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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4
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0answers
243 views

Better Tensor Notation

I am in a General Relativity class, and I am finding the usual tensor notation very difficult to think about -- it seems like there are too many names to express something simple. E.g., I think of ...
0
votes
2answers
152 views

How do you write the following in proper notation?

I would like help in determining the proper notation to say: The a group $G$ acting on a set of 3 points formed by the quotients $G/H$ where $H$ is a normal subgroup of $G$ is homomorphic to $S_3$ ...
2
votes
1answer
368 views

Predicate logic notation: where to put the parentheses, etc.

My math professor tends to write $\exists x\in\mathbf{X} \ni P(x)$. Is this a correct use of the such that symbol $\ni$? If not, what is the use of that symbol? Isn't it better to write $\exists ...
1
vote
1answer
168 views

Solving quartic equation - notation

I am going through Wikipedia's solution of a quartic equation and have got stuck with notation in the solution. The solution is given by this equation: What is confusing me is the significance ...
6
votes
3answers
1k views

How to write “let” in symbolic logic

How do I write let in symbolic logic? For example, if I am in the middle of a proof and there is a variable which I can assign to an arbitrary value, what would I write? My best guess is: $$ x := a ...
2
votes
1answer
1k views

Notation for modulo: congruence relation vs operator

If a and b are congruent modulo a number c, we might write $a \equiv b \pmod c$. When writing programs, it's often useful to compute the remainder after division, and in pseudocode we might write a = ...
2
votes
0answers
125 views

Notation for a canonical quotient of an abelian variety in positive characteristic

This may be a somewhat silly question, but there it goes. Let $k$ be an algebraically closed field of characteristic $p>0$ and let $A=A_{/k}$ be an ordinary abelian variety of dimension $g\geq1$. ...
0
votes
3answers
172 views

Why does it make sense to define the Probability mass function of e.g. the binomial distribution like this?

In Wikipedia (for example) the Probability mass function of for example a the binomial distribution is given by $$ f(k,n,p):=\binom{n}{k}p^k(1-p)^{n-k} $$ In some literature I read $$ ...
0
votes
1answer
6k views

Reading equations: Upside down A

what does this equation mean? I´m really bad in reading those, so if somebody explained it, I would really appreciate. $f_i(x,y)\ge 0\quad\forall i\{0,1,2\}$
0
votes
2answers
520 views

What's the point of dropping the multiplication sign before the parenthesis

What's the point of dropping the multiplication sign before a parenthesis? Sure,2(5+5) is shorter than 2*(5+5) - but I prefer ...
6
votes
2answers
1k views

What does this “subset” symbol mean?

I just came across this "subset" symbol in a PDF: $$\Omega \subsetneq T$$ I've never seen it before, and I tried looking for it via Detexify (to no avail). What does it mean?
0
votes
1answer
112 views

Definition of $\mathrm{Hom}_G (V, V') $

The following appears in my notes: Suppose $V$ and $V'$ are vector spaces over a field $F$. Let $G$ be a group, and let $\rho : G \to GL(V)$ and $\rho' : G \to GL(V')$ be ...
3
votes
1answer
88 views

Co-ordinate axes: What does the $e$ in ${\hat e}_x$ stand for?

In vector analysis for $\mathbb{R^3}$ we write standard basis vectors in various forms like $\{\hat{x}, \hat{y}, \hat{z} \}$, $\{ \hat{\imath}, \hat{\jmath}, \hat{k}\}$, $\{ {\hat e}_x, {\hat e}_y, ...
0
votes
2answers
53 views

Triple sequence

Suppose I consider a triple sequence indexed by $l,m,n$ and I take limits in the order of $l,m,$ and $n$. Then, should I write this sequence as $x_{l,m,n}$ or $x_{n,m,l}$?
0
votes
2answers
2k views

Mathematical notation for a conditional sum

I'm looking for the correct way to define a sum of all elements in a set that fullfill a certain condition. Example: $$ n(A) = \frac{\sum_{F \in A}{ \begin{cases} A_F\text{ is }\mathrm{NULL} & ...
4
votes
0answers
228 views

Where does the 'divides' sign come from?

When $a$ divides $b$ we say $a | b$. Where does the $|$ sign come from? This is not homework, just personal interest in the history of mathematical language.
7
votes
3answers
2k views

What does this “double less than or equals to” sign mean?

