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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1answer
38 views

What does $Z_2(S)$ mean where $S$ is a group.

In an article by Bob Oliver "Simple fusion systems over p-groups with abelian subgroup of index p" in Notation 2.2., he defines a set $Z_2 = Z_2(S)$ where $S$ is a nonabelian $p$-group. The problem is ...
3
votes
2answers
80 views

Examples of misleading notation that gives correct results

A lot of the time, in maths, especially when I'm trying to remember a formula, I'm taught to remember it in a way that is not notationally correct, but produces the right result. e.g. when learning ...
2
votes
1answer
54 views

What does an $\oplus$-sign in the superscript mean?

I've come across an expression $ M^{\oplus n_i}$ in an article and I have not seen this before? What does is mean? The whole expression looks like this: $$\large M=M_1^{\oplus n_1}\oplus M_2^{\oplus ...
3
votes
3answers
139 views

Do all mathematical symbols in LaTeX have a meaning?

I debated whether I should post this on the TeX forum or here. Mathematics seemed more appropriate. LaTeX has a ridiculous amount of symbols, including countless variations of the integral sign and ...
2
votes
0answers
85 views

How do we pronounce this symbol $'$ for $p',q'$, etc. And why?

This symbol $'$ for $p',q'$, etc; I know $'$, it is called prum(?) or something close to that, and $p',q'$ are p prum, q prum. But what exactly is $'$ written or pronounced? Thanks. And why is that ...
1
vote
1answer
38 views

Differential geometry notation (tensor vs. others)

As a physicist I am used to working with tensor notation in differential geometry, which is probably better for computation, but, e.g., I've seen $$R(u,v)w = \left( \nabla_u \nabla_v - ...
2
votes
1answer
19 views

$[R(T)]^o$ $?!?!$

I was studying linear algebra(Linear Transformations) a day back and came across this notation and couldn't understand what it meant. Is it the $interior$ of the $Range$ of linear transformation $T$? ...
2
votes
1answer
61 views

History of the Coefficients of Elliptic Curves — Why $a_6$? [duplicate]

I would like to know what is the motivation behind the naming convention of the Weierstrass form of elliptic curves given as $$E:y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6.$$ I can see that $a_1,a_2,a_3,a_4$ ...
1
vote
2answers
62 views

Counting numbers with the digit 5: How to express recurrence relation in closed form?

I figured out the algorithm for finding the count of numbers containing the digit 5 for any power of 10. What is the correct way to express y in this formula? $f(x) = 9y + (x/10)$ Where y is ...
1
vote
2answers
30 views

Notation question (factoral squares?)

Not sure whether factoral is even the right word to use in this context but I'm looking for how you write 'the sum of all the squares' eg 3 = 14 (3^2 + 2^2 + 1^2) 4 = 30 (4^2 + 3^2 + 2^2 + ...
3
votes
1answer
37 views

Notation for a set of objects expressed by symbols

I have two questions about set notation The first one is how you would write down a set of objects expressed by symbols? Let's say we have $n$ persons identified by $p_i$. Can I write: $$P = \{p_1, ...
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votes
0answers
71 views

What does $\langle A,B\rangle$ mean?

If $G$ is a group and $A,B$ are subgroups of it (or, I guess the definition just needs $A$ and $B$ to be subsets of $G$), what does $\langle A,B\rangle $ mean? I know what $\langle A\rangle $ means ...
0
votes
0answers
31 views

Using types instead for basic proofs

Disclaimer: I know close to nothing about formal type theory, but I program intensively so prefer to think in terms of types. In typical math you write $a \in A$ to speak of the nature of your ...
0
votes
1answer
28 views

Cone of convex solutions

I have been reading a paper, on monge-ampere type equations, and the existence of a unique convex solution has been proven to exist in $C^{3,\alpha}(\Omega)\cap C^{2,\alpha}(\overline{\Omega})$, for ...
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votes
0answers
20 views

Infinite Cartesian product - notation for inverse image

Suppose we have an infinite Cartesian product: $$\displaystyle \prod_{i\in I} X_i =\{f:I\rightarrow \bigcup_{i\in I}X_i : \forall i \in I (f(i)\in X_i)\}. $$ Denote by $\pi_j$ the natural projection ...
2
votes
1answer
33 views

Group order notation?

