The notation tag has no wiki summary.

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### 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 ...

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217 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 ...

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69 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 ...

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198 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 ...

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166 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 ...

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136 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 ...

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281 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 ...

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### 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? ...

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156 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 ...

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140 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! $.

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156 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 ...

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### 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 ...

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127 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 ...

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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 ...

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113 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, ...

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204 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 $x = a$:
$f'(a)$;
$\frac{\operatorname{d}{f(a)}}{\operatorname{d}x}$;
...

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194 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
...

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### 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 ...

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### 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 ...

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397 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 ...

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167 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 ...

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108 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 ...

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164 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 ...

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### 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 ...

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### 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 ...

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### 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 ...

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268 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 ...

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### 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 ...

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### 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 ...

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### 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 ...

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### 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 ...

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135 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 $\sigma \in Z^1(K,V/\Lambda)$, ...

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### 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 ...

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135 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

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### 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 ...

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### 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 ...

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### 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 $\bar{A}\setminus A$?

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### 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 ...

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431 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 ...

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315 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 ...

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712 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 ...

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### Why is there a discrepancy between the normalizations of the central terms for the commutation relations of the Virasoro versus Neveu-Schwarz Lie algebras?

Following the standard conventions in the literature, the commutation relations of the Virasoro Lie algebra are given by
$$[L_m,L_n]=(m-n)L_{m+n}+\delta_{m,-n}\frac1{12}(m^3-m)c,$$
$$[c,L_n]=0.$$
...

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### Notation for a canonical quotient of an abelian variety in positive characteristic

This is a light question about notation, but I received no answer in Stackexchange.
Let $k$ be an algebraically closed field of characteristic $p>0$ and let $A=A_{/k}$ be an ordinary abelian ...

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381 views

### Notation for ends of a string

I work now a lot with strings of characters and other finite sequences and found that I need many times a good notation for "cutting the end" a string. If $a$ is a finite sequence and $a'$ is its ...

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### Terminology for system of equations and…

I am looking for the standard term for a system that consists of things of the form
$p_i(x_1,\ldots ,x_n)=0$ and of the form $q_j(x_1,\ldots,x_n)\neq 0$ with the $p_i$ and $q_j$ polynomials. I have ...

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### Is $\{x_{zt}\}_{Z\times~ T}$ a good notation for specifying the indexed family of entities $x_{zt}$ with $z\in Z,\, t\in T$?

I have a model with lots of variables indexed over a few sets.
After having introduced the model, i.e. having already said that $x_{zt}$ has indexes $z\in Z$ and $t\in T$, instead of writing
"we ...

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### Terminology for the image of the diagonal embedding.

Let $X$ be a topological space equipped with maps into two spaces $\bar X_1$ and $\bar X_2$. Is there a standard notation/terminology for the closure $\bar X$ in $\bar X_1 \times \bar X_2$ of the ...

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281 views

### Name of a lattice-property

Assume that we have a complete lattice $(L,\leq)$.
I would like to know whether the following property has a specific name and whether lattices with this property have been studied somewhere:
For ...

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### Why is the identity element of a group denoted by $e$?

The question was asked by a student, and I did not have a ready answer. I can think of the German word ``Einheit'', but since in German that is not how the identity element of a group is called, I ...