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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16
votes
0answers
179 views

How and why did Weierstrass $\wp$ get its special symbol?

I kind of always hated drawing the Weierstrass $\wp$ symbol by hand, and it struck me as odd how and why it achieved its special status in the first place. After all, there are tons of other important ...
10
votes
0answers
89 views

$\sin$ vs. $sin$ - history and usage

One thing newcomers to TeX or MathJax often get wrong is that they write something like $sin(x)$ instead of $\sin(x)$ - the point being that common mathematical functions with names consisting of ...
9
votes
0answers
146 views

Why is $J$ sometimes used to denote $\mathbb{Z}_{>0}$?

In older books, such as Rudin's Principles of Mathematical Analysis and Herstein's Topics in Algebra, I've noticed that authors tended to use $J$ to denote $\mathbb{Z}_{>0}$. Does anyone have any ...
9
votes
0answers
4k views

What's more common? Re / Im or Fraktur-R / Fraktur-I for real / imaginary part?

Title says it all. What's more common? Is there one to prefere (maybe due to some norm)? This: $\operatorname{\mathfrak{R}} z, \operatorname{\mathfrak{I}} z$ or that: $\operatorname{Re}z, ...
8
votes
0answers
272 views

Identities for Sieve of Eratosthenes collisions.

Edited to define the last two tables Three Questions: 1) Is all notation correct? 2) Is there a symbol for flatten? 3) How would we prove the identities: the sum of the divisors in the symmetric ...
7
votes
0answers
70 views

Sets, that have $\operatorname{LCM}\left(|c_1|,\dots,|c_p|\right)=\sum_{k=1}^p |c_k|$

I found that the least common multiple of the sizes of conjugacy classes $c_k$ of the symmetric group $S_n$ is equivalent to $n!$ the order of the group. Equivalently the sum of all $c_k$ is also ...
7
votes
0answers
370 views

notation for ramification index and inertial degree

For a prime $Q$ lying over a prime $P$, I have seen the ramification index of $Q$ over $P$ denoted by $e(Q|P)$ and the inertial degree of $Q$ over $P$ by $f(Q|P)$. What is the origin of the ...
6
votes
0answers
64 views

Subgroup notation on Wikipedia

Surfing wikipedia about finite groups, I see a lot of notation similar to that found in this section (image below). Its meaning is not clear to me and I didn't find an explanation on wikipedia. Could ...
6
votes
0answers
96 views

A question about co-exponentials

An exponential object $B^{A}$ is defined to be the representing object of the functor $$\mathcal{C}\left(- \times A,B\right): \mathcal{C} \rightarrow Set$$ or equivalently, as the terminal object of ...
6
votes
0answers
235 views

Typesetting imaginary unit and bessel functions

I know that this issue has been treated in many places, but I have yet to reach something conclusive, hence I am herein seeking your help. Following the 260.3-1993 - American National Standard ...
6
votes
0answers
137 views

Origin of $\mapsto$ notation

Who invented the brilliant $\mapsto$ notation for describing a function's action on a point, as in $x \mapsto x^2$? This is in some sense a counterpart to Who came up with the arrow notation $x ...
5
votes
0answers
45 views

Symbols to represent each distinct symmetry of polyhedra

Is there a pictorial or symbolic way to represent each distinct symmetry of a polyhedron?
5
votes
0answers
78 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 ...
5
votes
0answers
282 views

Paul Erdős Joke.

I was watching the great documentary "$N$ is a Number" and in it Erdős tells a joke where he writes: PGOM LD AD LD CD Which means poor great old man, living dead, archeological discovery, legally ...
5
votes
0answers
268 views

Is there a name or definition for this popular notation?

I'm sorry if this is a silly question. I've done quite a bit of searching and have not found any definition or name for this symbol/usage, despite immense popularity and convenience. The sources I've ...
5
votes
0answers
224 views

Notation for n-ary exponentiation

We have $n$-ary sums ($\sum$) and products ($\prod$). Is there an $n$-ary exponentiation operator? $$\underset{i=1}{\overset{n}{\LARGE{\text{E}}}}\, x_i = x_1 \text{^} (x_2 \text{^} (\cdots \text{^} ...
5
votes
0answers
242 views

Where does the notation $\mathrm{Ad}(U)$ for $a\mapsto UaU^*$ come from?

