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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0
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2answers
32 views

How to notate a vector out of a $\mathbb{R}^+$

Say you have a set $\mathbb{R}^+$, (in other words the positive real numbers), how can one express a vector with $n$ elements out of it? $\mathbb{R}^{+n}$ might by confusing and $\mathbb{R}^{n+}$ as ...
0
votes
3answers
44 views

Notation for limit approaching from above/below

Consider the equation $$f(x)=\frac{4x+8}{x-3}$$ It is known that $$\lim_{x \to \infty} f(x) = 4$$ from above and $$\lim_{x \to -\infty} f(x) = 4$$ from below. How do you write the "from above/below" ...
1
vote
2answers
33 views

Iterated self-composition of arbitrary function

Does there exist some notation that represents the iterative composition of a single-input, single-output function with itself? As in, say, $f_5(x)=f(f(f(f(f(x)))))$. In other words, going by the ...
0
votes
1answer
27 views

Should random variables be italic or roman ($X$ or $\mathrm X$)?

I just recently learned that it is good style to write constants like Euler's number $\mathrm e$ and also functions and operators in roman letters while reserving italic letters for variables. ...
2
votes
1answer
24 views

limit notation syntax validity

If you know $$\lim_{x \to \infty} f(x) = -\infty$$ and $$\lim_{x \to -\infty} f(x) = -\infty$$, is it valid syntax to write $$\lim_{x \to \pm \infty} f(x) = -\infty$$?
3
votes
1answer
45 views

Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?

Title says it all - is there an accepted mathematical way in matrix notation to show those operations on a matrix? Thanks.
2
votes
3answers
150 views

Summation Notation Confusion

I am unclear about what the following summation means given that $\lambda_i: \forall i \in \{1,2,\ldots n\}$: $\mu_{4:4} = \sum\limits_{i=1}^{4} \lambda_i + \mathop{\sum\sum}_{1\leq i_1 < i_2 \leq ...
0
votes
2answers
23 views

Standard notation for sum of vector elements?

I can think of multiple ways of writing the sum of a vector $\mathbf{v}$'s elements, but is there a standard operator for this? Using "programming" notation it is typically sum($v$), but this seems ...
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votes
1answer
42 views

Strange Integral Notation? [duplicate]

When reading about an certain algorithm (about parameter estimation for Kalman Filtering page 7 eq 57) I found this notation: $\int dx f(x)$ which is normally written as $\int f(x) dx$. I spent a ...
0
votes
1answer
88 views

What does $\mathbb{Z}_2$ mean?

Wich number space is ment by: $\mathbb{Z}_2$ (I know that $\mathbb{Z}$ stands for Integer)
3
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1answer
1k views

How do we pronounce this symbol?

I would like to know how to pronounce in english this symbol $\nabla \phi$ It is something phi ... ? thank you
3
votes
2answers
30 views

Big O-notation and series

While there are many questions regarding Big O-notation and in particular, its usage when it comes to series, none fit my question perfectly: possibly because I am so unfamiliar with the notation. ...
0
votes
0answers
62 views

What does $\dot{\mathbb{R}}$ mean?

I just run into a notation like this: $\dot{\mathbb{R}}$ $-$ any idea what could it mean? I have guesses, but I'd like to be sure. Thanks in advance! [I ran into this notation in the introductory ...
0
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0answers
23 views

What is the symbol ≙ most commonly used for in a mathematical or math-related context?

What is the symbol most commonly used for in a mathematical or math-related context? LaTeX produces the symbol with \hateq. ...
0
votes
0answers
28 views

'monotone in (x,y)' vs 'monotone in x and y'

What's the difference between function being 'monotone in (x,y)' and 'monotone in x and y'? Or they denote the same?
1
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0answers
22 views

Correct notation for variable substitution?

Is this notation conventional to indicate that $M$ should be replaced with 2? $$ \left. \frac{(D + M - 1)!}{(D - 1)!M!} \right|_{M = 2} $$
1
vote
0answers
36 views

problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\ $ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\ $ is ...
0
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1answer
22 views

Y-Coordinate of a Point - Notation

Given point $P$ on curve $\omega$, what expression is generally use to denote the $y$-coordinate of point $P$, also, the $x$-coordinate. Would it be $P_y$? Also, let $\omega$ be in $\mathbb{R}^2$, not ...
3
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0answers
73 views

A name for something like a CW complex?

