The notation tag has no usage guidance.

**2**

votes

**1**answer

170 views

### Notation: $Sigma$ and $Pi$ of intersections

In Jech - Set Theory, the proof of Theorem 31.7, I came along some notations I wish to understand correctly.
For a countable elementary substructure $M \prec H_\lambda$ and $A \in M$ and a generic ...

**-4**

votes

**1**answer

132 views

### Looking for the name of a mathematical symbol that looks remotely like 1 (answer: indicator function) [closed]

Original question:
The symbol looks like a numeral 1 written like an R in $\mathbb{R}$. It has a double vertical line and a serif at the bottom. It represents a function of a parameter: ...

**0**

votes

**1**answer

229 views

### Meaning of $[A,B]$ when $A$, $B$ are self-adjoint

This is just a question about notation, but it got no useful answers on math.stackexchange.
Let $L$ be the Lie algebra of $n\times n$ Hermitian matrices, with Lie bracket $(A,B)\mapsto i(AB-BA)$.
...

**0**

votes

**0**answers

33 views

### Sobolev space notation for interpolation and Gagliardo norm best practice

I work on a compact manifold $M$. I'm using three different Sobolev spaces:
$A^s(M)$ defined set of functions $u$ with the Gagliardo norm.
$B^s(M)$ defined as interpolation space between different ...

**20**

votes

**1**answer

943 views

### What is $\infty^6$?

The title of this question may make you want to close it immediately, but bear with me a moment. In several older mathematics papers (early 20th century) I have seen statements such as
The ...

**3**

votes

**4**answers

489 views

### Notation for $\log \log \cdots \log n$? [closed]

Is there some accepted, more concise notation for expressions like $\log \log \log n$?
I just noticed an arXiv posting that quotes the bound
$$
\frac{\log X \log \log X \log \log \log \log X}
{ \log ...

**1**

vote

**0**answers

167 views

### Products between metrics in a product of manifolds

In the "Einstein Manifold" book written by Arthur Besse, chapter 16, there is a notation of a manifold composed by the Cartesian product between two others:
$(M_1\times M_2, f^p(g_1 \times g_2))$
...

**4**

votes

**2**answers

344 views

### Terminology for metrics?

For some reason, I'm currently interested in the following relation - let $d,\delta$ be two metrics on some space $X$. We call the metrics _______ if there are some constants $C,E>0$ such that for ...

**3**

votes

**1**answer

350 views

### Notation: Categories of measur(abl)e spaces

Is there a common notation in the literature for
the category of measurable spaces and measurable maps?
the category of measure spaces and measure-preserving maps?
The nlab suggests ...

**3**

votes

**1**answer

225 views

### Was $\Sigma x$ used as quantifier?

Kurt Gödel in 1931 used $x\Pi a$ where we in contemporary notation would use $(\forall x) A$ or $(x)A$, and $Ex a$ where we would use $(\exists x) A$. I believe that I remember that $\Sigma xA$ has ...

**0**

votes

**1**answer

87 views

### Help with notation for the state of a dynamical system defined by a PDE

Before my question let me briefly describe a simplified version of the dynamical system I'm working with. Suppose that I have a density function $m(\boldsymbol{x},t)$, that describes the abundance of ...

**3**

votes

**1**answer

229 views

### When was the “arrow notation” for functions first introduced?

When was the "arrow notation" $f: X \to Y$ for functions first introduced? Who introduced it and with which motivation?
I ask this question in order to understand whether it was, in part, this ...

**5**

votes

**1**answer

234 views

### Contexts and notations for composing asymmetric simplices

Imagine the elements of a group-like structure as puzzle pieces with essential two sides, an IN-side and an OUT-side.
You can compose two such pieces in two obvious ways:
Now consider triangular ...

**1**

vote

**1**answer

144 views

### Lefschetz fixed notation

If $f\colon X\to X$ is a self-map of a nice space with isolated fixed points, then the Lefschetz fixed point theorem relates a global number to local numbers. Some write: $L(f)=\sum_{x\in ...

**2**

votes

**1**answer

299 views

### Disruptive innovations in mathematical notations [closed]

I am wondering whether there are examples of mathematical notations that, once introduced, have drastically changed or simplified the way to address a problem or a mathematical area, or that have ...

**5**

votes

**1**answer

221 views

### Meaning of $g_d^r$ in algebraic geometry

As an editor I often encounter the symbol $g_d^r$ as a noun. I tried googling but I only get papers where the symbol is used without a definition. Can someone supply a reference to a definition? ...

