simplest of steps.  Thanks! How to handle fragmentation of auto_increment ID column in MySQL Some spells, such as Forbiddance, say that under certain circumstances, they last "Until Dispelled".  Other spells, such as Mordenkainen's Private Sanctum, say that under certain circumstances, they become "Permanent".  What is the difference between these two terms?  Does "Permanent" mean that the effect can never be dispelled? PHP Session data not being saved I have one of those "I swear I didn't touch the server" situations. I honestly didn't touch any of the php scripts. The problem I am having is that php data is not being saved across different pages or page refreshes. I know a new session is being created correctly because I can set a session variable (e.g. $_SESSION['foo'] = "foo" and print it back out on the same page just fine. But when I try to use that same variable on another page it is not set! Is there any php functions or information I can use on my hosts server to see what is going on?  Here is an example script that does not work on my hosts' server as of right now:  &lt;?php session_start(); if(isset($_SESSION['views']))     $_SESSION['views'] = $_SESSION['views']+ 1; else     $_SESSION['views'] = 1;  echo "views = ". $_SESSION['views']; echo '&lt;p&gt;&lt;a href="page1.php"&gt;Refresh&lt;/a&gt;&lt;/p&gt;'; ?&gt;   The 'views' variable never gets incremented after doing a page refresh. I'm thinking this is a  problem on their side, but I wanted to make sure I'm not a complete idiot first.  Here is the phpinfo() for my hosts' server (PHP Version 4.4.7): Proof of Heron's Formula for the area of a triangle Let $a,b,c$ be the lengths of the sides of a triangle. The area is given by Heron's formula: $$A = \sqrt{p(p-a)(p-b)(p-c)},$$ where $p$ is half the perimeter, or $p=\frac{a+b+c}{2}$.  Could you please provide the proof of this formula? Thank you in advance. What are best practices for blocking UI when application is busy I'm writing a web app using Twitter Bootstrap with PHP on server side. My app makes regular ajax requests via jQuery and i want to disable certain parts of the UI until the server completes processing and hands back the control to Client-Side.  I wonder what would be best practices for the same? Is it safe to give out one's bank account number? I'm managing the utility of the house and I'm sharing with another person. He asks me to provide my bank account number, so that he can transfer his money to my account when paying the utility.    I wonder if it is safe to give out my bank account number?   For example, if I'm correct, many online payments just need the account number to draw money out of it. Is giving out the bank account number safer than handing a check to another person, since there is also the account number printed on the check? Pytest is in PATH but not found After closing paint the last used settings went back to default. I want them to be saved. Like the selected Brush-Tool, Color, Line-strength, etc.  Either after every usage or I define one I use most. Maybe through the registry or by start parameters? YA dystopia novel of battle school with unusual military control scheme Some sort of battle school (no, not Ender's Game), where teens are being trained as military commanders.   The control system for their army hinges around some sort of system that requires extremely fine motor control -- being able to "push" around digital representations of military units using a special interface that interprets minute finger movements.  The boy protagonist eventually meets a girl in the battle school, and is astonished to learn that most people do not live as well as he does -- for instance, he gets a fresh jumpsuit outfit every day and disposes of the old one; this is a luxury.  One scene I recall is them kissing for a moment in some sort of underground passageway; the boy protagonist notes the exact length of the kiss, as he has been trained to have heightened time perception.  I don't recall much about other commander characters; I think they have different special abilities, and one other major character might have physical deformities, possibly because of postwar-radiation-related birth defects.  They have been training for an upcoming, prearranged final battle between all the existing national governments; the military units are very possibly robotic or entirely digital in nature, so as to avoid wasting materiel / human life.    They ultimately win the battle, just barely; I think the girl protagonist gives them an edge in the competition by hacking the timing / control system in favor of their team, causing a discrepancy which only the boy protagonist notices due to his heightened perceptions.  It was agreed that the winning government gets dominion over one of the few islands of land left that was not irradiated in some previous war; the protagonists get to live there as a reward for their victory.  I believe the boy protagonist later realizes he's gradually losing his ability to exactly quantify the passage of time.  Published no later than 2004, likely somewhere between 1980-2000, probably sometime in the '90s. Novel from 50s or 60s - Good vs. Evil I'm not sure I recall enough of this story for a good identification, and the below is definitely out of story order, but...  The POV character goes to his home town and finds it different. He later finds that he's trapped in the town; there are two young people who turn out later on to be ... avatars ... of Ormazd and Ahriman, and the town is a battleground; what he is seeing of the town is Ahriman's effect on the town, and he turns out to have some limited ability to see the original town, which is more-or-less Ormazd's version of reality. In the end, Ahriman's avatar is destroyed, and the town restored.  I read this in the '80s or earlier; it was part of my father's collection, and the book was showing its age; I think it more likely to be the '60s rather than the '50s, and was probably by a prominent name in SF, but not one of the Masters. Why is a home fiber connection asymmetric? I recently switched from an ADSL to a fiber connection and was surprised to see that the bandwidth is asymmetric (1 Gbps down / 250 Mbps up).  While this is understandable in ADSL, I do not understand why fiber at home is asymmetric as well? It is not a limitation of the technology (I have symmetric fiber at the office, and always had) How to count entities with commands/check if there are only one or a certain number of entities or players left? I want to run a command when there are only 10 entities left. I know you can use /execute unless entity to detect when all matching mobs have died, but it doesn't work if you want to run a command when there are for example 10 entities left.  A command like /execute if entity @e[limit=10] does not work, it also triggers if there is only one entity.  Such a counting system could also be used to determine once there is only one player left in an arena, meaning they have won a battle or similar. Another simple series convergence question: $\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$ I'm being asked to determine if $\displaystyle\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$ converges. So, using Cauchy's Condensation Test, I reduced the problem to one of determining the convergence of $\displaystyle\sum\limits_{n=3}^\infty\frac 1{n\ln (n\ln 2)}$. Am I on the right path, and how do I proceed from here? Combinatorial proof for Stirling number of 1st kind's generating function So I see this identity a lot but I can't find a detailed combinatorial proof for it.  $$n(n+1)...(n+k-1)=\sum_{j=0}^k \begin{bmatrix}k \\j \end{bmatrix}n^j$$ Can someone please help? I am designing a hobby project that will run on a battery so I am trying to reduce power consumption. The SoC I am using has the ability to go into a deep sleep mode where it consumes very little power, and then can be interrupted by a falling edge on a pin.  I want to generate a high-low-high pulse when the state of a reed switch changes in either direction. I have been reading a lot and it seems that a one-shot monostable circuit can be built from a couple of transistors and an RC circuit to generate an output pulse when an edge is detected. I understand how that works. However, I can't figure out the best way to also pulse on the opposite edge.  One thought, was to just combine two one-shots that are configured to trigger on rising and falling edges respectively, and use the transistors at the output to pull the common pull-up low (kind of like a NOR gate).  Since I am a hobbyist, I am mostly using passive components. What is the "real" way of doing this in a low-power configuration using logic devices?  Edit: I figure I should mention something about the timing requirements. Normally the reed switch will be either open or closed for many seconds at minimum before changing states.  Edit: Here is an example of the circuit I was using for detecting only the falling edge:    And here is the ~20ms pulse it was producing for ~200ms button press simulating the reed switch (Channel 1 is Vbe for T1 and Channel 2 is measured at RST): Is there a reason why ls does not have a --zero or -0 option