Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.

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2
votes
2answers
225 views

Using nabla with partial derivatives and the Laplace operation $\partial_x^2+\partial_y^2+\partial_z^2$

Source of the problem p.812 here. Suppose $$\bar{F}(x,y,z)=(xy-z^2)\bar{i}+(xyz)\bar{j}+(x-y^2-z^2)\bar{k}.$$ I am concerned where I need to nabla an unit vector for example with $$\triangledown ...
1
vote
2answers
153 views

Notation for denoting one argument fixed and acting upon the other

Given a function $f_1:\mathbb R^n\mapsto \mathbb R$, and a fixed vector $v\in \mathbb R^n$ I construct another function $f_2:\mathbb R^n \times \mathbb R^n\mapsto \mathbb R$ such that ...
2
votes
3answers
429 views

Field of fractions of $R[X]$

Let $R$ be a domain and let $Q$ be its field of fractions. Show that the field of fractions of $R[X]$ is isomorphic to $Q(X)$. By the way, I don't know exactly what $Q(X)$ is. It means $Q[X]$? Or ...
0
votes
1answer
33 views

Notation of instantiating variables by their value in a constraint set

I have a constraint set $C = \{1 \leq x \leq i, j \leq y \leq j+2\}$, now I would like to get another constraint set $C'$ from $C$ to instantiate all $j$ by a value 5, so $C' = \{1 \leq x \leq ...
3
votes
2answers
1k views

$\{0,1\}^n$ and $[0,1]^n$ notations

Can someone please help me clarify the notations/definitions below: Does $\{0,1\}^n$ mean a $n$-length vector consisting of $0$s and/or $1$s? Does $[0,1]^n$ ($(0,1)^n$) mean a $n$-length vector ...
1
vote
1answer
78 views

Product of ordinals notation

How to denote product of ordinals: $\cdot$ or $\times$? I'm not sure which of these two multiplication symbols to use.
2
votes
3answers
236 views

How to formulate a theorem about bijections between several sets

I have several sets $A_i$ and bijections between them. (As stated in my theorem) no composition of these bijections produces a permutation of $A_i$ not equal to identity. So every bijection is ...
4
votes
3answers
280 views

Is it mathematically correct to write $a \mod n \equiv b$?

This is not a technical question, but a question on whether we can use a particular notation while doing modular arithmetic. We write $a \equiv b \mod n$, but is it right to write $a \mod n \equiv ...
5
votes
2answers
2k views

How do you pronounce (partial) derivatives?

I am not an English speaker that is why I asked this question. In addition, I think english.stackexchange.com is not the proper place to ask this because (I am so sorry) I don't think most of them ...
1
vote
1answer
162 views

Name of binary relation: if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$

Is there a term for a binary relation $R\subset A^2$ on some set $A$ such that if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$ ? Are there any examples of it? Are there any related ...
2
votes
1answer
674 views

Uparrow sign (convergence?)

Im not entirely sure what this definition means, whilst I'm reading up. Let $X_n \in$ some sigma algebra $\mathcal{F}$. $X_n \uparrow X = X_n \subseteq X_{n+1}, \forall n \in \mathbb{N}$ and $\cup ...
0
votes
1answer
423 views

Query about Cartesian vector notation.

I'm just starting to teach myself about covariant and contravariant vectors. With the little knowledge I've acquired so far I'm wondering if, for an ordinary Cartesian vector $\mathbf{V}$, it's OK to ...
1
vote
2answers
170 views

The names of two unfamiliar operations

I am currently researching a QR-based root finding algorithm encountered two operations that I don't understand. I'd love to look them up, but I can't find the names of these operations/notations. ...
8
votes
3answers
3k views

A digital notebook for Mathematics?

When I studied math 15 years ago, I was dreaming of having a math repository with tags to navigate between the different entries. I imagined it would come eventually to the market, and was hopefull ...
2
votes
2answers
203 views

What does $\sqrt[n]{z}$ mean, when $z$ is an arbitrary complex number?

What does $\sqrt[n]{z}$ mean, when $z$ is an arbitrary complex number? Is it a single complex number, or the set of $n$-th roots of $z$?
0
votes
1answer
1k views

Right and Left arrow notation in proof.