I'm working with Dummit and Foote's Abstract Algebra text, and I encountered some notation that confused me. The theorem I saw it in reads as follows. Suppose $\varphi:G \rightarrow H$ is a ...
3
votes
2answers
72 views

If you were asked to evaluate $x^2$ for $x = -1$

Would you bracket the $x$? I ask this because $-1^2$ is equal to $-1$, but $(-1)^2$ is equal to $1$. Which is valid?
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0answers
45 views

A Question About Notation (Homology with Local Coefficients)

I am currently reading A J Berrick’s An Approach to Algebraic K-Theory, and I am stuck at one of the propositions there because he does not define homology with local coefficients. Proposition: ...
1
vote
1answer
66 views

Can someone what this notation means?

I don't understand what does $\phi_I$ mean The proof includes writing $\phi_I$ as a product of $\phi_{i_1}\phi_{i_2},\dots$, but it doesn't explain what the LHS really means
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votes
5answers
2k views

Why does two terms immediately adjacent “mean” multiply?

I am currently teaching a GED math class. While learning about the order of operations, the students asked why does a number next to a parentheses mean multiplication? I understand the rule that two ...
0
votes
1answer
23 views

Complexity class notation

In my CS courses we often use Big-O notation to denote the complexity of a certain calculation. However, we often also write stuff like: $$mO(1) = O(m),$$ or: $$O(m) + O(n) = O(m+n) = ...
6
votes
1answer
87 views

Why do so few people use the $\equiv$ symbol for identities?

I've always been taught to write, for example, $$\sin^2(\theta)+\cos^2\theta \color{red}{\equiv} 1,$$ rather than $$\sin^2(\theta)+\cos^2\theta \color{red}{=} 1,$$ and $$x(x+2)\color{red}{\equiv} ...
2
votes
0answers
49 views

Is $P(x,y)$ different from $P((x,y))$?

The symbols $P(x,y)$ and $P(z)$ indicate generally the concept of "predicate", but if $(a,b)$ is (ordered) 2-tuple, and in $P(z)$ I have $z=(a,b)$, Is $P(a,b)$ different from $P((a,b))$? .. Thanks in ...
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votes
0answers
22 views

Column or row of a matrix?

The question is so simple, but I cannot find the answer. Is $M_i$ (usually) the $i^{\text{th}}$ column of matrix $M$? Or the $i^{\text{th}}$ row? Since $M_{ij}$ is the $j^{\text{th}}$ element of the ...
0
votes
4answers
40 views

Why do you add +- to only one side when you remove square root from both sides?

As the title says, why when you take a square root of both sides of the equation do you add $\pm$ only to the side which is a number, as opposed to an unknown? For example: $$x^2 = 9 \implies x = ...
6
votes
4answers
131 views

Meaning of $\mathbb{R}^0$, $\mathbb{R}^{1/3}$, and $\mathbb{R}^{-2}$.

In mathematics, we take $\mathbb{R}^n$, where $n$ is a fixed positive integer, to represent the Cartesian product $$ \overbrace{\mathbb{R} \times \mathbb{R} \times \cdots \times \mathbb{R}}^{n \ ...
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votes
0answers
65 views

What's the meaning of $544/119 = 4 + 68/119$?

The Art Of Computer Programming Third Edition, page 4 While explaining Euclid's Greatest Common Divisor algorithm for the numbers $544$ and $119$, Knuth calculates the remainder of $544/119$ ...
3
votes
1answer
79 views

Polynomials vs polynomial functions

On my algebra course, sometimes we write, say $$f \in R[X], f= X^2 + X + 1$$ And sometimes we treat polynomials as functions, so $$ f(x) = x^2 + x + 1$$ What is the difference between these two ...
2
votes
3answers
76 views

What does mod mean in mathematics?

I have sometimes seen notations like $a\equiv b\pmod c$. How do we define the notation? Have I understood correctly that $c$ must be an element of some ring or does the notation work in magmas in ...
0
votes
0answers
111 views

What does a dot in a circle mean?

I'm looking at some formulas involving matrices (in the context of machine learning, but I'm not sure it's relevant) and I came across $\odot$. What could this mean? The context is $M \odot N$, where ...
2
votes
1answer
25 views

Ordered tuples of proper classes

From time to time I encounter notation like this: A triple $\langle \mathbf{No}, \mathrm{<}, b \rangle$ is a surreal number system if and only if ... The confusing part is that a proper class ...
1
vote
1answer
57 views

What does the symbol $\mathbb{R}(\zeta)$ denote?

I know hat $\mathbb{R}[\zeta]$ denotes the ring of polynomials in $\zeta$ with real coefficients. I came across the symbol $\mathbb{R}(\zeta)$. Which ring is this?
1
vote
1answer
38 views

$\mathbb{R}_*$ Notation

What does the notation $\mathbb{R}_*$ denote? I am seeing it used for showing domain of matrices, $M\in \mathbb{R}_*^{a \times b}$, which is different from $N \in \mathbb{R}^{a \times b}$. But I do ...
2
votes
2answers
53 views

How to write a counter in proper notation?

