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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23 views

Notation for vector of expectations

I have $n$ 'types' in a population. The frequency of each type is given by a $1 \times n$ row vector $\boldsymbol{x} = (x_{1},...,x_{n})$ (I'm treating this a random vector). I also have an $n \times ...
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0answers
37 views

What is this notation $\odot$ for?

(Note that symmetric algebra and symmetric tensor do not coincide when the characteristic is not $0$.) I'm reading this aricle:http://en.m.wikipedia.org/wiki/Symmetric_tensor And here it defines ...
3
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0answers
40 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
2
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1answer
38 views

Notation for the direct sum and Kronecker sum of matrices

The tensor product $w = u \otimes v$ of two vectors $u \in \mathbb{R}^m$ and $v \in \mathbb{R}^n$ is usually defined as \begin{equation} w_{in + j} = u_i v_j \text, \end{equation} and the Kronecker ...
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1answer
23 views

Clarification of absolute Galois group temrinology

In a paper by Mazur, he writes "the profinte group equal to $G_{K,S}$ for some algebraic number field $K$ and finite set of primes $S$ in $K$. I understand $G_K = \text{Aut}(\overline{K}/K)$ but not ...
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0answers
20 views

Product of the LU Factorisation - Correct Formula?

Let's say I have: $$ U = \begin{bmatrix} 1 &2 &3 \\ 0 &1 &1.3 \\ 0& 0 & 1 \end{bmatrix} $$ $$ L = \begin{bmatrix} 10 & 0 & 0 \\ 40 & -30 & 0 \\ 10 & 30 ...
0
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1answer
21 views

Symbol meaning in a paper about elliptic curves

I was reading an introduction on elliptic curves, when the symbol $$\mathbb{F}_p^{\ast}$$ showed up. I understand that $\mathbb{F}_p = \mathbb{Z}/p\mathbb{Z}$ is the Galois field of the integers ...
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5answers
110 views

Where could (do?) we go after exhausting greek letters?

I'm still in high schools but after all my various math and science classes including calculus, statistics, geometry, and physics, I think that we've pretty much run the course of both upper and lower ...
3
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0answers
35 views

Which symbol to use for composition of a sequence of functions [duplicate]

I know how to write the composition of two functions: $f\circ g$ but I don't know whether there's a standard symbol for a sequence (similar to $\sum_i{f_i}$, $\prod_i{f_i}$ or $\bigotimes_i{f_i}$, ...
2
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5answers
217 views

What does $\prod_{k=-2}^{11}(15-3k)$ mean--and how might I compute it?

$$\prod_{k=-2}^{11}(15-3k)=\;?$$ I'm new to this and have not seen this notation before. Can anyone explain to me what this is called and how to solve or compute it?
0
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0answers
34 views

How to explain such mathematical notation

I meet such math notation $\mathbb{R}^2_+$ in the paper. However, I wanna whether it means a vector of real number.
2
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2answers
29 views

Shorthand for elements in a set and elements in a vector/list?

Really basic notation questions ahead. For both cases below, suppose I have an arbitrary set of integers $S$, e.g., $S = \{2, 4, 6, 8\}$. I want to define a list/vector whose elements are ...
1
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2answers
64 views

The Operator '$d$' Apparently Having two Different Meanings in Differential Geometry.

Given a smooth map $f:M\to N$ between smooth manifolds $M$ and $N$, we denote the global differential of $f$ by $df$. Also, the letter '$d$' is used for denoting exterior derivative of a differential ...
2
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1answer
33 views

Notation of author-defined functions.

I have seen functions defined various ways, and I'm wondering which form I should use for some functions. I am hoping to learn what it might be read as, interpreted, etc. The most common definition ...
3
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0answers
36 views

Can We Write the Differential in Terms of Covectors?

Let $f:\mathbf R^n\to \mathbf R$ be a smooth map. We can write $df:T\mathbf R^n\to \mathbf R$ neatly as $$ df = \sum_{i=1}^n(\partial f/\partial x_i) dx_i $$ For a function $f:M\to \mathbf R$ defined ...
2
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1answer
50 views

Implementing the $\Rightarrow \Leftarrow$ contradiction symbol?