I'm studying vector spaces and I'm reading a proof where the authour uses the symbols $$(\Rightarrow)$$ and $$(\Leftarrow)$$ when proving a theorem. He doesn't use them in context, but rather ...
1
vote
1answer
221 views

What's are these index objects called? And $\mathrm{\LaTeX}$ \sum question

I want to refer to $$A_iB_jC_k$$ using $$\psi(ijk) = A_iB_jC_k$$ So that I can write out quite overwhelming-looking sums of ABC terms as sums of terms that look like 123, 231, 113, etc. If I am not ...
1
vote
1answer
462 views

Notation of partition

I look for an elegant way to notate a partition $\mathcal{Q}$ based on another partition $\mathcal{P}$. Two elements who are already in the same partition in $\mathcal{P}$ also belong to the same ...
1
vote
4answers
847 views

Coordinates notation in Spherical polar system

There is a number of conventions for specifying coordinates in Spherical polar coordinate system: ($r$, $θ$, $φ$), ($r$, $φ$, $θ$), ($\rho$, $\theta$, $\phi$) and even ($r$, $\psi$, $θ$). The article ...
0
votes
1answer
119 views

Are there names for the indices of the spherical harmonics?

I know that physicists call $\ell$ and $m$ the "azimuthal" and "magnetic" quantum numbers, respectively. But those sound very physics-y. (I am actually a physicist, but still.) Are there names for ...
2
votes
1answer
184 views

What do these notations actually mean?

I apologize if this question sounds weird, but I have come across this function (which I am trying to replicate using C# code), which has left me a bit confused. The way I am understanding, is that ...
1
vote
2answers
287 views

Particular Use of Big O Notation

I'm reading a theorem that states "...Then for each $j$ and $\epsilon>0$, there exists $n\leq 2^{O(j/\epsilon)}$..." What exactly is the big-oh notation saying in this case? I guess it must be ...
1
vote
1answer
506 views

Sequence Notation

I have come across the following in the book "Principles of Program Analysis" by Nielson, Nielson and Hankin to represent a sequence and I am unsure of what its constituent parts mean. Obviously ...
1
vote
2answers
642 views

What is the meaning of $\operatorname{ord}_{p}(n)$?

In number theory, where $p$ is a prime number and $n$ is an integer not equal to zero, what is the definition of the function $\operatorname{ord}_{p}(n)$ in the context of $p$-adic valuations?
0
votes
1answer
59 views

Representing relations among several long formulae

I have several long formulae, each formula occupies almost the whole width of the line: $$ 1 * 2 + 3 * 4 + 5 * 6 + ( 7 * 8 ) \tag{a}$$ $$= 1 * 2 + 3 * 4 + 5 * 6 + 7 * 8 ...
0
votes
4answers
484 views

Better ways to write the set $\{(i, x, y) \mid (i,x) \in \{(1,1), (2,1), (2,2)\}\}$

I would like to write $\{(i, x, y) \mid (i,x) \in \{(1,1), (2,1), (2,2)\}\}$ where $y$ could be any (integer) value. Is there a shorter way to write that... Also for $\{(i, x, y) \mid i = 2, x = ...
5
votes
2answers
2k views

Notation for sequences

I am trying to write a small article, and I just want to know how would be a good way to present the maths I have written so that it looks professional. I am trying to define a sequence $x_n$ of real ...
2
votes
0answers
276 views

Summation notation and a negative sign of some elements

Having sequence like $$ \beta_1 \cos\theta_1 + \beta_2 \cos\theta_2 + \beta_3 \cos\theta_3 + \dots + \beta_n \cos\theta_n$$ it is possible to present it using summation notation as follows: $$ ...
1
vote
1answer
324 views

In this algorithm what is “b”?

I'm trying to take an algorithm from this page: http://mathforum.org/library/drmath/view/65653.html and convert it to working code. The step-by-step is as follows: The following algorithm uses a ...
1
vote
1answer
120 views

Quick check on function composition notation [duplicate]

Does $f^n(x)$ always mean $f(f(f(f(...f(x))))....)$ [n times]? i.e. $f^3(x)$ always means $f(f(f(x)))$? Does $f^0(x)$ mean $x$? [where $f\neq id$] By always, I mean regardless of whether it's for ...
1
vote
1answer
274 views

Convention of writing constraint sets

As I will write constraint sets very often, I would like to make sure that I respect the convention. First, I would like to represent a set of constraints and their relation are conjunction. For ...
10
votes
10answers
766 views

How to pronounce $\setminus$

A question for English speakers. When using (or reading) the symbol $\setminus$ to denote set difference — $$A\setminus B=\{x\in A|x\notin B\}$$ — how do you pronounce it? If you please, ...
1
vote
1answer
77 views

scientific notation

If I were trying to change a problem with exponents into a scientific notation how would I do that? Example is $4(10^{50})^{100}$ I will have questions like this on an exam and I need to understand ...
1
vote
3answers
7k views

what is the right symbol for the “max” like Pi is for product?