The class $\mathcal{CW}_n$ of finite $n$-dimensional CW complexes can be defined recursively: $\mathcal{CW}_0$ consists of finite sets; If $X \in \mathcal{CW}_n$, $\phi:S^n \amalg \cdots \amalg S^n ...
2
votes
1answer
83 views

Which is the best notation for a sequence?

In a set, the order of its elements is (as far as I know) not important; in a sequence, the order of its elements is important. Which is the notation I should use in order to define a sequence? I ...
1
vote
2answers
71 views

Difference between limits $\infty$ and $+\infty$

Is there a difference between these two limits? $$\lim_{x\rightarrow\infty}f(x)=+\infty\text{ and }\lim_{x\rightarrow+\infty}f(x)=\infty$$
1
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1answer
51 views

Can someone explain this notation of a limit?

What is the explanation/motivation for this notation? tiontion $$\lim_{x\rightarrow a+0}f(x)$$ I understand it should be equivalent to this notation, which seems much more logical (and simpler): ...
1
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0answers
21 views

Notation for appending 2 submatrices

I have a matrix $M$ with $i$ rows and $(e+n)$ columns: $M_{i,e+n}$ I would like to express that $M_{i,e+n}$ is the result of appending $M_{i,e}$ and $M_{i,n}$ What is the algebraic notation to ...
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2answers
92 views

Can I use “: ,” instead of “, implies” for this example?

I've to write this statement in a formal manner: if $x>1$ then $x^{2}>1$. Writing the result of the exercise I face this problem, I wonder if these two statements are equivalent: ...
0
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0answers
50 views

Why is real part written first in complex numbers?

While expressing complex numbers as $a + \iota b$, is there a specific reason for writing the real part before the imaginary part? Who introduced this notation first? Is it a case where it just hung ...
1
vote
1answer
86 views

Notation: what is “arg min”

there is a function that says j=arg_min{ f(x),g(y) } What does that mean? As noted by the comment, arg_min(f(x)) is the x that gives smalles f. But what happens when arg_min takes two function, ...
1
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1answer
42 views

Strange notation for a decimal expansion of a transcendental number

I am checking page proofs for one of my papers right now and an editor changed $\zeta(3)=1.202$$\ldots$ to: $\zeta(3) = 1.202,...,$ I find this latter notation very strange and think it ...
0
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1answer
28 views

Notation: need help to understand the notation in the following formula

E is just a function such that E1=1, E2=2 and so on. But my question is the part of on "arg" and "min". 1) so "arg" stands for the angle of complex number? this doesn't make any sense. 2)If I ...
5
votes
1answer
72 views

Intuition for Integration of Differential Forms

In mathematics, we define $dx^i$ as linear functionals, when speaking of integration. However, in physics, we interpret $dx^i$ as very small quantities. There is nothing inherently small about a ...
0
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0answers
11 views

Coordinatewise vector operation notation

I have seen questions on Math.SE what is the typical notation for coordinatewise vector multiplication (Hadamard product), but I haven't found an answer to case of exponentiation. Given a vector ...
2
votes
1answer
78 views

The meaning of Differentials in Integration

This is further to the questions discussed in a previous post Here is an example of what I mean: Suppose that $C$ is a closed path in the plane and consider the line integral of $xy\,dx+x^2\,dy$ over ...
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1answer
17 views

Notation in modulo groups

What does ${\Bbb Z}_m^*$ mean? I know that $\Bbb Z_m$ is isomorphic to $\Bbb Z/m \Bbb Z$ but the asterisk tripped me up.
2
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4answers
109 views

Notation: is it correct to state $3a=a3$?

If $a$ is a real constant, do you regard $3a$ and $a3$ as equal or different?
3
votes
2answers
58 views

$\left(A\times B\right)^n=A^n\times B^n$?

