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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5
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1answer
218 views

Notation in Atiyah - Macdonald

I am now going through some problems in Atiyah - Macdonald Chapter 3. In problems 21 and 23 of chapter 3, they use the notation $A_f$ to mean something I don't know. I have not seen this before. ...
0
votes
1answer
330 views

Notation for extracting the index of an element from a set

OK I edited the question. Sorry for the wrong terms. What is the correct notation such that a specific function maps an element of a specific sequence/list/n-tuple to its index? I have researched ...
1
vote
2answers
736 views

What does this symbol mean? (looks like a lower-right corner — subject: manifolds theory)

Below I have posted an excerpt of Lee's Book "Introduction to Smooth Manifolds" (page 371). I don't know what the symbol means that looks like a lower-right corner, and I cannot find it via the index, ...
2
votes
3answers
669 views

notation of distribution

I have a question: Does $$N(0, x)$$ mean a normal distribution with mean $0$ and variance $x$? Or standard deviation $x$? The notation seems ambiguous sometimes.
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vote
1answer
415 views

Permutation Group Notation

I have a question about notation: For a permutation $\sigma\in S_n$, define the following quantities: $\text{ret}(\sigma)$ as the number of indexes $1\leq i\leq n$ such that $\sigma(i)\lt ...
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vote
2answers
242 views

summation notation for general sets

I'm working through an academic game theory paper and stumbled upon this summation notation in a proof and I'm not quite sure what it means: $$\sum\limits_{j \in M \backslash\ \{i\}}$$ There is a ...
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votes
5answers
10k views

Notation for “is divisible by”

Is there a standard way of writing $a$ is divisible by $b$ in mathematical notation? From what I've search it seems that writing $a \equiv 0 \pmod b$ is one way? But also you can write $b \mid a$ as ...
5
votes
3answers
200 views

Dealing with many entities that need a symbol

What does one do when one needs a lot of symbols and one has exhausted the useful symbols of the latin and greek alphabets? (I say useful symbols because letters like iota (ι) and upsilon (υ) seem too ...
2
votes
3answers
62 views

Clarification regarding a derivative symbol

I came across the following expression: $$\frac{\partial^{i_1+\cdots+i_m}P(x_1,\ldots,x_m)}{\partial x_1^{i_1}\cdot\cdot\cdot \partial x_m^{i_m}}$$ for $P(x_1,\ldots,x_m)$ a polynomial in $m$ ...
2
votes
2answers
522 views

Set operators vs. Logical operators while discussing probability theory.

Let $S = \{1, 2, \dots, 10\}$ Let $A$ be the event that a number selected from $S$ is even. Let $B$ be the event that a number selected from $S$ is a multiple of $3$. If any number is equally likely ...
2
votes
1answer
148 views

Is the notation for the definition of a set stricly formalized?

In the 800 pages set theory book by Jech, he uncommented starts using $$Y=\{ u\in X : \phi(u)\}$$ as equivalent to $$Y=\{ u:u\in X \wedge\phi(u)\}$$ on the first few pages. The fact that, in the ...
2
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1answer
224 views

What does $ \langle Y_{lm} | Y _{\lambda\mu} \rangle = \delta_{l\lambda} \delta _{m\mu} $ mean?

In Rotation Matrices for Real Spherical Harmonics. Direct Determination by Recursion, I can almost completely understand the recurrence relations described, but for one part. The $Y^l_m$ function is ...
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vote
1answer
104 views

Notation question (shorthand for dot products?)

I am reading a paper and trying to understand a calculation and all of a sudden I bump into the following term: $D^2_y p(t,y(t,x))(\partial_t y(t,x),y^\epsilon(t,x))$ where $p$ is a scalar field ...
0
votes
1answer
156 views

indicator function?

Does anyone know what $ 1_\omega v $ means where $v \in L^2((0,T) \times \Omega )$ and $\omega \subset \subset \Omega$? It should be an indicator function of $(t,x)$, but not sure how to interpret ...
0
votes
1answer
54 views

How to specify that if a denominator should not be 0

How can i specify in the otherwise condition of the following equation \begin{cases}\ U & \text{if $A_{U_{Max}} = A_{U_{Min}} =$ Null},\\ \ \frac{A_{U_{Max}} - A_{U_{Min}}}{U\sqrt{2}} & ...
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2answers
2k views

What does the syntax $P(X=n)$ mean?

I'm reading a text book about probability and this syntax $P(X=n)$ keeps resurfacing. I've googled around, but I keep getting results on binomial distributions. What does $P(X=n)$ mean? Does it mean ...
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votes
4answers
1k views

History of $f \circ g$

$f \circ g$ is usually interpreted as $f(g(x))$ although, as Google shows, $g(f(x))$ is used frequently too. My question: Does anybody know who was the first mathematician to use this symbol and what ...
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1answer
118 views

Correct precedence of division operators

Say i have the followingv operation - $6/3/6$, i get different answers depending on which division i perform first. $6/3/6 = 2/6 = .33333...$ $6/3/6 = 6/.5 = 12$ So which answer is correct?
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votes
1answer
764 views

Inserting if else in a mathematical expression is it possible

Hope you guys can help me out. I have a mathematical expression which I constructed its: $$ A_S = \frac{A_{U_{Max}} - A_{U_{Min}}}{U\sqrt{2}} $$ Is there a way in which I could mathematically specify ...
4
votes
2answers
589 views

Necessity of Brackets for Integration

Suppose I want to integrate $f(x)+g(x)$. Can this be written as $\int f(x)+g(x)\, dx$ or are brackets necessary, i.e. $\int \left(f(x)+g(x)\right) \,dx$?
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1answer
555 views

Square bracket notation in equation

I'm attempting to understand a paper[1] on contracting geometry for computer graphics. I have an undergraduate Physics degrees to give some indication of my experience, though that was 6 years ago ...
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2answers
293 views

Mathematical set notation

How would I write mathematically (using set notation): Let $F$ be the set defined by the distinct values of the function $f(x)$ for $a \le x \le b$ ($a$, $b$, $x$ and $f(x)$ are all natural ...
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votes
1answer
72 views

$T(n) = n^{O(1)}$ iff exists $k > 0$ such that $T(n) = O(n^k)$

I must use O notation to show that: $T(n) = n^{O(1)}$ iff exists $k > 0$ such that $T(n) = O(n^k)$ But, I don't understand what mean: $n^{O(1)}$
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1answer
529 views

How to denote a function mapping of two parameters to an output?

I am wondering how to denote something like this: I have a function mapping two sets to a set of vectors and am currently denoting it as so: $p: [F, \Sigma] \to S $ I am wondering if this is ...
2
votes
1answer
121 views

Notation for modules.

Given a module $A$ for a group $G$, and a subgroup $P\leq G$ with unipotent radical $U$, I have encountered the notation $[A,U]$ in a paper. Is this a standard module-theoretic notation, and if so, ...
2
votes
2answers
3k 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
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2answers
202 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
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1answer
167 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 "$>$" ...
7
votes
1answer
384 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, ...
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2answers
349 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: ...
2
votes
2answers
11k 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
194 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
119 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
4k 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
5k 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
2k 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
694 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
711 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
635 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 $\operatorname{Tr}$ ...
3
votes
2answers
201 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
144 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
901 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?
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2answers
765 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
382 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 ...
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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 // ...
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2answers
82 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
220 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 ...
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1answer
231 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 $u(\cdot, t)$ = ...