The other day I was thinking that whenever I'm presented in Uni with constants my teachers use letters like $c$, $k$, $n$, $a$, $b$, etc, and when encountered with variables they use letters like $x$, $y$, $z$, $w$, etc. However, these are only labels, there's nothing stopping me from using $c$ as a variable, or $x$ a constant; this led me to ask myself how are constants vs. variables formally defined. So far, I have only come up with the definition of a constant in a set by reading &quot;Introduction to Set&quot; Theory by Jech and Hrbáček:  According what they say, given a set $A$ and a $0$-ary operation $R$ on $A$, $(∅,a)$, such that $(∅,a)\in R$ and $a\in A$, is a constant and we can call it just $a$. Nonetheless, I haven't found anything on the book about the formal definition of a variable. Is my understanding of the definition of a constant correct? Do you know what's the definition of a variable? (if so, could you share it with me?) Thanks in advance.
This has been nagging me for a while and then I saw  asking what the difference is between variables and parameters. In the context of mathematics, what is the difference between  variables constants parameters arguments  I get 1. and 2. confused because, for example the general form of the quadratic function is often expressed $f(x)=ax^2+bx+c, a \neq 0$ and $x$ is the variable so what does that make a,b and c? I assume since math is so rigorous with precise definitions, these have one, but it is also a valid answer that as words they do not have a single precise definition.
How do you programmatically set an attribute? Would a Cup of Tea Be Hotter If you Add the Milk Before or After Boiling Water? This is a bit of dispute between work colleagues. An answer would be greatly appreciated.  My argument is as follows:  If you add X amount of milk at a temperature of M to a mug at room temperature R before adding X amount of water at temp W, the result would be a cooler cup of tea than if you'd added the hot water first. This would be due to the milk reducing the overall temperature of the mug in the time that has been in it resulting in the addition of boiling water having less of an effect and resulting in a slightly cooler cup of tea/coffee.   Conversely, if you add the hot water first, due to the mug being heated, the effect of adding the cool milk will be less and therefore the end result will be a hotter cup of tea.  My Colleagues arguement is simply that it would not make a difference but without any form of justification.   If anyone can give real scientific light to this issue it would be greatly appreciated :) Find the value of : $\lim_{x \to \infty} \sqrt{4x^2 + 4} - (2x + 2)$ Is there some rule against ending a sentence with the contraction "it's"? I heard this lyric in a song the other day and it just sounded so wrong that I assumed it must be incorrect grammar, but I can't find any specific prohibition that applies.     That's what it's.    That rolls off your tongue with the grace of a moose in a tutu, but I can't figure out why.  There is clearly no problem with ending other sentences with a contraction. These sound fine.     I thought I could, but I can't.   Stop touching that, it will fall off if you don't.   You say that the sky is green, but it isn't.   Also, it sounds just fine if you remove the contraction:     That's what it is.   So what's up with this construction? Should it be avoided? Apollonius circle, its radius and center How to see the error messages when I get the white screen of death? How to draw line through group plots in pgfplots? I was thinking of the noted 1980 paper by Sidney Coleman and Frank de Luccia--"Gravitational effects of and on vacuum decay"-- about metastable vacuum states that could tunnel to a lower energy "true vacuum" with catastrophic results. I suspect the answer is that if our vacuum is a false one, we wouldn't "see" the true one til it hit us. BAV99 forward voltage I am reading the  From the table on ELECTRICAL CHARACTERISTICS (page 2) (TA = 25°C unless otherwise noted) (Each Diode)     Forward Voltage mVdc     IF = 1 mAdc 715mV   IF = 10 mAdc 855mV   IF = 50 mAdc 1.0V   IF = 150 mAdc 1.25V     On page 3 there is the following VI curve graph:  Clearly at 25°C - 100mA is Vf = 0.9V. There is huge difference between the table and the IV curve.  