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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1answer
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The subcategory of commutative $R$-algebras is denoted by ???

Let $R$ be a commutative ring (with identity) and let $R\mathbf{Alg}$ denote the category of $R$-algebras. My question: is there a suitable notation for the full subcategory of commutative ...
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2answers
58 views

Very simple notation question

What notation is it called when a number is represented as a series of additions, for example: 124 = 100 + 20 + 4 This is a very simple question obviously but I don't remember what it's called! ...
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2answers
44 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? ...
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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!
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2answers
43 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 ...
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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 ...
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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: ...
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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...
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1answer
47 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 ...
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2answers
111 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?
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3answers
102 views

What is the $\lor$ symbol?

In researching the consensus algorithm, I came upon the consensus theorem: How does the $\lor$ symbol function?
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2answers
73 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.
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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 $a_i$ ...
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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
26 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 ...
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1answer
22 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 ...
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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 ...
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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 $[3, 4, 5]$.
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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 ...
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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 ...
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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?
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1answer
37 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 $g$ ...
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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 ...
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1answer
61 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 ...
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2answers
163 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?
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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 ...
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7answers
56 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 ...
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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 $$ ...
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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 ...
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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 ...
2
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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 ...
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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 ...
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2answers
291 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 ...
3
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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
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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 ...
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2answers
251 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 ...
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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 ...
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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
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3answers
181 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 ...
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0answers
16 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
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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 $$ ...
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1answer
175 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
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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.
0
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1answer
47 views

Mathematical notation to represent x% within x%

What is the proper way to represent mathematically the expresion $x\%$ within $x\%$? For example, $90\%$ of the bottles are $95\%$ full.
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2answers
31 views

Scalar to the power vector

I have a formula that contains $\log (I + e^{X})$ term where $X$ is an $N$ dimensional vector ($x_0, x_1, ..., x_{N-1}$) and $I$ is the unity vector. I don't know how the exponentiation and log ...
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3answers
41 views

Formal Notation - A simple example

I'm taking Formal Languages and Automata Theory course and i couldn't understand the notation below. Can someone explain me this please? $\{ d \mid d \in \{ b f \mid b, f \in \{ a, c, e \} \} \}$
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34 views

What does this notation mean for calculating prime?

I'm not very proficient with math, but Ive managed to make my way to problem 7 of Project Euler using python. I have to now find the 10,001st prime number. I'm reading about Eucilid's theorem. But I'm ...
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3answers
651 views

Who named “Quotient groups”?

Who decided to call quotient groups quotient groups, and why did they choose that name? A lot of identities such as $$\frac{G/A}{B/A}\cong \frac{G}{B}$$ suggest that whoever invented the notation ...
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2answers
120 views

What is the intutive explanation of why the notation of matrices is as it is?

If I want to solve a system of linear equations, like 2x-y=1 x+2y=4 Then the matrix notation for the same would be: $$ \begin{bmatrix} 2 & -1 \\ 1 & 2 \\ \end{bmatrix} \begin{bmatrix} X\\ ...
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0answers
29 views

set notation for the maximum value in a mathematical equation

I am trying to represent the maximum value in a mathematical equation. Currently, I am representing the maximum value as below. max{leva,b(|a|,|b|)} ...