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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112 views

Notation for “parallel” morphisms in a diagram

Suppose $f\colon A\to B$ and $g\colon A\to B$ are possibly-distinct morphisms. How do I stick them both in a diagram (along with, e.g., their (co)equalizer) without suggesting that they are equal?
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2answers
50 views

notation question re: function space

This is a quick notation question: when one writes $X: C[0,\infty) \to \mathbb{R}$, what does that mean exactly? Is $C[0,\infty)$ the space of continuous functions with a domain of $[0,\infty)$ and ...
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1answer
17 views

Unfamiliar with notation : $S \subseteq [d]$ where {$d, w_{1},w_{2}, …, w_{d}$}

What does $S \subseteq [d]$ mean in the context of {$d, w_{1},w_{2}, ..., w_{d}$}? I don't get what [d] stands for.
3
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0answers
58 views

Complex root notation

Is there a standardized way to distinguish between real and complex roots? In other words, is there a convention about how to I formally write that I expect $\sqrt[3]1$ to be solved in $\mathbb C$, ...
5
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3answers
823 views

Group theory notation

What does the notation $(G,.)$ mean in group theory? I have seen in places that $.$ implies the binary operation multiplication on group $G$. But then, why do we show an abelian group as $(G, +)$? And ...
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1answer
18 views

schematic representation of circular permutation in a set?

I would like to represent digits in a set in a way that the set emphasizes the order of the digits schematically in the set in order to avoid confusion with a set of combinations. For example, how ...
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2answers
191 views

Notation: Why do we learn to write the higher powers in an equation first?

I have always written equations in the form $y=ax^2+bx+c$ but after entering an equation into Wolfram Alpha I noticed that the answer was displayed in the form $y=c+bx+ax^2$. I know that there is no ...
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1answer
379 views

Symbol of equivalence for comparing two equations?

If I need to compare two distinct equations, such as $y=\log_a x$ and $x=a^y$, is there any symbol that I can use in order to compare them instead of using words: "[equation 1] is equivalent to ...
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1answer
49 views

Notation of double-sided infinite sum

The notation $\sum_{k=1}^\infty a_k$ always means $$\lim_{n\rightarrow\infty}\sum_{k=1}^n a_k.$$ What about $\sum_{k=-\infty}^\infty a_k$, such as in the Laurent series? Does it always means ...
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1answer
60 views

Notation for signatures

A (multi-sorted) signature consists of some sort symbols, say $X$ and $Y$, together with some constant symbols, say $0,1 : X$, some function symbols, say $f : X \times Y \rightarrow X$ and $g : Y ...
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1answer
94 views

Correct interpretation of Kleene (Intro to Metamathematics) symbol $\vdash^x$ in Predicate Calculus

Rif. S.C.Kleene, IM (1952) : which is the correct interpretation (or the "modern equivalent") of the "x" used as exponent of the "turnstile" as in: $$A(x) \vdash^x \forall xA(x)$$ [see Derived Rules ...
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1answer
96 views

What does the notation $G /^r H$ mean?

$G /^r H$ I saw this notation in an answer to a question and am not sure what it means. The exact context is as follows: $G=Sym(5)$ acts on the set $G/^r H$ of all right cosets of $H$ in $G$.
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2answers
34 views

$\mathbb{F}_{p}A$-module

Yesterday I was introduced to the definition of a module in a course: "Homological Algebra". I'm doing a project involving $p-$groups and in the text I got from my supervisor they use the word: ...
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1answer
53 views

Notation for exists two elements in a set with properties

I'd like to say: for any x in set X, if x is colorful, there must be t1 and t2, both in set T, such that t1 < t2 and green(x,t1) and red(x,t2). I believe this is the correct notation, but I'm not ...
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1answer
100 views

What does $F\left(x\right) \in L$ mean?

This is a notation question: In R. Duffin, “The Reciprocal of a Fourier Series,” Proc. Am. Math. Soc., vol. 13, no. 6, pp. 965–970, 1962. After Eq. 1, the author says "The Fourier coefficients of a ...
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1answer
275 views

Notation for differentiable

The conditions for the Mean value theorem is that if $f$ is defined on a closed interval $[a,b]$, f is continuous on [a,b] and differentiable on $(a,b).$ Then there exists a $\xi$ in [a,b] such that ...
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3answers
366 views

Prime notation in integral?