I found this in a Computer Science pseudocode context (see page 4 of this paper).
1
vote
0answers
93 views

Meaning of $\ker(x)$ when $x$ is an element of a Hilbert space

The follow question arose from the paper: The Hundal Example Revisited We consider a separable Hilbert Space $X$ with countable ortho-normal basis $\{e_n\}_{n=1}^\infty$. The following is an excerpt ...
2
votes
3answers
585 views

What is the “status” of the rule that multiplication precedes addition.

What is the source, or "status", of the rule that multiplication is performed before addition? Is it a definitive property of $\mathbb R$, a property that can be derived directly from the definition ...
1
vote
0answers
75 views

How do I write this in functional notation?

Let's say I have the following: $u=t^4+2t$ $\frac{du}{dt} = 4t^3+2$ $du = (4t^3+2)dt$ Now, if I wanted to write this in functional notation: $f(t) = t^4+2t$ $f'(t) = 4t^3+2$ What is the ...
0
votes
2answers
762 views

Is this the notation you use?

I've noticed that my terminology is a bit haggard. I do math on my own so I'm not entirely sure how everyone else refers to things and so I need a check. so is this correct: $\lim\limits_{\delta x ...
1
vote
4answers
173 views

Meaning of $f:[1,5]\to\mathbb R$

I know $f:[1,5]\to\mathbb R$, means $f$ is a function from $[1,5]$ to $\mathbb R$. I am just abit unclear now on the exact interpretation of "to $\mathbb R$". Is $1\le x\le 5$ the domain? And is ...
2
votes
1answer
515 views

Explicit description in set-builder notation of an arbitrary open set of the product topology

Short version: Is it possible to explicitly describe the open sets of the product topology (of arbitrary topological spaces) via set-builder notation? (Or differently formulated: What do to if set set ...
2
votes
3answers
688 views

Meaning of $f:[a,b]\to\mathbb{R}$

I was reading this definition and I have always been stuck as to what it means in words. Could someone explain what the function below means in words? $f:[a,b]\rightarrow \mathbb{R}$ is a continuous ...
1
vote
2answers
152 views

Is $i\in n\Leftrightarrow i\in\{0,\ldots,n-1\}$ a common knowledge?

Is $i\in n\Leftrightarrow i\in\{0,\ldots,n-1\}$ for every $n\in\mathbb{N}$ a common knowledge? I am to publish a research article which uses this notation for convenience. The question: Should I ...
3
votes
1answer
391 views

Two questions regarding the ergodic decomposition theorem

In Walters' An Introduction to Ergodic Theory, page 153, Remark (2), he writes If $E(X,T)$ denotes the set of extreme points of $M(X,T)$ then for each $\mu \in M(X,T)$ there is a unique measure ...
1
vote
3answers
149 views

Question about Notation

What does $\mathbb{R}∗\mathbb{R}$ mean? I'm sure this has been asked before, but I do not know how to search for notations in past questions.
1
vote
2answers
194 views

Trying to identify mathematical symbol

I encountered this symbol in an old Adobe mathematical character set, and I'm trying to identify it. I can't find it on Wikipedia's list of mathematical symbols, and it's difficult to describe it for ...
3
votes
1answer
110 views

How should I interpret a set with notation like $\{x | x \in A \Rightarrow x \in B \}$

I've seen it in exercises from a few texts, but it isn't obvious to me. Thanks.
0
votes
2answers
408 views

How to denote a singleton?

I usually denote a set whose elements are distinct by $\{a_p\}_{p \in P}$. And I have a function $f$ which takes a set as argument, so we could write $f(\{a_p\}_{p \in P})$. My question is how to ...
3
votes
3answers
546 views

What are some good examples for suggestive notation?

Motivation: Today I first wondered about and later remembered why the set of all functions from a set $X$ to $Y$ is denoted $Y^X$. They wikipedia page gives the explaination "The latter notation is ...
1
vote
1answer
75 views

Question Concerning The Solution Of A Differential Equation

Here's another question from Advanced Engineering Mathematics by Greenberg [Ex 1.2 Q5]: For what values of the constant $\lambda$ will $y = \exp(\lambda x)$ be a solution of the differential ...
3
votes
1answer
495 views

What's a correct symbolism for “value that maximizes” [duplicate]

Possible Duplicate: Math notation for location of the maximum Given a function $f(x)$, we can normally find $\max_i f(i)$. This expression evaluates to the maximum value of $f(x)$. ...
4
votes
4answers
602 views

Name for “decimals” in other bases?

