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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25 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
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1answer
497 views

What is the difference between single and double modulus signs. Do they both mean magnitude?

What's the difference between a set of single modulus and a set of double modulus signs? On textbooks I have seen the magnitude of two vectors vector as $|\mathbf{x} - \mathbf{y}|$ but I've seen ...
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2answers
567 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 ...
0
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0answers
59 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 ...
0
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1answer
53 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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2answers
76 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
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2answers
165 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
128 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
86 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
49 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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vote
1answer
50 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
35 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
23 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
17 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 ...
2
votes
0answers
45 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
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1answer
91 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
46 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
61 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
116 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
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2answers
340 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
43 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
97 views

Any way to represent number that comes after repeating decimal? [duplicate]

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
26 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
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1answer
76 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
37 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 ...
3
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2answers
111 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
100 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 ...
3
votes
1answer
222 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 ...
10
votes
2answers
302 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
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0answers
56 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 ...
0
votes
2answers
26 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
197 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
27 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
84 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 $$ ...
11
votes
1answer
240 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
29 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.
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1answer
53 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.
0
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2answers
38 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 ...
0
votes
3answers
51 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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2answers
45 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 ...
22
votes
3answers
774 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 ...
3
votes
2answers
149 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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votes
1answer
25 views

How to design notation for a mapping of elements belonging to different sets?

I am trying to design a particular notation, described as follows: $X$ is a finite set of elements. $s_k, k = 1...n, n < 10$ are few, different, mapping function. Each $s_k$ function maps ...
1
vote
1answer
53 views

What is the difference between $\mathcal{X}\subseteq\mathbb{R}^n$ and $\mathcal{X}\subset\mathbb{R}^n$

Let $\mathcal{X}$ be a non-empty set. For instance, let it be a set of vectors of the form $\mathbf{x}\in\mathbb{R}^n$, i.e., ...
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1answer
33 views

Help with mathematical notation for selecting a function's argument

I am trying to write the following in a mathematical notation. I have a monotonically decreasing function $V(\bullet)$, and I need to choose the argument of the function based on its amplitude. ...
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1answer
22 views

Definition of the Domain of a Function when the sets are the elements

In case I have a function that calculate the normalized distance of elements in two sets $A$ and $B$ I can define the function as $\mathrm{elementDistance} : A \times B \rightarrow [0,1]$. But if I ...
0
votes
2answers
115 views

Why do we denote $S^1$ for the the unit circle and $S^2$ for unit sphere?

Maybe a quite easy question. Why is $S^1$ the unit circle and $S^2$ is the unit sphere? Also why is $S^1\times S^1$ a torus? It does not seem that they have anything in common, do they?
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2answers
66 views

Abbreviate a tuple with a variable?

In a book I found the following notation $M = \{(x_1,y_1,z_1), \ldots, (x_n,y_n,z_n)\}$ for a set of 3-tuples. The author always refers to a tuple by writing $(x_i,y_i,z_i) \in M$. I'm wondering if I ...
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0answers
49 views

Should I use the minus sign when writing papers in characteristic two

Is there any consensus regarding whether one should write both "+" and "-" or only "+" when performing computations in characteristic two fields? To give some context, I am writing my thesis, which ...
2
votes
1answer
63 views

Number theory notation

I am confused with the below notations . I know that ($a \equiv b \mod {n} )\iff ( n|(a-b)$ ) but what the below notation says ? $a = b \mod {n}$ and in theorem 16 in this ,it's given as below ...