Which source of information I should trust? Is this (typical) and (maximum) where the table guarantees the diode won't exceed Vf 1.0v at 50mA while the graph is just typical values? With ksh I'm using read as a convenient way to separate values: $ echo 1 2 3 4 5 | read a b dump $ echo $b $a  2 1 $  But it fails in Bash: $ echo 1 2 3 4 5 | read a b dump $ echo $b $a     $  I didn't find a reason in the man page why it fails, any idea? What is a good general document size for web page mockups and prototypes? I do mockups and prototypes of sites and designs all the time, but I've always wondered if there is a standard size or width I should be using. Generally I'll make my document either 1024, 1200, or 2560px wide, depending on what I'm doing.  So what do you think? What is a good or standard size for this? What type of differential equation is $f'(x) = f(x/2)$ and how do you solve it? I have the following different equation $$f'(x) = f(x/2)$$ with $f(0)=10$. What type of DE is this, and how would you solve it? It seems $f(x)$ is likely to be some relative of $e^x$, since $f'(x) = f(x)$, which is close, but I don't even know what that type of DE is called with that $f(x/2)$ feature, so I'm not having any luck searching for a tutorial. The best candidate I've found was a &quot;delay differential equation&quot;, but that seems more suited to $f(x-3)$ than $f(x/2)$. I am trying to retrieve VersionData with a standard REST API call from a VisualForce Page a then upload it to a S3 bucket but end up with corrupted files. I believe this is an encoding problem on the client side as plain text or CSVs work like a charm. I can upload VersionData from Apex but there are heap and request size limitations so I need to send the data from the client.   This is the call and returned string, I tried changing mimeType and encoding on both sides (SF call and S3 upload) with no luck.   Any ideas how to properly process images or pdf files? Thanks a lot  THE PROBLEM IS NOW SOLVED  Files should not be treated as strings. I solved the problem by leaving jQuery's ajax as I did not succeed to request a response type. By switching to plain JS and making a GET call (XMLHttpRequest) with response type set to blob I received an Object, instead of a string. Base64 string can be then retreived using JS FileReader. Dirichlet's problem in the unit disk is to construct the harmonic function from the given continuous function on the boundary circle. It is solved by the convolution with the Poisson kernel, and we know that the constructed function has uniform limit which is the given continuous function as $r\to 1$, and we can complexify the solution by taking the Schwarz integral formula. Now (in this very particular case) does the imaginary part has a uniform limit? If it does, why don't we prove the uniqueness of the solution by a simple application of the Cauchy integral formula? Here is the proof that I reckon to be reasonable(which is what I expose here to be criticised)  We construct the Schwarz integral, or $\frac{1}{2\pi}\int _{0}^{2\pi}\frac{\exp(it)+z}{\exp{(it)}-z}u(\exp{(it)})\mathrm{d}t$. This function is an analytic function in the interior unit disk, and is continuous in the closed unit disk(its closure). Let this analytic function denoted by $f$, and another analytic function that has the same uniform limit function on the circle be $v$. Then $u-v$ is an complex analytic function in the interior of the unit disk, continuous on the closure, with boundary value identically zero. An application of Cauchy's integral formula gives rise to the conclusion that $u-v$ in identically zero on the entire disk.   Another question being if the boundary function has finite jump discontinuities, what is the behaviour of the convolution with the Poisson kernel near the discontinuous points? "'void' type not allowed here" error (Java) problems installing mathtools How to create a label combining different font sizes or types? I would like to place the elevation-number of a point in a different front size and centred under its name:    Is that possible?  (That is my actual labeling: label || '\n' || elevation) Sci-fi novel involving living forever through teleporter copies Why do PBX systems use -48 V? It seems common that PBX and other telephone hardware use a positive-ground power supply, where the "hot" line is at -48v.  What's the reason for that? Like the title said, I want to install Celestia. I already downloaded the packages  and then, I tried all the things that I found on some posts (also, they're outdated, cause the last one is for Ubuntu 16.04) but nothing works.  How can I install it on Ubuntu 18.04.1?