I have often seen, in the context of operator theory and operator algebras, the notation $\mathrm{Ad}(U)a=UaU^*$, where $U$ is a unitary operator on a Hilbert space $H$ and $a$ is a bounded linear ...
4
votes
0answers
27 views

How to read an expression that is ambiguous?

(1) How should I parenthesize $\log n \log \log n$? Also: (2) What general rule/rationale is used to do this parenthesization? To elaborate; I see why $\log\log n$ is unambiguous, but $\log n \log ...
4
votes
0answers
106 views

Why is the Euclidean metric called the prime at infinity?

I've been studying p-adic analysis recently and after a bit of searching on the web, I haven't found an answer as to why the Euclidean metric is referred to as the 'prime at infinity', and given the ...
4
votes
0answers
63 views

What is the name of the function that indexes Grothendieck universes?

Assume Tarski-Grothendieck set theory. Then Grothendieck universes form a well-ordered proper class, so we can let $U_\alpha$ denote the $\alpha$'th Grothendieck universe, where $\alpha$ is an ...
4
votes
0answers
247 views

Divisibility notation history

I'm writing a paper project for school about divisibility, so I'd like to include a bit of history about that subject. I'm mostly interested in notation of $|$ sign used in past, but everything else ...
4
votes
0answers
319 views

Is there a notation for $f(x,y) - f(y,x)$?

Suppose we have a function $f(x,y)$ in two variables. Is there an operator on the function, say, $$([]f)(x,y) = f(x,y) - f(y,x)?$$ In other words, I'm looking for a commutator in terms of function ...
4
votes
0answers
110 views

Harmonic measure or harmonic kernel

In the theory of discrete-time stochastic processes on a measurable space $(\mathscr X,\mathscr B(\mathscr X))$ one usually starts with a Markov kernel $$ P:\mathscr X\times \mathscr B(\mathscr ...
4
votes
0answers
227 views

Where does the 'divides' sign come from?

When $a$ divides $b$ we say $a | b$. Where does the $|$ sign come from? This is not homework, just personal interest in the history of mathematical language.
3
votes
0answers
26 views

What is the product of an empty family of similiar algebras, that is $\prod\langle \mathbf{A}_i \ | \ i \in I \rangle $, where $I = \emptyset$?

What is the product of an empty family of similiar algebras, that is $\prod\langle \mathbf{A}_i \ | \ i \in I \rangle $, where $I = \emptyset$? The family $\langle \mathbf{A}_i \ | \ i \in ...
3
votes
0answers
50 views

Notation $(a,b)$ for $]a,b[$.

Is there any logic or justification for the notation $(a,b)$ to represent $]a,b[$? To me this notation is very ambiguous and confusing because it looks like a couple of numbers and not an interval. ...
3
votes
0answers
69 views

Can $\mathbb A=\{f(x)\mid x\in\mathbb R\}$ be shortened as $\mathbb A=f(\mathbb R)$?

Can $\mathbb A=\{f(x)\mid x\in\mathbb R\}$ be shortened as $\mathbb A=f(\mathbb R)$? I saw this notation in the IMO olympiad training materials (the solution to the Problem 16 (IMO 1999 Problem ...
3
votes
0answers
20 views

Equivalent to proportionality sign for additive constants

Short question Is there an equivalent to the proportionality sign $\propto$ for additive constants? The proportionality relation $y\propto x$ implies that $y=kx$ for some constant $k$. Is there a ...
3
votes
0answers
58 views

Etiquette for proper usage of Greek letters and other notation

I've progressed to the "output" point in my mathematics career and have run into a slightly embarrassing problem while writing a paper. Clearly, certain Greek letters are suitable for some situations ...
3
votes
0answers
76 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 ...
3
votes
0answers
75 views

A name for something like a CW complex?

The class $\mathcal{CW}_n$ of finite $n$-dimensional CW complexes can be defined recursively: $\mathcal{CW}_0$ consists of finite sets; If $X \in \mathcal{CW}_n$, $\phi:S^n \amalg \cdots \amalg S^n ...
3
votes
0answers
62 views

Good confusion-avoiding notation for gluing toric varieties from fans?

$ \newcommand\R{\mathbb R} \newcommand\C{\mathbb C} \DeclareMathOperator\Cone{Cone} $I'm trying to establish a good notation to avoid confusion when we glue toric varieties from affine pieces. A ...
3
votes
0answers
121 views

Why do Mathematicians use $u$ and $v$ as variables?