In grade school, numbers that use a positional notation along with a decimal point (to delimit integer and fractional parts of a number are called "decimals". This "point" notation is easily ...
2
votes
1answer
113 views

Help on mathematical notation and formalisation for the following description

I would like to describe a hypothesis, formally. So I have defined $p = {t_1,t_2,t_3, \cdots, t_n}$ and I would like to say "A pattern $p_i$ is more important than $p_j$, if $t \in p_i$ is more ...
0
votes
2answers
77 views

What is $C^{2,1}(\Omega)$ for general $\Omega$?

What is $C^{2,1}(\Omega)$ if $\Omega$ is arbitrary (i.e. neither open nor closed in general)?
0
votes
1answer
98 views

Notation for $f(n) = \frac{\Lambda(n)}{\log n}$?

Is there any sort of standard notation for the value represented by $f(n) = \frac{\Lambda(n)}{\log n}$, where $\Lambda(n)$ is the Mangoldt function? So essentially a function that is $\frac {1}{a}$ ...
1
vote
0answers
927 views

Notation for a subsequence of a sequence

If we have a sequence (an ordered list) $$ S=(s_0,s_1,...,s_n). $$ What is the notation for expressing that $S'$ is a (ordered) subsequence of $S$?
0
votes
2answers
187 views

Radix point notation and significant digits

So, we represent numbers usually in a form of a sequence of digits where each one of them multiplies the power of a base: $13.2 = 1 * 10^1 + 3 * 10^0 + 2 * 10^{-1}$ So that much is clear, perfectly. ...
2
votes
1answer
74 views

Question about a proof of a theorem about roots of polynomials in field extensions

There is a theorem in my book which says the following: Let $K$ be a field and let $f(X) \in K[X]$ be irreducible over $K$. Then there exists a field extension $L/K$, such that $\exists u \in L$: ...
1
vote
1answer
66 views

Notation question involving discriminant identity

Let $f \in K[X] $ be an irreducible, separable polynomial, and let $M/K$ be a splitting field for $f$. Let $\alpha \in M$ be a root of $f$. Then $D(f) = (-1)^{d(d-1)/2} N_{K/k} (f'(\alpha))$, ...
6
votes
3answers
912 views

What's the difference between “$\to$” (implication) and “$\vdash$” (therefore)?

In Wikipedia, here in the last axiom of the Natural deduction system, it says "From [accepting $p$ allows a proof of $q$], infer $(p \to q)$." Isn't that a tautology? In the big table "Basic and ...
0
votes
3answers
214 views

confusing in SEAL (Software-Optimized Encryption Algorithm) mathematic notation

I'm developing an encryption software based on SEAL algorihm for my research. I found the paper in here My Question is what is the meaning of $$ H_{i \operatorname{mod} 5}^i $$ in page 5? ...
0
votes
1answer
72 views

What exactly is the structure $IM$ for $I$ an ideal and $M$ a module?

If $M$ is an $R$-module, and $I$ is an ideal of $R$, then what is $IM$? That is, does it consist of all products of some form or finite sums of some specific form?
0
votes
1answer
68 views

What is the name of the mathematical structure $y_{ij}$?

I understand $y_{ij}$ can be used to represent a cell in a matrix (i.e., the value in row $i$ and column $j$), particularly where the length of $j$ is equal for all $i$. I know it can also be used to ...
4
votes
2answers
242 views

What is $\gneq$?

I've seen someone asking a question with $\gneq$ ($\gneq$) in it. What does it mean? What's the difference with $\geq$ ($\geq$)? ...
1
vote
0answers
348 views

Notation for limit points of a minimizing sequence: $\arg \inf$

Could you tell me what is the accepted notation for the set of limit points of a minimizing sequence. For example, if I have a function $f(x)$ and a sequence $x_t$ such that $\lim f(x_t) = \inf ...
3
votes
2answers
83 views

Origin of the notation $(x-h)$ and $y-k$ in shifting

Does anyone know the origin of the notation $(x-h)$ and $(y-k)$ when shifting functions in algebra? Why $h$ and $k$?
1
vote
2answers
100 views

Standardized Notation for Well-Known Categories

It seems that every author has rather personal and unique conventions for designating "well-known" categories. This raises the question: Is there a reference available, on-line or otherwise, that ...
2
votes
0answers
167 views

Mathematical Notation questions reading SLAM papers

I'm working through a pair of papers on Simultaneous Localization and Mapping and I'm having trouble with some of the notation as I lack some formal math education. The papers can be found here: ...