Is this property true: For any set $A$ and $B$: $$\left(A\times B\right)^n=A^n\times B^n?$$ Where $A\times B$ is the Cartesian product and $A^n=\underbrace{A\times A\times \cdots\times A}_{n\, ...
1
vote
1answer
22 views

Derivative Notation Question (Contravariant vs. Covariant)

I know how to write a covariant derivative in Leibniz notation: $$\partial^\mu\equiv \frac{\partial}{\partial x^\mu}$$ Does that mean that a contravariant derivative in Leibniz notation would be ...
0
votes
1answer
47 views

How to write $A\cup\emptyset\times A\cup\emptyset$

How to write the cartesian product of this? $$(A\cup\emptyset)\times (A\cup\emptyset)$$ Is it: $$A^2\cup\emptyset^2?$$ What does $\emptyset^n$ means?
1
vote
1answer
27 views

What is the meaning of this notation?

I am watching this video on maximum likelyhood estimation. I'm confused by the notation when the presenter says "assume a set of distributions P-theta." (the URL links to the relevant part of the ...
3
votes
2answers
76 views

In probability notation: what does a tilde over a letter mean?

I am reading this paper. In section 1.1 he says: What do the tildes above the letters mean? How can I translate these two sentences into ordinary English?
3
votes
1answer
89 views

$f_{n+1}(x)=f_n(x+1)-f_n(x)$ functional equation and “classification of functions”

Doing a quiz I found a question of this kind "given $a_0, a_1, a_2, ...,a_n$ find $a_{n+1}$" In order to find the $f$ such that $f(a_n)=a_{n+1}$ I tryed for a function like $f(x)=k+x$ ...
0
votes
1answer
26 views

Is there a symbol used to say “is well ordered by?”

For example, we know that $\Bbb N$ is well-ordered by $<$. Is there a standard way of representing this using some notation?
2
votes
2answers
92 views

What does $\frac{d^2}{dx^2}$ stands for

I would like to know what is $\frac{d^n}{dx^n}$. I think it stands for dervation of $n-$th order but I am not sure.
0
votes
0answers
25 views

Misleading tensor notation for Jacobian inverse?

In Schutz, Geometrical Methods of Mathematical Physics, is written a Jacobian coordinate transform $\Lambda$, $$ \Lambda^i_j = \frac{\partial x^i}{\partial y^j} $$ The inverse matrix is written $$ ...
0
votes
1answer
43 views

Notation regarding the maximum function over a list of naturals

So I'm trying to write down the maximum function(with a precise mathematical notation) over a set of integers by utilizing the generic maximum function which takes two integers, $max: \mathbb{N} ...
1
vote
1answer
41 views

Notation for the set of monomorphisms in $\mathrm{Hom}(A,B)$

Let $\mathcal{C}$ be a small category, and let $A$ and $B$ be objects in $\mathcal{C}$. Is there any standard notation for the subset of all monomorphisms $A\hookrightarrow B$ in $\mathrm{Hom}(A,B)$? ...
2
votes
0answers
89 views

what does mean of notation comma?

I confused the notation comma. I know that the comma means 'AND' in Set theory as gate($a$^$b=a$ AND $b$), But we write solution of equaiton as $x=1,2$ (the equation: $x^2-3x+2=0$) the question is ...
0
votes
0answers
23 views

meaning of tensor “component”

In Schutz, Geometrical Methods of Mathematical Physics, it is written The components of a tensor are its values when it takes basis vectors and one-forms as arguments. It then gives an abstract ...
0
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1answer
30 views

Formalizing a permutation as a bijection between the same set?

The standard definition I usually find regarding permutations is a bijection from a set to itself, in other words: $\text{a function }f:\{ 1, 2,\dots,n \} \mapsto \{ 1, 2,\dots,n \} \text{ which is a ...
-1
votes
1answer
72 views

How to explain why one should use lowercase letters for variable names?

How can I explain to an Algebra I student why he should use lowercase letters when naming his variables (i.e. $q = $ number of quarters $vs.$ $Q = $ number of quarters? I am not interested in the ...
0
votes
1answer
36 views

$\mathcal N (A):=\mathcal P(A)-\varnothing$ notation

Define $\mathcal N$ $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ Does $\mathcal N$ has a special name and standard notation?
13
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3answers
2k views

What does this symbol mean? (looks like a 1 with double vertical line)

I'm studying a course on probability and statistics and at some point this symbol comes up without introduction. It looks like the number one, but slightly bigger and with a double vertical line. ...