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
votes
1answer
132 views

Is there a standard or common way to concisely write scientific notation in different bases?

Is there a standard or common way to write scientific notation in different bases that doesn't require repeating the base in both the coefficient and the exponent base? For example, this notation is ...
3
votes
2answers
189 views

What notation should I use to describe circular motion using only 2D vectors?

According to wikipedia, the vector equation describing velocity during circular motion is $ \mathbf{v} = \boldsymbol{\Omega} \times \mathbf{r} $, where $\Omega$ is the axis of rotation, with a ...
2
votes
1answer
152 views

$u \in L^2(R^n)$ what does this mean?

$u \in L^2(R^n)$ I am guessing that $L^2(R^n)$ means the $L^2$ norm over an n-dimensional vector. The context is an energy minimization function : total variation–based model of Rudin, Osher, and ...
4
votes
1answer
253 views

What does the notation $1_\Omega(x)$ mean?

An author in a paper suggests that a binary function f(x) can be expressed as $f(x) = 1_\Omega(x)$ where $f(x) \in \{0,1\}$ for all $ x \in R^2$ $\Omega$ is an arbitrary bounded measurable subset ...
1
vote
2answers
233 views

question on jargon and notation of higher order functions

I'm looking for the right jargon and notation to represent the following situation: Let's say you have two functions, one that maps values from $A$ to $B$ and one that maps values from $C$ to $D$. ...
1
vote
0answers
768 views

Modulo operation notation

I would like to write that some polynomial $p(x)$ is the sum of polynomial $d(x)$ and the remainder of division of polynomial $b(x)$ by polynomial $w(x)$: $$p(x) = d(x) + b(x)\bmod w(x)$$ But from ...
1
vote
1answer
90 views

Naming: How to call a direct product of elementary abelian groups?

Is there an accepted name for abelian groups of the form $\prod_{i=1}^n \mathbb{Z}_{p_i}$ for some primes $p_1,\dotsc,p_n$? (i.e: direct products of cyclic groups of prime orders, or in other words - ...
1
vote
3answers
130 views

Terminology for combining ordered pairs?

Suppose I have two ordered pairs $(a_1, b_1)$ and $(a_2, b_2)$, each of type $A \times B$ I want to combine them into a single pair of type $A^2 \times B^2$: $(a_1,b_1)$ OP $(a_2,b_2)$ = $( ...
9
votes
1answer
10k views

Mathematical notation for the maximum of a set of function values

I have a question about the proper notation of the following (simplified) example: I want to express that I have a value alpha, which is the maximum of a set of n values. Each value in the set is the ...
5
votes
2answers
822 views

Formal notation related to a sequence or a set

My question is quite naive... I just want to represent a finite sequence of Natural number, is it the best way to write it like this?: $\langle a_0, \ldots, a_n \rangle $, where $\forall i \in [ 0, ...
4
votes
1answer
309 views

Notation - Two adjacent vectors?

I'm studying multivariable calculus at the moment and have come across equations involving two bolded variables placed side by side, like so: $$ \nabla \mathbf{f}=\frac{\partial {{f}_{j}}}{\partial ...
2
votes
1answer
422 views

Formal notation related to Cartesian product

I have defined a set L and another set R, and a set S = L x R for the Cartesian product of the two sets. My question is quite naive. Given an element $s \in S$, is there a formal way to express its ...
4
votes
2answers
331 views

Meaning of $\lim_{p\to 0^+}$

I would like to know the interpretation of limit expression which calculates the number of non-zero entries in vector $x$ in the expression below: $$\lVert x\rVert_0 = \#\{i \mid x[i] \neq 0\} = ...
3
votes
1answer
931 views

Determine if function is little-o, little-omega or big-theta

Let $f(n) = n^3(5+2\cos(2n))$ and $g(n) = 3n^2+4n^3+5n$. Given these two functions, I must determine the appropriate symbol where the underscore is: $f(n) \in \_(g(n))$ So, first thing to do is take ...
5
votes
1answer
312 views

Notation for different sizes of infinity?

i realize that there are multiple sizes of infinity so one can be larger than another, but how do you show that one infinity is larger. I'm not looking for proofs or anything but I just want the ...
2
votes
2answers
199 views

Tensor power- Notation question

I have a notational question, which is written usually in papers, but I can not figure it out what could be. Let $M$ be an $A$-module. I have seen this notation $$M^{\otimes -n}$$ I think this would ...
0
votes
2answers
290 views

What does $\langle x,3\rangle$ mean if I'm talking about $\mathbb Z[x]$

I know this sounds like a basic question but I'm really confused. What does the notation $\langle x,3\rangle$ refer to for $\mathbb Z[x]$? Can someone write out what this is?
5
votes
1answer
402 views

What is the meaning of superscript ⊥ for a vector space

This should be an easy question, if A is a matrix, then the nullspace of A is a vector (sub)space. Then, what is the meaning of superscript inverted T on a vector (sub)space? e.g. $(\mathrm {nullspace ...
3
votes
2answers
369 views

What does $(x, y) \in \mathbb{R}^2$ mean?