How is the $\Rightarrow \Leftarrow$ symbol actually used in practice? I think my issue here is that I don't know what the symbol is meant to mean. For example, I know that $\implies$ means "which ...
3
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2answers
59 views

what does $[0,1]^\omega$ mean

The question is, Give $[0,1]^\omega$ the uniform topology, find an infinite subset of this space that has no limit point. I just want to know what does $[0,1]^\omega$ mean so I can proceed. I'd ...
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2answers
102 views

What does this notation mean: $\mathbb{Z}_2$

$\mathbb Z$ (Our usual notation for the integers) with a little subscript at the bottom. This is the question being asked: what are the subgroups of order $4$ of $\mathbb Z_2 \times\mathbb Z_4$ ...
6
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0answers
95 views

Why use Einstein Summation Notation?

Einstein summation convention dictates that repeated indices should be summed. Thus the equation $a_{ij} = b_{ik}c_{kj}$ is taken to mean $a_{ij} = \sum_k b_{ik}c_{kj}$ where in both cases the range ...
1
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0answers
20 views

Denoting bijection (conjugation) in a commutative diagram

I have a simple notation question: I there a standard way how to denote in a commutative diagram that a map is a conjugation? I thought of the following three, but: The left one (simple arrow) ...
0
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0answers
23 views

When to use $argmin$ and $Argmin$?

What is the difference between the notations $argmin$ and $Argmin$ precisely? If I'm not mistaken one is used when the set of points attaining a minimum of a function has more than one point and the ...
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0answers
26 views

Mathematical (and any other related e. g. statistical/economic…) Notation System

I would like to ask where I could find really extensive source (websites, books, whatever you are aware of) for studying purposes in terms of mathematical notations. This is really a must for me, ...
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1answer
42 views

What this notation R^3 ∖ (0, 0, 0) means?

I was reading a "Projective Space" article on Wikipedia, when I came across this line "equivalent definition is the set of equivalence classes of $\mathbb R^3 \setminus (0, 0, 0),$ i.e. 3-space ...
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0answers
13 views

The definition of $C(\bar U)$.

In 'Partial differential equations, Evans', $C(\bar U)$ is defined by the space of continuous functions $u\in C(U)$ such that $U$ is uniformly continuous on bounded subsets of $U$. But I have known ...
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1answer
53 views

Why is the notation $f=f(x)$ mathematically correct?

Looking at the equation, which is written all over my textbooks, $f=f(x)$ or $\mathbf r = \mathbf r(x,y,z)$ or what-have-you, I can't help but think that that is just wrong. On the LHS is a function. ...
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2answers
65 views

“for almost all” symbol

Is there a standard symbol for “for all but finitely many”? I had a professor who used to make an inverted capital lambda crossed by a little concave arc. And I found it in Super-recursive ...
6
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2answers
39 views

Is there any convenient notation for a vector entry j at iteration step i?

I have a stupid question: I'm writing a master thesis and I have to describe an iterative method of an algorithm. The method uses vectors which are manipulated at each iteration step. Now my ...
0
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1answer
16 views

Notation for disjoint inequalities

Is there a standard notation for representing disjoint inequalities? For example, let's say that I have an equation that may be solved under the following conditions: $ x \leq a$ OR $ x \geq a+b$ is ...
0
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1answer
29 views

Correct notation for “slice” of Integers

Say I want to have the set of all integers between any two given integers $a$ and $b$. For example, if I want the set of all integers between $-3$ and $7$ I would get: $$ \{-3,-2,-1,0,1,2,3,4,5,6,7\} ...
0
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0answers
54 views

How to present set of point in mathematical way

I have a question about presenting the set of point in the math. I have two sets in domain $\Omega$. $M$ is set of $m$ point locations, $N$ is set of $n$ point locations. In which,some points in the ...
0
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2answers
18 views

Is there any difference between those two notations of a quantum state?

In "Quantum Computing verstehen", the author uses both $|ab>$ and $|a,b>$ to describe the state of a 2-bit quantum register. Is there any important difference between those two notations or do ...
0
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0answers
19 views

Notation for image and kernel capitalization of first letter

In the mathematical notation for image and kernel one usually writes $\ker$ for kernel and $\DeclareMathOperator{\img}{Im}\img$ for image. Why is the "k" small but the "I" big?
1
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0answers
26 views

Notation $\mathrm{mod} $ in ergodic theory

Does someone know, what exactly is meant by the following: $$T^{-1}A=A \mod \mu$$ where $\mu$ is a $T$-invariant measure?
0
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1answer
20 views

Representing textual solution to problem using Math notation

If I person $A$ & $B$ both have $40$ dollars, how much must $A$ give $B$ so that B has $10$ dollars more that $A$? Answer is $5$ dollars. $A$ now has $35$ dollars while $B$ has $4$5 dollars. How ...
4
votes
4answers
132 views

Why can you not omit the '*' sign for multiplication in Sage, Matlab, and other mathematical software?

