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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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
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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.
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4answers
108 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?
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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\, ...
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1answer
21 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
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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?
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1answer
26 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 ...
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2answers
72 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 $f(x)=k+x$ ...
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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?
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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.
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0answers
23 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 $$ ...
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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} ...
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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 $\mathrm{Hom}(A,B)$? ...
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0answers
84 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 ...
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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 ...
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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 ...
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1answer
71 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
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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?
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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. ...
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1answer
34 views

Doesn't the $p$ depend on $m$

Consider the following text: where $p \in \mathbb Z$. Can you tell me please: doesn't $p$ depend on the $m$? So it is preferable maybe to write $p_m$? Or does $p$ not depend on $m$?
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2answers
36 views

Notation for Derivatives with Respect to Time

My math teacher writes $\frac{dx}{dt}$ as $x'$, and makes us do the same for homework. (in a particle motion context, where $t$ is time) I am aware that the standard notation is usually $\dot{x}$, ...
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2answers
46 views

Quick question about notation and pronunciation of indices: (i+1)st or (i+1)th?

I have a somewhat silly question: What are you calling the index after the $i$th index? The $i+1$st or the $i+1$th? How do you pronounce it and how do you write it down? I like to write $i+1$ in ...
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1answer
24 views

math notation of iterated function

I'm trying to determine the proper notation for the following loop I have written in computer code: Set x = 2 set y = 3 For z=1 to z=5 (increasing the value of z by 1 each ...
5
votes
1answer
75 views

Who introduced the finite difference notation using $\Delta$?

We all know that Leibniz introduced the differential notation $dx, dy$, and that in developing his calculus for infinitesimal differences he was inspired by his previous work on finite diffences. ...
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1answer
15 views

Express dissolved multi-summand binominal equation

After dissolving an multi summand binomial equation $$f(x)=(x_0+x_1+x_2+x_3+\ ...)^2$$ I got $n*(n-1)/2$ of these terms: $$x_0x_1+x_0x_2+x_0x_3+x_1x_2+x_1x_3+x_2x_3+\ ...$$ How do I write them in a ...
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0answers
19 views

A notation question about the centralizer - or?

I am reading an article where the author considers an abelian $p$-group $A$ and lets $G\le \text{Aut}(A)$ and $S\in \text{Syl}_p(G)$. Then he talks about $C_A(S)$, but what does this mean? Is it some ...
2
votes
2answers
54 views

Notation for vector space dimension and usage of $\times$ operator

I would like to describe a real vector space with dimension $a \times b$ (as in $a$ times $b$). Is it correct to describe it with $$ \mathbb R^{a \times b},$$ or would that imply the space of matrices ...
0
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1answer
28 views

Proper convolution notation

What would be the correct way to write down the convolution in "star" notation for these two functions; $h(t)$ and $\delta(t-x)$. $\delta$ is the Dirac delta function. The integral notation should ...
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0answers
37 views

What is the math symbol ~ with ind over it?

The symbol I'm talking about is from a statistics article here:
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votes
2answers
28 views

Why is scientific notation of the form a.bcd×10^n?

More specifically, my question is why is the point always after the first digit? Why have (for example), 7.5 x 1018 as opposed to 75 x 1017? The former makes it easier to read (when you literally want ...
1
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2answers
17 views

How should I signify the $y$ value of a given point

This is more of a aesthetics question than maths. But if I want to use the $y$ value of a given point $P$ in an equation how to I write this? I can't really show any working since I've just googled ...
1
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1answer
18 views

Permutation cycles in Jacobson's Basic Algebra I.

Nathan Jacobson's Basic Algebra I Second Edition, Section 1.6 Cycle Decompositions of Permutations, page 51, exercise 4 says: Show that if $\alpha$ is any permutation then $$\alpha (i_1 i_2 \cdots ...
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0answers
8 views

Question about notation matrix of partial derivatives where one component has two indices

lets suppose we have a vector ($\delta_{11}, \delta_{12}, \dots, \delta_{jk}$) where $\delta_{jk} = \alpha_j + \beta_k$, i.e., each element is build up of two components. The first index $j$ specifies ...
0
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1answer
43 views