**1**

vote

**1**answer

165 views

### Is the notation ${}^t g$ for the transpose of a linear transformation intended to be suggestive?

The notation ${}^t g$ for the transpose of a linear transformation is, in my view, quite unusual: otherwise (at least in many areas of math), one almost never sees subscripts or superscripts appearing ...

**2**

votes

**1**answer

145 views

### A question about some notation involving the exclamation mark [closed]

What does the symbol ‘!’ signify? Is it $ \text{argmin} $? For example, $ \| A x - y \| = \min! $.

**2**

votes

**3**answers

160 views

### How to Express Undirected Integration

Is there an agreed way of expressing undirected integration in formulas?
my idea of doing so would be to use the absolute value of the differential
$$\int_a^b f(x)|dx| = \int_b^a f(x)|dx|$$
but I ...

**1**

vote

**0**answers

108 views

### Default Orientation of Vectors [closed]

When I started studying math in 1982 in Germany, there seemed to have been a change in the choice of the default orientation of vectors; while it was row-vectors till then, it changed to ...

**0**

votes

**2**answers

136 views

### Conventional notation for the probabilistic functor

The probabilistic functor $P$ sends a measurable space $X$ to the space of probability measures on $X$ endowed with $\sigma$-algebra generated by evaluation maps, and measurable maps $f:X\to Y$ to ...

**25**

votes

**3**answers

2k views

### Who invented diagrammatic algebra?

There is a strong and growing trend to do mathematics via diagrammatic algebra, which involves constructing and manipulating equations whose elements are diagrams drawn in the plane. The manipulations ...

**1**

vote

**1**answer

118 views

### Formula for the Ordinal Number of k-Sets of Positive Integers

Background of my question is, that I would like to store flags indicating the relation between a pairs of non-adjacent edges of a graph (that relation could for example be, whether the edges cross, ...

**0**

votes

**1**answer

241 views

### Choosing Notation for Variable Substitution into Derivative Expressed with Differentials [closed]

Consider function $f(x)$. I've counted 4 possible notations to write a derivative of $f(x)$ at point $x = a$:
$f'(a)$;
$\frac{\operatorname{d}{f(a)}}{\operatorname{d}x}$;
...

**3**

votes

**1**answer

303 views

### Random weighted selection without replacement

I am using the following procedure to select $m$ different numbers $\{i_1,\ldots,i_m\}$ from the set $\Omega = \{1,\ldots,N\}$, with $m,N\in\mathbb{N}$ such that $m< N$.
Selection procedure
...

**7**

votes

**0**answers

437 views

### Is there a theory of abuse of notation? [closed]

Is there any theory about the different ways notation can be abused and which abuses are ineliminable without complicating the notation in some essential way? We can define "abuse of notation" as any ...

**10**

votes

**2**answers

423 views

### Historical quotation search: Equations/formulae in (Latin?) prose, before modern symbolic notation

I have been trying, without success, to find a vaguely-remembered quotation: the quadratic equation (or perhaps the quadratic formula), given in (Latin?) prose, along lines like “Consider that ...

**6**

votes

**1**answer

442 views

### Origin of symbols used for half-sum of positive roots in Lie theory?

The Weyl character formula is a central result in the finite dimensional representation theory of semisimple Lie groups, algebraic groups, Lie algebras. Related questions on MO include these here ...

**3**

votes

**0**answers

193 views

### Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$?

I want to express the following statement about a function $f(n)$: there exists $f_\Omega\in\Omega(h(n))$ such that $f\in O(g(f_\Omega(n))$. What's the correct notation for this? Is it $f\in ...

**1**

vote

**1**answer

125 views

### Understanding Sweedler's notation for the structure map of a comodule

I was hoping someone might be able to shed some light on the choice of indices for expressing the coaction using Sweedler notation.
For example, in the paper of Andruskiewitsch About ...

**2**

votes

**1**answer

173 views

### Meaning of notation $\mathbb{Q}^\wedge k$, $-\infty^\wedge \mathbb{Q}$ for linear orders

I am reading Friedman & Stanley A Borel reducibility theory for classes of countable structures (J. Symbolic Logic 54 (1989), 894–914; MR1011177) and a caret (${}^\wedge$) appears as notation in ...

**3**

votes

**1**answer

598 views

### Equal signs with fancy marks

Some people use $\stackrel{\mathrm{def}}{=}$, $:=$ or $\stackrel{\Delta}{=}$ for definitions.
In more informal contexts, I have also seen $\stackrel{?}{=}$, for "I wish to prove this equality, which ...

**6**

votes

**1**answer

461 views

### Where does the notation $\pi_1(X,x)$ for the fundamental group first appear?

I've spent the last half hour browsing Stillwell's translation of Poincaré's Analysis Situs and Dieudonné's History of Algebraic and Differential Topology, and I haven't found the source of this ...

