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
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2answers
4k views

Notation : What is the meaning of the (mod n) in factoring algorithms?

Pretty much every thing is in the title, really! I'm trying to come up with an efficient algorithm to factorize large integer as an homework for a parallel programming course. I've seen a few pages ...
2
votes
2answers
230 views

Set of subsets notation. [duplicate]

Why is it that we denote the set of all subsets of $A$ by $2^A$? Is there any historical or logical cause that motivated this notation?
0
votes
1answer
169 views

Notation: What is the meaning of “$(a,b)$”

I am reading an article about counting hexagonal p-minos (the article is in a combinatorics book) and I saw a notation I don't understand: $0>(a,b)>-p$ . $a,b,p$ are integers and so "$>$" ...
6
votes
1answer
418 views

Was the definition of $\mathrm{erf}$ changed at some point?

I have seen two competing definitions of the error function. When I was an undergrad, Spiegel's Mathematical Handbook of formulas and tables (mine is the 1968 edition) was the definitive authority, ...
0
votes
2answers
400 views

Proper name or term of comma thousandths grouping notation

What is the proper name or terminology of notation for using a comma to separate and group thousandths of a number? As in, formatting large numbers for readability: ...
4
votes
2answers
20k views

What does ! mean in sequences?

I'm doing a sequences problem where I have to write the first five terms of a sequence. It looks normal, but there is an exclamation mark on the denominator: $$a_n = \frac{1}{(n + 1)!}$$ & ...
3
votes
1answer
204 views

What does $\mathbb{N}_0 \cup \{\infty\}$ mean?

A random variable $X$ takes values in $\mathbb{N}_0 \cup \{\infty\}$? Does it just mean $X$ takes values $0<X<\infty$? The part Im confused with is $\mathbb{N}_0 \cup \{\infty\}$. What does ...
2
votes
1answer
158 views

Precedence of exponentiation

The set of functions from a set $X$ to a set $Y$ is denoted $Y^X$. Now a question about precedence of operations: Should I write $X^{(Y^Z)}$ or $X^{Y^Z}$ is enough?
2
votes
1answer
6k views

Boolean algebra operation precedence?

In my discrete mathematics class we wrote down the truth table for some Boolean functions and in that table they go in the following order: ¬, ∧, ∨, →, ~, ⊕, |, ↓ So, I assumed that this is the ...
0
votes
1answer
6k views

How to write such sqrt (sqrt(x)) in equation?

Is it correct to write sqrt(sqrt(x)) as equation/formula ? or root4(x) ? I mean if x = 10000 it will be 10
5
votes
2answers
3k views

Ideal Generated by two elements (Notation question)

given two elements $r$,$s$ in a ring $R$, are the following two notations equivalent? $(r,s)$ $(r)+(s)$ For example, in the ring $\mathbb{Z}[X]$, is $(2,X)=(2)+(X)$? Thanks a lot.
1
vote
1answer
863 views

This multiple integral notation, has it got a name? $\int dx \int dy \, f(y,x)$

I've encountered, on Wikipedia (examples below), an integration notation which seems to be prefix-style: the integral sign is immediately followed by the $\mathrm dx$ (or $\mathrm dy$, or what have ...
2
votes
2answers
2k views

Is the notation for '$a$ divides $b$' standard?

I know that the notation $a | b$ means that there exists an integer $c$ such that $ac=b$, but is this notation completely standard and there's no way that it could be the other way round?
7
votes
4answers
712 views

What does the symbol $\operatorname{Tr}$ in the Yang-Mills action mean?

I find that many authors write the Yang-Mills action as follows: $$\mathcal{J}= \int \operatorname{Tr}(F \wedge \star F).$$ I have yet to find a formal description of the symbol $\operatorname{Tr}$ ...
4
votes
2answers
204 views

Is $\infty$ enough or do I need to write $+\infty$

This is a question of notation. I have seen in many articles that people often denote $+\infty$ when talking about 'positive infinity' of the real numbers. Is that a convention, or it can be written ...
2
votes
4answers
2k views

Second order partial derivatives - notation

I have seen both of these used, and people around me seem to disagree, so which one is correct: (first derivative with respect to x, then y): (1) $$\frac{\partial }{\partial y}(\frac{\partial ...
1
vote
1answer
34 views

writing a formulation in a smaller form

Is it possible to write this in a smaller form: $(A \neq \emptyset) \vee (B \neq \emptyset)$ ? is it for example mathematically correct to write it as: $A \vee B \neq \emptyset$ ?
3
votes
2answers
149 views

What is the difference between these two derivative expressions?

is there a difference between $\frac{\partial^2 }{\partial x^2}$ and $(\frac{\partial }{\partial x})^{2}$? I have to tell if a differential equation is linear, and $(\frac{\partial }{\partial x})^{2}$ ...
0
votes
2answers
1k views

function, vertical line and two values (notation for evaluation at 1 point or 2 endpoints)

What does it mean when you have notation like this $$F\bigl(g(u)\bigr)\Bigr|_0^t,$$ where $F$ and $g$ are some general functions?
3
votes
2answers
921 views

What do curly brackets mean in this formula?

