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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4
votes
1answer
84 views

How do you write an integral and why

A. Year 1 Calculus Student Approach $$ F(x) = \int f(x') dx\, $$ B. Random math paper you find online approach $$ F(x) = \int dx f(x') \, $$ C. Spivak $$ F(x) = \int f(x) \, $$ D. ??? (Edit) ...
1
vote
3answers
30 views

Notation: the set of two-element subsets of $\Bbb N$

Let $\{a,b\}\subseteq \Bbb N$. Is there a special name or notation for sets of this type, for example $\Bbb N^{2\ge}$? Any subset size may be used, but the specific size and denoting that order does ...
6
votes
5answers
3k views

Negating A Mathematical Statement

Regard this statement $ x \ge 0$. According to my teacher, by negating this statement, it will become $ x < 0$. Why is this so; why does the $\ge$ morph into $<$, and not into $\le$?
8
votes
1answer
259 views

Looking for an approach to mathematical notation wherein the universe is divided into disjoint worlds.

Is there a rigorous approach to mathematical notation wherein the "universe" is divided into disjoint "worlds," and the meaning of notation is world-dependent? This would solve a few pesky problems. ...
0
votes
1answer
41 views

How to find the ratio of two numbers written in scientific notation, such as $ 2.69 \cdot 10^{-8} $ and $ 2.23 \cdot 10^{-7} $?

The numbers are forces and he wants us to put them in a ratio in order to compare them, but I'm really bad at ratios so. $ 2.69 \cdot 10^{-8} $ Newtons is obviously smaller than $ 2.23 \cdot 10^{-7} ...
0
votes
0answers
46 views

Alternatives to the notation $\|x\|$ for the norm of $x$?

For aesthetic reasons, I don't like the notation $\|x\|$ for the norm of $x$. Have any alternatives been proposed?
0
votes
1answer
34 views

Definition of Kronecker Delta

Is $\delta _{mn}=1$ when $m\neq n$, and $\delta _{mm}=0$? I am not very good at Math. So would you give me the answer and explanation please?
4
votes
4answers
740 views

Why don't we indicate the variable to summed as we do for integrals?

When integrating over a certain variable $x$, we make sure to end the integral with $dx$, like so: $$\int_{1}^{\infty}\frac{1}{x^2}dx$$ The reason for this of course becomes more clear as one goes ...
0
votes
0answers
14 views

tuple of tuples notation

Is the following notation right for indicating a $\mathit{m}-$tuple of $\mathit{n_{j}}-$tuples (I mean that each tuple of the $\mathit{m}-$tuple has a different number of elements)? ...
2
votes
1answer
61 views

What is the notation for taking negative imaginary values for roots of negative numbers?

I have a formula which is analytic in its argument $x$. In it, there is a square root of a variable as in $\sqrt{x}$. Although meaningful results are obtained when positive roots are taken for for ...
0
votes
1answer
37 views

Is there a name for a property defined in terms of open sets?

We know that if a property is defined in terms of open sets then the property is preserved under a homeomorphism. Is there a name for such a property?
0
votes
1answer
17 views

Ever thought of differentiate brackets for function and for order of operations?

Now parentheses "()" is used for both function, e.g. $f(x)$, and for order of operations, e.g. $(3+5)*2$. Ever in math history be suggested to differentiate? for example square bracket "[]" can be ...
1
vote
0answers
21 views

Why abstract index notation should not be confused with the Ricci calculus?

Considering this answer, it is mentioned that the range of indices $a, b, c,\dots$ are seen as abstract and coordinate-free and linear operations can be represented with them; and the range of indices ...
1
vote
1answer
57 views

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 ...
1
vote
0answers
17 views

Notation for vectors that exclude zero

Is there a conventional notation for the set of all vectors of length $n$ such that not one element of the vector is equal to zero? Right now I have to write out something like "vector $B$ blah blah ...
0
votes
2answers
57 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. ...
2
votes
0answers
33 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 ...
0
votes
1answer
27 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 ...
3
votes
0answers
61 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 ...
1
vote
1answer
26 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 ...
0
votes
2answers
66 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 ...
1
vote
3answers
27 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.
0
votes
0answers
19 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], ...
2
votes
1answer
53 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 ...
2
votes
3answers
1k views

Notation of random variables

I am really confused about capitalization of variable names in statistics. When should a random variable be presented by uppercase letter, and when lower case? For a probability $P(X \leq x)$, what ...
0
votes
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! ...
0
votes
1answer
20 views

Notation for the mean within a set of divided values multiplied by another value

This is my very first crack at notation and I'm very unsure about the results: With two sets with values: QTY: [4, 5, 5, m...], DOSE: [20, 10, 10, n...], and the number 30. The formula is: ((30 / ...
0
votes
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? ...
0
votes
1answer
21 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
44 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
96 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
625 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
5 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
70 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
17 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
106 views

What is the $\lor$ symbol?

In researching the consensus algorithm, I came upon the consensus theorem: How does the $\lor$ symbol function?
0
votes
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.
1
vote
1answer
48 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
115 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 ...
-1
votes
0answers
27 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
23 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
22 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
231 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
36 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 ...