**2**

votes

**1**answer

1k views

### Maximum/Minimum operator precedence

Is there any standard preceding order for the operators $a \wedge b = \min{(a,b)}$ and $a \vee b = \max{(a,b)}$ with respect to the arithmetic operators.
For example
$$ a \wedge b + c = (a \wedge ...

**4**

votes

**2**answers

287 views

### Name and notation for a binary operation

Is there a standard name or standard symbol for the binary operation that combines $x$ and $y$ to give $xy/(x+y)$, or equivalently $1/(1/x+1/y)$? (At least the expressions are equivalent if we ignore ...

**7**

votes

**3**answers

342 views

### Meaning of historical fluxion notation

I've noticed that in 18th century English books on calculus writers would say that 'the fluxion of $ax$ is $a\dot{x}$' and 'the fluxion of $x^n$ is $n x^{n-1} \dot{x}$'. What does this extra ...

**1**

vote

**0**answers

638 views

### What does this notation mean: matrix norm with a two-number subscript

I recently came across this notation, without explanation, in a paper:
$||\mathbf{W}||_{2,1}$
From the context, I know that $\mathbf{W}$ is a matrix, which could be any size, and that ...

**1**

vote

**1**answer

198 views

### Notation of a pregallery

I'm transcribing parts of Harm van der Lek's thesis 'The homotopy type of complex hyperplane complements' and due to it being written in 1983 the typesetting isn't very detailed. In latex, how should ...

**0**

votes

**0**answers

103 views

### Notation for substructure, especially for permutations?

Is there a standard notation that expresses substructure?
The specific case that I care about is the following:
Suppose $\sigma,\tau$ are permutations such that $$\sigma(x)\not=x\implies ...

**1**

vote

**1**answer

140 views

### What's the name of “twisted semidirect products”?

Let $V$ be an $n$-dimensional real vector space, $\Lambda\subseteq V$ a lattice, and $K$ a subgroup of $Aut_{\mathbb{Z}}(\Lambda)\cong GL(n,\mathbb{Z})$. Let also $\sigma \in Z^1(K,V/\Lambda)$, ...

**1**

vote

**1**answer

664 views

**4**

votes

**1**answer

213 views

### Notation for upperbound power sets.

There is a standard notation $\mathrm{ZF}[n]$ for Zermelo Fraenkel set theory with the power set axiom restricted to saying the set of natural numbers has $n$ successive power sets ...

**1**

vote

**0**answers

142 views

### Notation for the subobject classifier

Does anyone know why in books on category theory the notation for the subobject classifier is almost everywhere the capital greek letter $\Omega$?
Gérard Lang

**2**

votes

**1**answer

205 views

### How many flavors should a notational system offer for rank-1 tensors?

The notation for tensors is like the plumbing in a very old Vermont farmhouse. It may once have been intentionally designed, but after that it just evolved. As an example, it seems that depending on ...

**2**

votes

**1**answer

353 views

### Notation arb(x)

Suppose we have extended $ZF$ by adding to $ZF$ an unary function symbol $arb$ (an arbitrary element of a set) and a corresponding axiom "For every non-empty set $S$, $arb(S)$ is in $S$".
Will be the ...

**4**

votes

**3**answers

568 views

### Is there a (standard) name for $\bar{A}\setminus A$?

This is a notation question:
If $A$ is a set in a topological space and $\bar{A}$ is its closure, is there a (standard) name for $\bar{A}\setminus A$?

**11**

votes

**5**answers

6k views

### If d/dx is an operator, on what does it operate?

If $\frac{d}{dx}$ is a differential operator, what are its inputs? If the answer is "(differentiable) functions" (i.e., variable-agnostic sets of ordered pairs), we have difficulty distinguishing ...

**1**

vote

**1**answer

463 views

### Set Exponentiation: Is Y always disjoint from Y^X? [closed]

If $y \in Y$ and $g \in Y^X$, we often write $y+g$ as shorthand for the map $x \mapsto y+ g(x)$. Similarly if $f \in Y^X$ then $f+g = x \mapsto f(x)+g(x)$. However this presupposes that we can ...

**1**

vote

**2**answers

347 views

### Standard notation/symbol for an embedding function

Hello everyone,
Suppose that I am defining a function which embeds a surface (manifold) in $\mathbb{R}^3$.
Is there a standard symbol or letter that is used for this function?
Additionally, is ...

**3**

votes

**3**answers

794 views

### notation for formal Laurent series

I've found a few articles that write the ring of formal Laurent series in $t$ as $R((1/t))$, but what's the underlying meaning of $\cdot ((\cdot))$?
A mathematician of my acquaintance swears that ...