Recall the definition of potential energy: $$ U_x-U_{x_0} = -\int^x_{x_0}F_x(x')dx' $$ I've seen the integral definition of work, but not this - the thing I'm specifically interested in is the ...
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1answer
81 views

Notation for derivatives at a certain point

Is the notation for values of a derivative at some point that I used in this question commonly accepted and understandable? Is there a more preferred one? For those who familiar with Mathematica ...
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1answer
29 views

Validity of notation from the aspect of function description

I have the following notation that should describe the nature of my function $for \forall a \in A \exists f:A \rightarrow S, A \subset N, S \subset [0,1]^n,|S|=n$ Can anyone tell me is the notation ...
2
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1answer
60 views

Notation for translating vectors

I'm completely new to vector geometry and recently encountered some new notation (and wholly unfamiliar) for the translation of vectors. $$T:Z \mapsto A + Z$$ The above is described as A ...
2
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1answer
73 views

Notational Alternatives to Subsubscript

I find myself using expressions like $$a_{0_2}, (a_{n_k})_{k \in \mathbb{N}}, b_{i_{j_k}}, etc.$$ I find subsubscript and more generally, $(n \cdot \text{sub})$script for $n\geq 2$ pretty ugly and ...
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1answer
90 views

Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$?

I want to express the following statement about a function $f(n)$: there exists $f_\Omega\in\Omega(h(n))$ such that $f\in O(g(f_\Omega(n))$. What's the correct notation for this? Is it $f\in ...
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2answers
175 views

The notation $\mathbb{Z}[\alpha]$

Let $\alpha$ be a real number. I'm studying group theory from the notes of my brother (I'm 16) and I often jump into the notation $\mathbb{Z}[\alpha]$, which, however, is defined nowhere through the ...
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1answer
934 views

Difference between $\mathbb Z^+$ and $\mathbb N$

$\mathbb Z^+$ stands for the Positive Integers: $\{1,2,3,4,5\dots\}$ $\mathbb N$ stands for the Natural Numbers: $\{1,2,3,4,5\dots\}$ So what is the difference between $\mathbb Z^+$ and $\mathbb N$? ...
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1answer
117 views

Vector by integral, notation convention or mistake?

A part of a formula in my engineering book states $$\int_S\overrightarrow D\,\mathrm d\!\overrightarrow S$$ What I'm wondering about is bounds of integrals being a scalar, and the differential being ...
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1answer
36 views

Which set is this $I_p(p)\cdot \Gamma(E)$?

Let $\pi:E\rightarrow M$ be a smooth vector bundle and $p\in M$. Consider $$I_p(M)=\{f\in C^\infty(M): f(p)=0\},$$ and $\Gamma(E)$ the $C^\infty(M)$-module of smooth sections over $E$. Notice $I_p(M)$ ...
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1answer
403 views

Symbol for “is closest to”?

I am writing a paper on probabilities and we have to find a $k$ such that $P_n(k)$ is "closest to" $P_0$. $P_0$ is getting 4-of-a-kind in a five card hand in a standard 52 card deck. $P_n(k)$ is ...
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1answer
1k views

How to find the ratio of two numbers written in scientific notation, such as $ 2.69 \cdot 10^{-8} $ and $ 2.23 \cdot 10^{-7} $?

The numbers are forces and he wants us to put them in a ratio in order to compare them, but I'm really bad at ratios so. $ 2.69 \cdot 10^{-8} $ Newtons is obviously smaller than $ 2.23 \cdot 10^{-7} ...
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3answers
283 views

Basic question: what does the notation $[A,B]$ mean?

If $A$ and $B$ are both matrices, what is $[A,B]$? I understand that it is a commutator and that $[A,B]=AB-BA$, but since I don't know what a commutator is, none of this information is telling me ...
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2answers
6k views

What is the use of Delta symbol in set theory?

What is the use of $ \Delta $ in set theory?
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3answers
36 views

significant figure representation?

I was wondering: Why does $1.30 \times 10^3$ have $3$ significant figures while $1300$ has $2$ significant figures (they are both the same number) Why is that distinction ? When should I use ...
3
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1answer
2k views

What does 'sign' mean in an equation?

I'm curious what sign means in the context of mathematical notation. I'm reading a paper right now and it uses: $$ sign \overrightarrow{\lambda} \cdot ...
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4answers
114 views

When are square and curved brackets interchangeable?