I have a set of variables that have a value, and i want to find the max of those values. Here is the equivalent of what I want to do with "sum" $$\sum_{j:~N_j \in U_i}~ DA_j$$ For all j subject ...
2
votes
1answer
814 views

The big $O$ versus little $o$ notation.

I'm familiar to both the $O$ and little $o$ notation. I know they are of great use when studying limits, asymptotics and series. However, I'm not sure when to use one over another, particularly when ...
5
votes
2answers
622 views

Notation for: all subsets of size 2

How would one denote the set of all subsets of $A$ which have size $2$? Would $$\binom{A}{2}$$ be a good idea?
4
votes
1answer
117 views

Notation for some integrals

I've seen some problems where the OP writes integrals in this form $$\int {dt} f\left( t \right)$$ or for double integrals $$\int {dx} \int {dtf\left( {t,x} \right)} $$ Do they represent another ...
2
votes
1answer
59 views

what is the right notation for this operation on two vectors?

I am trying to find the right notation for this operation on two vectors of size N and M. I do not believe it is the dot product, because there is no sum for the multiplication of each element. ...
1
vote
3answers
2k views

Shorthand notation for “increases” and “decreases”

I want to write out something like: "As $x$ increases, $y$ decreases." Is there a standard symbolic notation for this, such as an up arrow and a down arrow? (And if you can tell me how to write it ...
2
votes
0answers
305 views

Confused about notation and derivatives inside integrals

EDIT: To make what I am asking more clear. I've simplified it and have a more direct question. Let's say I am writing out an expression, and I want to write: $$\int_0^xF'(y)\,dy$$ However, for ...
6
votes
2answers
4k views

Notation of the summation of a set of numbers

Just a quick question for which I've yet to managed to find an answer using Google. Given a set of numbers $S=\{x_1,\ldots,x_{|S|}\}$, where $|S|$ is the size of the set, what would be the ...
3
votes
2answers
5k views

What does horizontal line above variable means?

I have a simple equation which looks like that except that there placed vector signs there are straight horizontal lines: \begin{equation} \ z = i^8 + \overline{z_1} \cdot \overline{z_1} -z_1 ;\\ \ ...
2
votes
3answers
180 views

Mathematical function for the powers

I have this formula $$\underbrace{2^{2^{2^{.^{.^{.^{2^2}}}}}}}_n$$i.e. where the total number of 2's is $n$. Is there any way to write it as a single mathematical function?
2
votes
2answers
316 views

What is the product of the empty set?

Give: $fn(S)=\prod_{x\in S}x$ what is: $fn(\emptyset)$ I can see reason that it would be defined as 1 or 0. Note: I thought about restricting the domain of $S$ but that would make the problem ...
9
votes
1answer
360 views

What is the “etymology” of the notation “:=”?

I've noticed that sometimes people use ":=" to set variables, like "With $f(x):=x^{2}$, we have $f(1) = 1$." This is also the variable definition operation in Mathematica. My question is, did ...
1
vote
1answer
54 views

Are segments and intervals always subsets of $\mathbb{R}$?

Which of the following is the accepted mathematical practice? Any segment $(a, b)$ or interval $[a, b]$ contains only real numbers. If you want all the rational numbers between $a$ and $b$, you ...
1
vote
1answer
62 views

Is there a simplified equation for doing something like this:

Is there a simplified equation for doing something like this: $$(1x) + (2x) + (3x) + (4x) + (5x)$$ but the number it goes to (the example goes to 5 ) can be variable?
4
votes
3answers
1k views

Notation for image and preimage

Let $X$, $Y$ be sets and $f:X\rightarrow Y$ be a map. Denoting the image of $D\subset X$ under $f$ by $f(D)$ can sometimes be confusing. As for preimages, I've seen unambiguous notation like ...
3
votes
2answers
998 views

Big O notation, $1/(1-x)$ series

I am doing calculus and I find this notation extremely confusing even after reading textbook and notes. Here is a question I was trying to do and I think I cannot do this yet because I dont fully ...
4
votes
1answer
199 views

Notation: $L_p$ vs $\ell_p$

$L_p$ is often used to describe a norm, or a vector space with that norm (see e.g. wikipedia). Is $\ell_p$ (typically, or canonically) a different notation for the same concept, or is it used to ...