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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2answers
38 views

Which letters to use as index in sequences?

Usually the latin letters $i,j,k,l,m,n$ are used as indexes in sequences or sets with $k$ elements ($A = \{ a_1,...,a_k \} $). But when we already used all these letters is there any recommendation? ...
0
votes
1answer
20 views

Using $\pm$ to express “in the range of” statement.

Does it make sense to write: $x = \left\{A\pm B\right\}$ To mean that $x$ falls in the range of $\left\{A-B,A+B\right\}$? If not, what would be the correct way of expressing this? Many thanks!
0
votes
2answers
42 views

Probability notation P versus Pr

I have come across both $P(…)$ and $Pr(…)$ being used to represent probabilities. Is there any difference in the meaning of these notations, or are they just different shorthands? I seem to come by ...
3
votes
3answers
95 views

Conventional set notation for integers between m,n CS Theory/Math literature

This is a pretty simple, straightforward question. I've seen in the literature $[n]=\{0,1,2,\dots,n-1\}$ and $[n]=\{1,2,3,\dots,n\}$. Is there a similar convention for ...
2
votes
2answers
620 views

Bar symbol over a matrix

So I am reading a paper (not online) and I come across a definition: $$\mathbb E=R\bar R$$ Where R is a complex matrix. I am thinking that it means complex conjugate, but I honestly have never seen ...
0
votes
0answers
4 views

Notation for concatenation of indexed vectors/matrices

Is there any standard notation for concatenation of matrices/vectors where their indices are taken from a set. I have matrices $A_{ij}$ where $(i,j)\in S$. I want to denote a matrix $A$ which is the ...
2
votes
2answers
2k views

What does $\propto$ mean?

From this article: $\ldots$a maximum-a-postiori "a maximum-a-posteriori $(MAP_{x,k}^{\,\,\,\,\,1})$ estimation, seeking a pair $(\hat{x}, \hat{k})$ maximizing: $$p(x, k\mid y) \propto p(y\mid ...
0
votes
1answer
69 views

Notation for dimension of vector space

Is it an unusual notation to write $|V|$ for the dimension of a vector space $V$? Is it ok to use it if you blur the distinction between the grid for the finite element method and its associated ...
0
votes
1answer
16 views

Max/Min Notation Question

In a paper I'm currently reading it gives alpha to be the following value. $\alpha = \max_t \min_{t_j \in T_N} ||t-t_j||_2$ I am wondering what exactly this means? I have the following code: ...
0
votes
3answers
99 views

What is the $\lor$ symbol?

In researching the consensus algorithm, I came upon the consensus theorem: How does the $\lor$ symbol function?
-7
votes
0answers
20 views

How to check the availability of particular function [on hold]

I want to check the availability of particular function that returns the value of results in binary like 0 or 1....How to check these function using mathematics...
0
votes
2answers
71 views

$\Bbb Z^\ast$ What is this notation?

What does $\Bbb Z^\ast$ mean? I would think some subset of the integers but I cannot find a definition. Thank you.
1
vote
1answer
44 views

Notation for Surface Integral in $\mathbb{R}^3$

Recently, a paper of mine got accepted, but the reviewers are struggling with the (in my view) standard notation for surface integrals in $\mathbb{R}^3$: Let $\Gamma \subset \mathbb{R}^3$ be a ...
4
votes
2answers
107 views

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?
1
vote
1answer
70 views

tensor notation surprise

I'm trying to study tensors from several textbooks. One early example completely confuses me: Islam, Tensors and their Applications, in the "Preliminaries" chapter, gives this example (page 3, using ...
0
votes
1answer
21 views

Express function counting number of elements in subsets

I wish to express a function $freq(x)$ as an equation but I have no clue how to properly do this. Basically I have the following: Let $a_i \subset A$ be one of many subsets of A. Each subset $a_i$ ...
0
votes
0answers
24 views

Correct Way to Describe the Following Set

I have a set $X \subset \mathbb{R}^6$ in which three of the entries belong to $\mathbb{R}$ and the other three belong to $[0,360)$ (they are angles). How do I write this set in formal notation (I'm ...
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0answers
25 views

Schanuel's conjecture and field extensions.