Is it ever acceptable to interchange square and curved brackets? E.g. are the following both acceptable (and identical)? $$x = t(a + [b + c])$$ $$x = t(a+(b+c))$$
2
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1answer
307 views

Problem with notation: Laplacian on a manifold

In the Aubin's book "Nonlinear analysis on manifolds" the Laplacian operator on functions on some smooth manifold is defined by the formula $$ \Delta = -\nabla^\gamma\nabla_\gamma, $$ where ...
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1answer
89 views

The difference between a / and ÷ use

I'm confused with the $/$ symbol meaning the same as $÷$ $4+2(8-3)÷2-1$ should equal $8$ using PEMDAS. However if using the Wikipedia's definition of the slash "Used between numbers slash means ...
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1answer
156 views

Category of topological pairs

Is there a standard abbreviation for the category of topological pairs? I have searched for it in vain.
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1answer
170 views

notation for a torus

I am trying to search for the meaning of this notation but unfortunately it seems that wikipedia even doesn't have it. The book I am following uses the following notation for a torus: $\mathbb{T}^d = ...
2
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1answer
89 views

How to read this mathematical expression?

I am very much interested in machine learning. I would like to do research in this subject. But presently the mathematical language used in this subject is hard for me. Here is an expression in wiki ...
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2answers
101 views

Meaning of the set $\mathbb N^\mathbb N$

I came across a question which requires one to check if there's a bijection from the set $ \mathbb N^\mathbb N$ to another set. I've never seen a set defined this way and was wondering if this was ...
2
votes
3answers
143 views

What does $|A|$ denote in set notation?

What does $|A|$ of a set $A$ denote? Also, what does $A\leftrightarrow B$ of sets $A, B$ mean? I encountered this in one of my textbooks which said: Of two sets $A, B$ we know $|B|$ but $|A|$ is ...
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1answer
352 views

Why are Set Cardinality and Absolute Value denoted the same way?

When we have a set $A$, it is conventional to denote the cardinality of $A$ as $|A|$. When we have some number $n$, it is conventional to denote the absolute value of said number as $|n|$. My ...
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4answers
265 views

Correct formal interval notation

I can't find any definitive answer on this topic, maybe that's because there isn't one, but I figured if there was a place to ask then SE was it! To describe a set in which $x$ and $y$ are in the ...
2
votes
1answer
75 views

What is the meaning of $1_{a>b}$?

What would this mean: $1_{a>b}$ .. Based on the context, it could mean "$1$ if $a>b$ else $0$", but it's the first time I see it so help would be appreciated.
2
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1answer
241 views

Notation in group theory?

I have three questions on notation. What does the squiggly line mean in the following: $Aut(G) \cong Aut(G) \wr \mathbb{Z}_2$ What does $\rtimes$ mean in the following: $ \varphi :(Aut(G)\times ...
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1answer
81 views

Can the elements of a direct sum be thought of like that?

I've asked here about the tensor algebra, and I think that my problem is being able to realise the elements of a direct sum as linear combinations. Indeed the rigorous definition I have of the direct ...
2
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0answers
229 views

About the raised negative sign in some basic textbooks

In a math document recently (a UK A level test paper from the EdExcel board), I noticed that the negative/minus sign was raised and aligned to the top of the number. I'm interested to know whether ...
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3answers
62 views

Where V is a Vector Space, $\forall \overrightarrow{v} \in V, 0\overrightarrow{v} = \overrightarrow{0}$

I'm denoting all vectors as such: $\overrightarrow{v}$. Any variable without an arrow above is a scalar. Suppose $V$ is a vector space over $F$, with additive identities $\overrightarrow{0}$ and $0$ ...
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1answer
294 views

Probability, mathematical symbol

Good day, Would like to ask about the meaning of ^ in P(S^B) as shown in the image below. Thanks for your help!! Regards, Math noob
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2answers
86 views

Notation for the Set of All Finite $n$-Tuples from a Set $A$

Let $A \ne \emptyset$. Let $S = \{(a_1, a_2, \ldots , a_n) : a_i \in A$ and $ n \in \mathbb{N}\}$. Now I'm curious if there is a more concise (and standard) way of writing this set down?
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28answers
8k views

What are some examples of notation that really improved mathematics? [closed]

I've always felt that the concise, suggestive nature of the written language of mathematics is one of the reasons it can be so powerful. Off the top of my head I can think of a few notational ...