I'm sure this has happened to you as well: you are reading some hand-written work, the variables used are $u$ and $v$, and at some point the handwriting becomes unclear and you cannot distinguish the ...
3
votes
0answers
600 views

What symbol expresses “less than approximately”?

Suppose, I want to state that $a$ is less than $b$. However, I do not know $b$ exactly, but only that it is approximately $c$. With other words I want to state that $a$ is lesser than some value which ...
3
votes
0answers
106 views

What does $\cos(n,t)$ mean?

In the book by JL Lions "Quelques methodes...", (Chapter 2, Section 3.3, page 197), he uses the notation $$\cos(n,t)$$ in a boundary condition on a domain $\Omega(t)$, where $n$ denotes the normal ...
3
votes
0answers
86 views

What is a common symbol for angles and what are semantic differences?

I've just seen that LaTeX offers at least three symbols for denoting angles: $\text{\sphericalangle}:\sphericalangle ABC \\\text{\measuredangle}:\measuredangle ABC\\\text{\angle}: \angle ABC$ I ...
3
votes
0answers
51 views

Curve of centers of curvature

I really can't find the English name of the curve of the centers of curvature of a curve. Formulated more precisely: Suppose $\alpha$ is a regular curve in $\mathbb{E}^2$ and $||\alpha(t)'||=1$. How ...
3
votes
0answers
63 views

partial derivative notation question

I'm reading a book called Correlated Data Analysis, Analytics, and Applications and I simply don't understand some notation. The author says, in chapter 2, page 26: A unit deviance is called ...
3
votes
0answers
367 views

Notation for the pushforward measure

Given a measure space $(X,\Sigma,\mu)$, a measurable space $(Y,\Xi)$ and a measurable map $f\in\Sigma/\Xi$, the pushforward measure $\nu:=\mu\circ f^{-1}$ is given by $$ \nu[A] = \mu[f^{-1}(A)] $$ ...
3
votes
0answers
39 views

notation for invariation

Let $\Lambda = \{T \in \operatorname{Her}_2(\mathcal{O}) ; T \ge 0\})$ and $\mathcal{O}$ the maximal order of some quadratic imaginary number field. I write $T[U] := U^* \cdot T \cdot U$ where $U$ is ...
3
votes
0answers
125 views

Definition(s) for variable binding in first-order logic

The following statement made me realize that variable binding can be defined in first-order logic: The same holds for λ terms to define functions. There is no reason that they could not be ...
3
votes
0answers
99 views

Mathematical notation for formulas involving trees

I am working on document that requires me to write such things as "$T_1$ is a descendant of $T_0$", or "$N_1$ is an parent of $N_2$". For now, I've been highjacking set notation for use in formulas, ...
3
votes
0answers
70 views

Define composition of small cyles and making a big graph

I am having following sub graphs and wish to compose all and make a one bigger graph (say G). After that, I want to select the closed path where it is passing along the outer vertices of that ...
3
votes
0answers
254 views

What kind of matrix/tensor notation is this?

I'm hoping someone on here recognises this and has an answer, because I'm having serious memory issues. About a year ago, I came across the following way of representing tensors of rank $n$ in matrix ...
3
votes
0answers
123 views

How write Dirichlet character sums for the terms of the von Mangoldt function?

The way to separately write the terms of the von Mangoldt function $\Lambda$ as Dirichlet character sums seems to be: $$\Lambda (1) = \sum\limits_{n=1}^{\infty } \frac{(e^{\Lambda (1)} \chi ...
3
votes
0answers
86 views

What's this called? $\mathbb{C}[d/dx]$

The 'ring of differential operators wrt x' ? Thx.
3
votes
0answers
226 views

Better Tensor Notation

I am in a General Relativity class, and I am finding the usual tensor notation very difficult to think about -- it seems like there are too many names to express something simple. E.g., I think of ...
3
votes
0answers
473 views

Notation for sampling random variate

Is there standard notation for sampling a value from a probability distribution? Like, if I had a random variable $X$, setting $x$ to whatever value I happened to sample from $X$ on this occasion? I ...
3
votes
0answers
202 views

How did Bessel functions come to be denoted by $J_n$?

The $n$th Bessel function of the first kind is usually denoted $J_n(x)$. Where did the use of the letter $J$ to indicate the Bessel function come from?
3
votes
0answers
150 views

bar index notation

For complex manifolds , people usually write the first fundamental form as $ds^2=g_{a\bar{b}}dz^ad\bar{z}^b$ (at least physicists) with a bar over the second index of the metric, but don't usually ...