I have made a system where I count every hour that meets a certain condition. I would now like to express this in a simple formula but sadly can not come up with a solution. This is what I need. ...
0
votes
2answers
84 views

Are subscripts 0 or 1 based?

Being a programmer by nature I can never remember when looking at a math formula if the subscript that indicates which value in a series starts at 0 or 1. I know computer arrays start at 0 so that is ...
0
votes
1answer
12 views

How to state each individual solution of an expression is evenly divided by n as opposed to their sum being divided by n

Given that for k2n (n=4 and k takes all integer values from 1 to n) If we want to state the sum of all solutions is evenly divisible by n we write: n ∑ k2n = 0 (mod n) k=0 ...
0
votes
1answer
29 views

Quick question about contravariant and covariant tensors

I have seen many different notations to denote contravariant/covariant and mixed tensors. For example, I think the notation $\omega^{v}_{\,\,\,\mu}$ stands for a mixed tensor, where one index ...
0
votes
0answers
28 views

Notation of the Weierstrass Sigma Function

This is with regards to the Weierstrass $\sigma$-function belonging to a pair of periods $(\omega$,$\omega')$ where $\frac{\omega}{\omega'}\notin \mathbb{R}$. The notation of this function in my ...
0
votes
1answer
36 views

A notational confusion on gradient

Given a parametrized function $f_{w}: \Bbb R ^{m} \to \Bbb R ^{k}, w \in \Bbb R^d$, I see in a book the following notation $\bigtriangledown ^ {w} f_{w}(.)$ denote its gradient w.r.t. $w$. What is the ...
3
votes
3answers
81 views

Notation for choosing the k smallest elements from a set of integer

Is there any specific notation for picking $k$ elements from a set which are the smallest? Ex: {$1,3,5,7,9,11$} with $k = 3 \Rightarrow$ We want $1,3,5$
1
vote
1answer
84 views

What is the difference between a sequence of functions $(f_n)$ and a sequence of functions $f_n(x)$?

What is the difference between a sequence of functions $(f_n)$ and a sequence of functions $f_n(x)$? I am reading my textbook on analysis, and it seems to use 'sequence of functions' to describe both ...
1
vote
0answers
37 views

Integration notation

could someone explain the following notation: $u(x,t):=\int^t_0 v(x,t:\tau)d \tau$ It's come up but I don't understand how to interpret the semicoloned tau
0
votes
1answer
28 views

How to notate a set of point meeting a given condition?

How do you formulate the set of the n closest neighbours within the radius r of point P with proper mathematical syntax?
2
votes
1answer
51 views

Meaning of dot symbol “·” in this context?

In this context, what does the dot symbol "·" mean? Multiplication? I looked it up on Wikipedia but couldn't find it.
0
votes
1answer
70 views

Notation for dimension of vector space

Is it an unusual notation to write $|V|$ for the dimension of a vector space $V$? Is it ok to use it if you blur the distinction between the grid for the finite element method and its associated ...
2
votes
1answer
31 views

What is the meaning of $<$ in a preorder?

Let $(P,\le)$ be a preorder, i.e. $P$ is a set and $\le$ is a relation on it that is reflexive and transitive. In this context for myself I can find two interpretations for the symbol $<$ 1) ...
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0answers
47 views

Given a line bundle $M$ and ascheme valued point $a$, what is $M(a)$?

I am reading Olsson's book http://math.berkeley.edu/~molsson/mono020807.pdf . If $M$ is a line bundle on an abelian group algebraic space, he considers scheme valued points $a \in A$ and $M(a)$. I ...
1
vote
1answer
32 views

The origin labelled on a graph: $0$ or O?

When one draws a graph, say in the x,y plane, we label the origin with a circular/elliptical symbol. Now is this a $0$ (zero), or is it O (for Origin), or simply just a circle/ellipse? Can it be ...
0
votes
3answers
66 views

Set question - $ ℤ^+ = ℕ$ [duplicate]

I am not sure whether the following statement is true: $ ℤ^+ = ℕ$ if not, why? Thank you in advance! I appreciate your help!
0
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5answers
52 views

Kronecker delta versus identity matrix

How should $\delta_k^j$ be regarded? Is it a scalar that takes on variable values? A 3x3 identity matrix (in 3 dimensions)? The wikipedia article on raising and lowering indices with the metric ...