Notation question in elementary set theory

Let $A$ be a set. What is defined as $UA$? Is it the union of all sets that $A$ includes? Could someone provide an example for this notation? Thank you!
0
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1answer
16 views

Pairing of Sigma and Pi in notation

Why do $ \Sigma $ and $ \Pi $ appear together so frequently in related topics. For example: Product and Sums Borel sets, such as $ \Sigma_0^1, \Pi_0^1 $ First order formulas, such as $ \Sigma_1, ...
0
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1answer
44 views

Notation for the horizontal line found in sequent calculus for linear writing

Is there any known Unicode character which can be used as a substitute for the horizontal line which is normally used in texts presenting sequent calculus? I actually use the oblique bar ...
2
votes
1answer
44 views

Notation in set theory.

What is the difference between these two notations? $\{a_k\}_{k\in K}$ $\{a_k, k\in K\}$ Is this correct? $\{a_1\}$, $\{a_2\}$, $\dotsc$ $\{a_1, a_2, \dotsc\}$ Or 1. and 2. are the same? Is ...
0
votes
1answer
48 views

Trouble understanding $\sum$ notation

Question: What does $$\left(\sum_{a, b, c}a\right)^2$$ mean ? The answer given is $(a+b+c)^2$. However, I am having trouble understanding this. I have seen this, this and this. But none helped. ...
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votes
2answers
39 views

Anti derivative notation?

For derivatives, we use $f'(x), f''(x),$ etc. until that comes too unwieldy so we just use $f^{(n)} (x)$ What about for anti derivatives? I've seen using $F(x)$ to denote the first antiderivative of ...
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0answers
22 views

What is the interpretation of $\mathcal{F}=\{0,1\}^{\Omega}$?

In the context of probability theory, if I have a regular dice then $\Omega = \{1,2,3,4,5,6\}$. The $\sigma$-field, $\mathcal{F}$, will be all the subsets of $\Omega$. But the book I am studying from ...
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3answers
29 views

How can I express, “The set of integers greater than x and less than y”?

I know I could express it this way (x = 0, y = 10): $$ \{ 1, 2, 3, 4, 5 , 6, 7, 8, 9 \} $$ in simple cases. This is what I could come up with for the more general case: $$ \mathbb I = \{ i_n | i_n ...
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0answers
17 views

How to quickly reference to two subsets of the same set

Suppose $A\subset F$ and $B\subset F$. Would the following be a valid shorthand? $A,B\subset F$? What is the convention on this? Similar question for elements of a set: Suppose $a\in F$ and $b\in F$. ...
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0answers
18 views

Standard notation for the indicator function of the odd integers

Is there a commonly used notation for the indicator function of the odd integers? One candidate I think is $$1_{2\mathbb{Z}+1}(x),$$ and I could always define one, $$\chi(x)=\left\{\begin{array}{ll} 1 ...
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1answer
27 views

How to formally write $f\left(k\right)={1\over p_1}+{1\over p_1p_2}+{1\over p_1^2p_2p_3}+{1\over p_1^4p_2^2p_3p_4}+\dots$

How do I write the following finite series as a sum of products: $$f\left( k \right) = {1 \over p_1} + {1 \over p_1p_2} + {1 \over p_1^2p_2p_3} + {1 \over p_1^4p_2^2p_3p_4} + \dots + {1 \over ...
0
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1answer
30 views

How to formally write $f\left(k\right)={1\over p_1}\left(1+{1\over p_2}\left(1+{1\over p_3}\left(1+\dots\right)\right)\right)$

How do I write the following finite series as a sum or product: $$f\left(k\right) = {1 \over p_1} \left(1 + {1 \over p_2} \left(1 + {1 \over p_3}\left(1+\dots \right) \right) \right)$$ …all the way ...
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1answer
48 views

Meaning symbol $\overline{\lim_{n\rightarrow \infty}}$ [duplicate]

I found this symbol on a math book that I'm studying. It had never happened before. What does this mean? $$\overline{\lim_{n\rightarrow \infty}}$$
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10answers
994 views

Challenge: Demonstrate a Contradiction in Leibniz' differential notation

I want to know if the Leibniz differential notation actually leads to contradictions - I am starting to think it does not. And just to eliminate the most commonly showcased 'difficulty': For the ...