Question I have some experience with Sage and Matlab. Both mathematical software packages require you to have the '*' sign when multiplying symbolic variables with integers. For example, in Matlab ...
2
votes
1answer
58 views

What does $E^{\mathbb{C}}$ mean?

I was reading a book (Symplectic Geometry and Quantum Mechanics) and find it hard to understand this following example: Definition: a "complex structure" on a vector space $E$ is any linear ...
1
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1answer
29 views

Slice, projection, contour: A terminology question.

Consider a multivariate function, say $y=f(x_1,x_2,\dots,x_n)$, and suppose that $z=f(x_1,x_2,\dots,x_{n-1},g(x_1,x_2,\dots,x_{n-1}))$. What do we call $z$ with respect to $y$? Projection, level set, ...
0
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1answer
40 views

Mathematical notation: sorting nonzero elements in a matrix

I have a set $X = \{X_1,\ldots,X_n\}$ where $X_i = [x_1,\ldots,x_m]$ and $x_k$ can be any positive integer value including zero. I want another set $Y$ such that only the values of $X$ that are ...
1
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0answers
52 views

What's the definition of $x^g$?

My question is really simple. I'm studying a book of group rings which doesn't define what is $x^g$, where $x,g$ are elements of the group $G$: Thanks
1
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2answers
32 views

Meaning of notation $v \mapsto ( x \mapsto f(x,v) )$

I came across this notation in this wiki article. Can anyone tell me the meaning of this notation? What exactly is happening here? $v \mapsto ( x \mapsto f(x,v) )$ What I understand here is $x, v ...
4
votes
2answers
37 views

Should I use different parenthesis in calculations?

I was taught in a school that one should denote the order of computations by different brackets like $2\cdot \{3+[2\cdot (8+9)]\}$ Do the teachers taught me wrong as for example the notation $\{\}$ ...
1
vote
1answer
24 views

how to express finite set of finite sequences

I want to define a finite set of finite sequences and they may have distinct cardinality. Is it correct to express this as follows: Let $S=\{x_{n_{i}}: n=0,1,...,m \quad \text{and} \quad ...
7
votes
1answer
94 views

What came first, the $\forall$ or the $\exists$? [closed]

I imagine that these symbols originated in one of the following ways: "I will declare a symbol for "for all." I will just use the letter "A" flipped upside-down. Yes, let $\forall$ represent "for ...
1
vote
2answers
32 views

Curious about some (basic?) linear algebra notation

I was reading an old linear algebra textbook today, and I was actually having some trouble understanding the notation given in a problem. Here is what it said (or something similar): Consider the $n ...
5
votes
3answers
89 views

Integration with $d($“some function”$)$ instead of $d($“some variable”$)$.

$$\int x\,d(x^2)=\;?$$ I am confused with this. Usually we have $d($"some variable"$)$, not $d($"some function"$)$. My attempt is the following: $$\int x\,d(x^2)=\int ...
16
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5answers
3k views

How many digits does the integer zero have?

Should zero be classified as having no digits, or 1 digit?
1
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4answers
69 views

How to represent sign function in range $[-1, 1]$

I have a function that is defined as follows: $$f(x) = \begin{cases} 1 & \text{if $x \ge0$}, \\ -1 & \text{if $x<0$}. \end{cases}$$ I would like to represent the above function by the ...
0
votes
3answers
70 views

Formal notation for representing decimal numbers

What is the formal mathematical notation for representing a decimal number using variables as it's digits? I am honestly surprised that this has not been asked yet on MSE. Let me clarify a ...
2
votes
1answer
41 views

Writing an expression as a product of products

I am currently dealing with the following expression: $$\left(\prod_{i=1}^{N-1}(\lambda_N-\lambda_i)\right)\left(\prod_{i=1}^{N-2}(\lambda_{N-1}-\lambda_i)\right)\cdots (\lambda_2-\lambda_1)$$ Is ...
5
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4answers
88 views

What does $\Bbb{C}(X)$ refer to?

I have from a book (b) Let $E = \Bbb{C}(X)$. Then $\operatorname{Aut}(E / \Bbb{C})$ consists of the maps $X \mapsto \dfrac{aX + b}{cX + d}, ad-bc \neq 0\ldots$ Not sure what $\Bbb{C}(X)$ is. ...