Doing a little bit of reading over the summer break before going into my masters year of my maths degree and i have been looking at Schanuel's conjecture which states that; Given any $n$ complex ...
1
vote
1answer
20 views

How to denote a set of nested tuples?

I want to define a set that elements that are nested tuples, like this one: $$a =((1, 2), (1, 2, 3), (1, 2))$$ I want this so I can index elements and write $a_{2,3} = 3$. My first idea was simply ...
0
votes
1answer
20 views

What's the correct notation for a minimum of a row of a matrix?

Let I=1,...,m denote the indexes of the rows of a matrix A Let J=1,...,n denote the indexes of the columns of a matrix A Let xi,j denote the value of the element A[i,j] I need do use a notation to ...
0
votes
1answer
14 views

Mathematical notation of choosing randomly one element from a vector

What is the mathematical notation for choosing randomly one element from a vector length $n$? For example our vector is $[3, 4, 5]$.
0
votes
0answers
15 views

Correct way of expressing the values a parameter can have

I have something similar to this sum (just a quick example): $$f = \sum^{N_x} g(z)$$ where $x$ stands for either $A$ or $B$ since I have two values $N_A$ and $N_B$ that could be used in the above ...
0
votes
1answer
230 views

A question regarding case notation

Consider the parameter $P$ and a property $S$ associated with this parameter represented as $P_S$. For example, consider that the height of a tree (“H”) is my parameter and the property is the tree’s ...
2
votes
0answers
34 views

What is the notation for a sub-expression?

For set theory, we have notation to denote subsets, e.g.: $$S \subset X$$ When working with expressions (arithmetic, Boolean, etc.), is there a notation to denote expression $S$ is a valid ...
0
votes
1answer
72 views

What does the colon use in the decimal place mean?

When I type into wolfram the query, exp(1) in base 100, the answer comes back "2.71:82:81...." What does the colon (:) mean?
1
vote
1answer
36 views

Confused by the task given (involves identical inequality of functions)

The task says: Show that if some function $\;f(z)={1\over g(z)}$, where $g\not\equiv0$ is an entirely analytic function, then the isolated singularities of $\;f$ are exactly zeros of $g$ ...
1
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0answers
50 views

Manifolds and Varieties

In my language, spanish, the word for (topological) manifold and (algebraic) variety is the same: "Variedad". This happens also in some other languages, like french (variété) or portuguese ...
5
votes
1answer
60 views

Space of Alternating $k$-Tensors Notation

I will be taking a Differential Geometry class in the Fall, so I decided to get somewhat of a head start by going through Spivak's "Calculus on Manifolds." Before reading, though, I saw the Addenda at ...
4
votes
2answers
162 views

Notation for the smallest number in a set?

Let's assume I have a set like $S = \{2,1,3,4,8,10\}$. What's the math notation for the smallest number in the set?
1
vote
7answers
55 views

Any way to represent number that comes after repeating decimal?

Essentially, I am wondering if you can represent a repeating decimal and have a number. For example, perhaps 0.9 repeating with an 8 at the end, the largest decimal less than one (because 0.9 ...
0
votes
0answers
21 views

Set-builder defining set size and valid elements? Notation help.

I'm working on some documentation for a system that uses an arbitrary waveform generator that accepts data with a number of requirements. I would like to include some formal definitions of the ...
1
vote
1answer
22 views

Product of operators - what is the standard notation

Given $P_i$, $i=1,\ldots,n$ operators on a Hilbert space $H$. For $x \in H$, Does $\left( \prod_{i=1}^n P_i\right) (x)$ mean $$ \left(\prod_{i=1}^n P_i\right) (x) = P_1 \cdots P_n (x)$$ or $$ ...
3
votes
1answer
61 views

Is my use of $\pm/\mp$ in answers allowed notation?

