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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How can $A \supset B$ be a synonymous of $A \Rightarrow B$? [duplicate]

From time to time, although not so commonly, I see $A \supset B$ written with seemingly the same meaning as $A \Rightarrow B$. Ex. in Constructive Type Theory and Interactive Theorem Proving, on page ...
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0answers
39 views

What does the notation $\textbf{x} \langle\textbf{Y} \rangle $ mean if $\textbf{Y} \subseteq \textbf{X}$ for random variables?

I was reading daphne's Probabilistic Graphical Models book and she introduces some notation about sets of random variables that I am confused about (on page 21 section 2.1.3.2). Before I ask my ...
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1answer
32 views

How to make clear a letter is a function?

How should I make clear that a symbol is a function? Usually a function is denoted by the letter $f$ or $g$, or is directly applied to arguments (e.g. $c(x,y)$) or is implied to be a function by an ...
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2answers
59 views

Clever Substitution Notation for Logic Formulae

Assume I have a first order- ($\mathsf{FO}$-) formula $ \varphi(x)$ with free variable $x$ and bounded variables $x',x''$. Then, $\varphi(x) \in \mathsf{FO}^3$ since it has $3$ distinct variables. ...
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0answers
69 views

Why not defining a measure as a function on functions?

A measure $\mu$ is a function to $\left[0,\infty\right]$ on the sets belonging to a $\sigma$-algebra. Then for integrable functions $f$ the integral $\int fd\mu$ comes in, having nice properties ...
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1answer
32 views

Notation for rounding function

The Wikipedia article http://en.wikipedia.org/wiki/Nearest_integer_function mentions the following notation for the rounding or "nearest integer" function. (That is, the function that corresponds to ...
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2answers
75 views

Usage of capital and small letters

Are there rules for when small, capital and greek symbols are used? Simple example: The volume left in a cube with a sphere in it is V=C-S with capital standard latin letters, meaning "if you don't ...
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3answers
29 views

Writing down solutions notation

How do you write solutions to a simple equation in set notation? For example: - the solution to $x-4=0$ - the solutions to $x^2-x=0$? Thanks in advance.
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0answers
20 views

What is $P[a, b]$?

I started a fresh course in functional analysis. In the course syllabus, some examples of Banach spaces are required to be studied rigorously: $\mathbb{R}^n, \, \mathbb{C}^n, \, l^p, L^p, C^k[a, b], ...
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1answer
55 views

Notation for the subcategory of commutative $R$-algebras

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
59 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
45 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
23 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
53 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
14 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
21 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
70 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
139 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
111 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
78 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
25 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
30 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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1answer
30 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
24 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
16 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
40 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
76 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
39 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 $g$ ...
2
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0answers
56 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
73 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
194 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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27 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
64 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 ...
1
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1answer
23 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
65 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 ...
0
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0answers
24 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
88 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
33 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
329 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 ...
4
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0answers
67 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
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1answer
71 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
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2answers
268 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
27 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
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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
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3answers
188 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
20 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 ...
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3answers
67 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
186 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
25 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.