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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PEDMAS in RPN needed?

In RPN do we still have to take into note the PEDMAS rules? For example these questions: 3 – 4 * 2 3 * 4 – 2 3 * (4 – 2) (3 – 4) * 2 3 – 4 + 2 Answers 342*- ...
8
votes
1answer
457 views

What does **Ens** stand for?

Earlier someone was asking about the category "Ens" described in Categories for the Working Mathematician. My question is more basic: What does Ens stand for? Most of the categories have names that ...
12
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3answers
451 views

Uses for esoteric integral symbols

A while ago, I was searching for a TeX package which would provide a double integral symbol with a circle which I could use to typeset some lecture notes on surface integrals. I happened upon the ...
4
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4answers
183 views

Want to understand a set notation

I cannot picture $$\bigcap \{X\subseteq A| F(X)\subseteq X\}$$ in my head. Perhaps I could better understand it in symbolic logic. How do you write it in symbolic logic ?
8
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2answers
2k views

Is there an analogue to the “Delta” symbol for ratios?

A capital delta ($\Delta$) is commonly used to indicate a difference (especially an incremental difference). For example, $\Delta x = x_1 - x_0$ My question is: is there an analogue of this notation ...
0
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1answer
137 views

Does $f \sim g$ imply $f \asymp g$ in certain conditions?

I got a good answer to this question over on MathOverflow a while ago. Harald Hanche-Olsen claimed that, if $f, g: D\to \mathbb{R}^+$, then $$ f(x) \sim g(x) \implies f(x) \asymp g(x) \qquad \qquad ...
2
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1answer
275 views

Linear Algebra: A matrix vs a determinant

I would like to clarify something in regards to finding a determinant of a matrix. For example say I have this problem where I have to evaluate the determinant: Is the determinant notation simply a ...
0
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2answers
371 views

What do you call a number that represents 20 Percent written as “0.2” and “20%” respectively

Lets say I want to represent 20 Percent What do you call/name the "0.2" and "20%" notations I am calling them Fractional and WholeValue notations for the time being, but wondering if there was ...
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2answers
195 views

What does the notation $x \in \mathbb{R}^V$ mean where V is a set?

In the context of submodular functions, I encountered the following statement : For a vector $x \in \mathbb{R}^V$ and a subset $Y \subseteq V$ we define the expression $x(Y)$ as $\sum_{u \in ...
5
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3answers
305 views

Help on notation: $\mathbb{Z}/n\mathbb{Z}$ vs. $\mathbb{Z}_n$

I have difficulties understanding the difference between the following two notations: $\mathbb{Z}/n\mathbb{Z}$ (which denotes a quotient group) and $\mathbb{Z}_n$. Are they equivalent? PS1: The ...
2
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1answer
129 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
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2answers
178 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
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1answer
148 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
247 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 ...
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2answers
219 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 $D$. ...
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0answers
715 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 ...
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1answer
89 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 - ...
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3answers
129 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 $(a_2,b_2)$ = $( ...
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1answer
8k 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
706 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
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1answer
287 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 ...
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1answer
381 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
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2answers
320 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\} = ...
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1answer
882 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
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1answer
299 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
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2answers
196 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 ...
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2answers
282 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
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1answer
356 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
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2answers
354 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 ...
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2answers
115 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
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2answers
387 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
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5answers
1k 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
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2answers
289 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 ...
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0answers
126 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 := ...
5
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2answers
1k 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 ...
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3answers
163 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?
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7answers
826 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
322 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
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1answer
306 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
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3answers
315 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
272 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
232 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 ...
3
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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.
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0answers
248 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
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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
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1answer
131 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 ...
5
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4answers
529 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
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1answer
163 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?
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1answer
116 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)$
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4answers
127 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 ...