In this paper, in the Formula at the beginning of 2.2, we have $B=\{b_i(O_t)\}$ where $i=0,1$ - the number of probability formula $O_t$ - the state at moment $t$ $b_i(O_t)$ - two probabilities ...
3
votes
3answers
395 views

Notation pedantry (integration by substitution)?

In a summative assessment, I lost a mark due to this: $$f_X(x)=\frac{\lambda}{\sqrt{2\pi}}\int_{-\infty}^\infty y^2\exp\left\{-\left(\frac{1}{2}+\lambda x\right)y^2\right\} \; dy$$ Now let ...
1
vote
1answer
2k views

How should one interpret a double slash, //?

Example usage I've seen: $x^2 / (y // z)$ Context: I recently started learning some fundamental electrical engineering, where I saw I calculated the power doing $vs² / (r1 + ron + ron // ...
2
votes
2answers
84 views

How do I describe summations across sets of data?

Assume that there are several geographical regions and within each region there may be many buildings. Buildings may or may not be created and destroyed from time to time hence the requirement to ...
0
votes
1answer
307 views

What’s the significance of o(delta) notation

In my notes I have a definition for $o(\Delta)$ which states that if a function $f$ is $o(\Delta)$ then as $\Delta$ approaches zero, $f(\Delta)/\Delta = 0$. Then the notation gets used in equations ...
1
vote
1answer
315 views

What does $~ u(\cdot, t)$ mean when referring to a function?

I sometimes stumble over professors defining a function $u$ using regular (but quite sloppy) notation like $u(x,t) = A\sin(x)e^{-kt}$. Later in their notes, they state something like $u(\cdot, t)$ = ...
1
vote
1answer
865 views

Notation for an arbitrary set of N elements

Is there any notation for referring to a general set of $N$ elements? Currently I'm using $\{1, \dots, N\}$, but the fact that the set consists of natural numbers is irrelevant. I'd prefer to just ...
1
vote
3answers
469 views

Sum without an index

Is $\sum a$ a customary (standard) shorthand for $\sum_{i\in\operatorname{dom}a} a_i$, where $a$ is an indexed family of say integers?
0
votes
1answer
648 views

Represent loop nests as multiple summations?

This may be trivial but I would appreciate if someone could point me in the right direction here.. I am trying to express the number of instances in a loop nest in a general form. As a mathematical ...
2
votes
2answers
2k views

Convert for-loop into mathematical expression

I'm facing a simple problem actually: for (int i = 0; i < noutput_items; i++){ out[i] = in[i] * in[i]; } When I want to formalize this as a math ...
4
votes
0answers
309 views

Divisibility notation history

I'm writing a paper project for school about divisibility, so I'd like to include a bit of history about that subject. I'm mostly interested in notation of $|$ sign used in past, but everything else ...
4
votes
1answer
2k views

Limits notation

I'm wondering what is the difference in the use of $$\lim\limits_{x \downarrow a}$$ $$\lim\limits_{x \searrow a}$$ $$\lim\limits_{x \nearrow a}$$ $$\lim\limits_{x \uparrow a}$$ I see them ...
4
votes
1answer
239 views

Why does no one use the notation $f(x)^2$?

It seems to me that "$f(x)^2$" couldn't mean anything other than "$[f(x)]^2$", so there shouldn't be any ambiguity involved, but people always tend to put an extra pair of brackets around the "$f(x)$" ...
14
votes
1answer
19k views

What's the correct notation for log squared?

I ran across these two notations for the log function (squared), which one is more conventional. $\log^2(n)$ or $[\log(n)]^2$
1
vote
0answers
241 views

A contradiction in notation

How to deal with the following contradiction in notation? $\bigcup a$ may mean both: the union of a collection of sets $a$; $\bigcup_{i\in \operatorname{dom}a} a_i$ for an indexed family $a$ of ...
0
votes
1answer
121 views

notation for symmetry types

I am reading an article and in one of the sections the article mentions the symmetry group. The symmetry group of one of the objects the article talks about is the dihedral group of order 12, using ...
3
votes
1answer
144 views

What do mathematicians call the Two's Complement on 8-bits group?

It is isomorphic to $\mathbb{Z}_{2^8},$ only difference is the symbols usually identifying the elements of the set are from $\{-128, \ldots, 127 \}$ and not $\{0, \ldots, 256\}.$ What is an elegant ...
8
votes
4answers
35k views

What do Subscripted numbers in an equation mean?

$F_n= F_{n-1}+ F_{n - 2}$ I know that when a number is superscripted it means "to the power of", but what does the subscript mean?
3
votes
2answers
339 views

Notation for covariant derivative

I'm reading John M. Lee's book " Riemannian Manifolds". On page 57, the covariant derivative of $V$ along a curve $\gamma$ is defined, where $V$ is a vector field along $\gamma$. It is denoted by ...
1
vote
0answers
35 views

About order of an index

I have a simple question on precedence of operators, especially applying a function and an index. Can we write $q(F)_i$ (without an additional pair of parentheses) for $(q(F))_i$? Maybe, it would be ...
2
votes
2answers
289 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
164 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
604 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
35 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
2k 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
82 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
259 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
297 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 ...
7
votes
2answers
3k views

How do you pronounce (partial) derivatives? [closed]

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
168 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
981 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 ...