If we solve the equations: $$x^3+2x^2-9x+2 = 0\\\therefore x = 3, -3, -2\\\therefore x = \pm3, -2$$ $$x^3-4 x^2+9 x-10\\\therefore x = 1+2i, 1-2i, 2\\\therefore x = 1\pm 2i, 2$$ It seems to me that $x ...
4
votes
1answer
248 views

Derivative $\Delta x$ and $dx$ difference

This may seems like a dummy question but I need to ask it. Consider the definition of derivative: $$\frac{d}{dx}F(x) = \lim_{\Delta x->0}\frac{F(x+\Delta x) - F(x)}{\Delta x} = f(x)$$ Also: ...
0
votes
0answers
21 views

Frequency distribution, notation problem with the classes

I would like to create a frequency distribution. The range of my data is the interval $[a,b]$. I divide this interval into $n$ equal length part intervals (or classes). So each part interval has the ...
6
votes
2answers
290 views

How would you change math notation? [closed]

Mathematical notation has been evolving for hundreds of years (really thousands, I guess, but most of the noteworthy examples seem to be only a few hundred years old). Sometimes we are stuck with old ...
2
votes
2answers
77 views

$\forall$ At the beginning or at the end?

I have a set of real numbers $x_1, x_2, \ldots, x_n$ and two functions $f:\mathbb{R} \rightarrow \mathbb{R}$ and $g:\mathbb{R} \rightarrow \mathbb{R}$. What are the differences between the following ...
0
votes
0answers
29 views

Italic notation in logic

I have seen some books on formal logic where variables are written in italic, while statements are upright. Hence a statement could like like $\mathrm A(x_1, \ldots, x_n)$. How much of a standard is ...
3
votes
0answers
59 views

Modern notational alternatives for the indefinite integral?

I like the Leibniz notation, and I think the reason it's survived for over 300 years and continued to be almost the only game in town is that in many respects it's a miracle of design. Nevertheless ...
4
votes
1answer
37 views

Big $O$, little $o$ Notation

So I've gone through the typical undergraduate math sequence (two semesters of real analysis, two semesters of abstract algebra, some measure theory, but I haven't taken discrete math) and in various ...
9
votes
2answers
250 views

Difference between “≈”, “≃”, and “≅”

In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators ...
0
votes
0answers
14 views

Hypergraph notation and hypergraph morphisms

There are two parts to my question. The first part is about notation for hypergraphs. The sconed is about the notion of morphisms for hypergraphs. For the notation part, the context is that I make ...
5
votes
3answers
2k views

Parenthesis vs brackets for matrices

When I first learned linear algebra, both the professor and the book used brackets like [ and ] to enclose matrices. However, in ...
0
votes
2answers
23 views

Cannot understand a mapping function which include some sets

I have kept a screenshot of my problem below which describes about the various sets. At the last line, there is an expression where a function delta uses those sets and maps them into another. I am ...
2
votes
3answers
180 views

What is the name of this notation?

What is the name of a notation that looks as follows: "1 2 9 8 4 6 + * / + *" But is evaluated as "1 + 2 * 9 / 8 + 4 * 6" EDIT: I do think it's RPN now and my ...
11
votes
1answer
174 views

Is the equation $\phi(\pi(\phi^\pi)) = 1$ true? And if so, how?

$\phi(\pi(\phi^\pi)) = 1$ I saw it on an expired flier for a lecture at the university. I don't know what $\phi$ is, so I tried asking Wolfram Alpha to solve $x \pi x^\pi = 1$ and it gave me a bunch ...
0
votes
0answers
15 views

Question about set and series notation in the GSP Algorithm

I tried this in programming forums with no luck and since my primary issue is with the notation, I'm asking here: I have the definition of the GSP Algorithm: Definition However I don't understand ...
0
votes
3answers
45 views

A question on function notation

Forgive me if this does not belong here. All throughout primary school I've seen the notation $f(x)$ to denote a function, that is, if we are talking about the squaring function, we would write $$ ...
0
votes
1answer
22 views

Meaning of the Notation $\mathcal{F}[X,F(X)]$

I came across the following theorem. What is the meaning of the notation $\mathcal{F}[X,F(X)]$? Thanks, Jay.
3
votes
2answers
1k views

Sigma notation only for odd iterations

$ \sum_{i=0}^{5}{i^2} = 0^2+1^2+2^2+3^2+4^2+5^2 = 55 $ How to write this Sigma notation only for odd numbers: $ 1^2+3^2+5^2 = 35 $ ?