In my homework, we are given the following set $M = \{ (x, y) \in \mathbb{R}^2\, |\, x^2 + y^2 \leq 1 \}$. Obviously, this represents the set of all points $(x, y)$ that lie within a circle of radius ...
0
votes
2answers
116 views

What is the correct notation to state that a variable can either be empty or not?

I want to express through a variable, that a certain action is either done, or not. When the action is done, the variable should have value 1, if not, the variable should be empty. How do I express ...
3
votes
2answers
564 views

What is the notation for calculating the mode?

Question: What is appropriate notation for calculating the mode of a function? In this case, I use the mode of a Gamma(a,b) distribution in a cost-function. I am looking for something analogous to ...
7
votes
5answers
2k views

'is odd' / 'is even' notation

I would like to write down that $x$ is $true$ if $n$ is odd and $false$ if $n$ is even. So far I made this up: $x = ( n - 2⌊\frac{n}{2}⌋ = 1)$ However, I was wondering whether this can be expressed ...
0
votes
2answers
318 views

Notation question: $x\ln^2(1000/y)$ into MATLAB

I've been tasked with working out how much some incorrectly entered calibration coefficients have affected some measurements we've taken. I have the algorithm used, which I can use to work backwards ...
1
vote
0answers
138 views

Notational question on generalized scalar product

Maybe not precisely a math question, but certainly related, and apparently there even is a notation tag :) We can think of the standard vector scalar product, $$ \langle \vec{x}, \vec{y} \rangle := ...
6
votes
2answers
2k views

Formally writing about lists (tuples), and notation analogous to set notation

Is there any formal notation for dealing with lists, rather than sets? e.g. if I have a set $X=\{x_1,\dots,x_n\}$ and I want to add a new item to the set, say $x_{n+1}$, I can say "Let $X = X \cup ...
1
vote
3answers
170 views

Is there a mathematical symbol for a reversed, palindromic number?

If there is X, can it be reversed (made palindromic) by simply adding a character, a mathematical symbol?
13
votes
7answers
886 views

What does $\ll$ mean?

I saw two less than signs on this Wikipedia article and I was wonder what they meant mathematically. http://en.wikipedia.org/wiki/German_tank_problem EDIT: It looks like this can use TeX commands. ...
3
votes
1answer
332 views

Infinite limits on integration: acceptable notation

So you have an integral like $$ \int_{-\infty}^\infty{ \frac{dx}{1+4 x^2} } $$ Schaum's Calculus 5e recommends you write this as $$ \lim_{a \to -\infty} \int_a^b{ \frac{dx}{1+4 x^2} } + ...
1
vote
1answer
400 views

Is there more than one meaning of the notation “f(x)=[x]”?

In my real analysis text book there is a question that says: Decide whether $f(x)=[x]$ is bounded above or below on the interval $[0,a]$ where $a$ is arbitrary, and whether the function takes on it's ...
2
votes
3answers
323 views

what does the notation $g\colon X\to Y$ mean?

What does the notation $g\colon X \to Y$ mean in this Wikipedia page, under the section "Problem statement (supervised version)"?
0
votes
1answer
304 views

Multiset indicator function

I'm writing a report and was wondering wheter my notation is understandable? I'm fairly new to using the maths notation. A similarity measure between a multiset $u$ and a set $c$ is defined as: ...
0
votes
2answers
241 views

Is there a difference between these integral notations?

I've come across these two notations for calculating an indefinite integral but I'm not sure whether or not they are equal: $f(x)dx$ $\int f(x)dx$ When calculating the indefinite integral, the ...
4
votes
3answers
2k views

What does the notation n* mean?

Are there any conventions about the use of $n^*$ as notation of a variable? I have seen it for the first time here.
5
votes
1answer
270 views

Where does the notation $\mathrm{Ad}(U)$ for $a\mapsto UaU^*$ come from?

I have often seen, in the context of operator theory and operator algebras, the notation $\mathrm{Ad}(U)a=UaU^*$, where $U$ is a unitary operator on a Hilbert space $H$ and $a$ is a bounded linear ...
6
votes
1answer
157 views

Why is there a derivative in this formula?

This is a very simple question. Why is Rademacher's formula presented with d/dx in it? Why not just "do" the derivative? Then replace x with n? Is it so there is only one transcendental ...
1
vote
1answer
136 views

rational functions notation in Dummit&Foote

A problem in Dummit and Foote states: Let $k$ be a field and let $k(x)$ be the field of rational functions in $x$ with coefficients from $k$. Let $t \in k(x)$ be the rational function ...
6
votes
4answers
565 views

What differences are between $\mathbb{E}^n$ and $\mathbb{R}^n$

What differences are between the two notations $\mathbb{E}^n$ and $\mathbb{R}^n$? Do they represent/define the same space set with the same structure(s)? Thanks and regards!
1
vote
1answer
164 views

What does the notation $A_a^n$ mean?

Given a set of matrices $$M = \left\{\begin{bmatrix}1&a\\0&3\end{bmatrix} \mid a \in \mathbb R\right\},$$ what does the notation $A_a^n, n \in \mathbb N$ mean?
0
votes
1answer
122 views

what is the meaning of the notation $ C^q_c(0,1)$

Please let me know the meaning of the notation $ C^q_c(0,1)$
3
votes
4answers
134 views

fractions inside of a decimal?

$\frac{1}{3} = 0.333333.... $ $\frac{1}{3} = 0.33\frac{1}{3} $ I ran into this fraction-in-a-decimal notation in a course I'm helping somebody with. I have never seen this before, and google ...
4
votes
3answers
8k views

What is “multiplication by juxtaposition”?

I was reading http://www.purplemath.com/modules/orderops2.htm it shows = 16 ÷ 2[2] + 1 (**) ... = 5 The general consensus among math people is that ...
3
votes
0answers
207 views

How did Bessel functions come to be denoted by $J_n$?

The $n$th Bessel function of the first kind is usually denoted $J_n(x)$. Where did the use of the letter $J$ to indicate the Bessel function come from?
12
votes
4answers
20k views

What is 48÷2(9+3)? [duplicate]

There is a huge debate on the internet on $48÷2(9+3)$. I figured if i wanted to know the answer this is the best place to ask. I believe it is 2 as i believe it is part of the bracket operation in ...
13
votes
2answers
1k views

Etymology of $\arccos$, $\arcsin$ & $\arctan$?

Does anyone know the origin of the words $\arccos$, $\arcsin$ & $\arctan$? That is to say, why are they named like this? What connects "arc" with inverse? Can't seem to find out via Google. ...
1
vote
0answers
109 views

How to interpret the sum notation on $\sum_{r:i(r)=i} \langle R_{r\alpha} \rangle^{(t)}$

While doing research for my thesis, I ran into a paper called "Statistical Models for Co-occurrence Data". In the early pages, when talking about an iterative numerical method (a custom EM-method, to ...
3
votes
1answer
219 views

Question on notation of differentials

Is the following notation acceptable, specifically last part of the last line? $$f(x) = \csc^4(x) = (\csc(x))^4$$ Let $$u =\csc(x) \rightarrow f(x) = u^4$$ $$f'(x) = \frac{du}{dx} \times ...
1
vote
1answer
167 views

Notation to describe vector

I want to describe a vector of n length, where each element is described by it's index. What is the correct notation? As it is now, to describe the vector [ 1 4 9 16 ] i write: ...
1
vote
1answer
76 views

Any concise way to represent this in a formula?

I'm doing a presentation and I have to include this in it: for j in 1..j_max b_offset = copy(b) b_offset[j] = b_offset[j] + 1 I can't do b_offset = b + ...
1
vote
2answers
413 views

A question on notation: What does $\nabla |\vec{a} \times \vec{r}|^n$ mean?

I sort of asked a version of this question before and it was unclear; try I will now to make an honest attempt to state everything clerly. I am trying to evaluate the following, namely $\nabla w = ...
0
votes
2answers
551 views

a question on notation for function spaces

If $X$ is some topological space, such as the unit interval $[0,1]$, we can consider the space of all continuous functions from $X$ to $R$. This is a vector subspace of $R^X$ since the sum ...