The notation tag has no wiki summary.

**0**

votes

**0**answers

37 views

### Notation for near optimal solution [closed]

Usually, $x^*$ is used to denote the optimal solution to a maximization problem.
I need a notation to describe a solution that is not optimal but "good enough." In my case this solution is the ...

**3**

votes

**1**answer

46 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

269 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 ...

**9**

votes

**2**answers

347 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

287 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 ...

**4**

votes

**0**answers

109 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 ...

**2**

votes

**1**answer

78 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

149 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 ...

**2**

votes

**0**answers

242 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 ...

**7**

votes

**1**answer

385 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

315 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

231 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 ...

**5**

votes

**2**answers

253 views

### Meaning of historical fluxion notation

I've noticed that in 18th century 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 '$\dot{x}$' at ...

**1**

vote

**0**answers

291 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 ...

**0**

votes

**0**answers

101 views

### Notation to distinguish simplicial sets and semisimplicial sets

Usually one writes $X_\bullet$ both for simplicial sets and for semisimplicial sets. But this is potentially confusing if I want to consider maps $X_\bullet\to Y_\bullet^\text{forget}$ in the ...

**1**

vote

**1**answer

180 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

95 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

113 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

480 views

**4**

votes

**1**answer

169 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

125 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

182 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

337 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 ...

**3**

votes

**3**answers

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

**8**

votes

**5**answers

3k 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

385 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

270 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

548 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 ...

**4**

votes

**1**answer

161 views

### 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
$$[L_m,L_n]=(m-n)L_{m+n}+\delta_{m,-n}\frac1{12}(m^3-m)c,$$
$$[c,L_n]=0.$$
...

**2**

votes

**0**answers

136 views

### 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 ...

**1**

vote

**1**answer

352 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 ...

**2**

votes

**1**answer

150 views

### 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 ...

**0**

votes

**0**answers

61 views

### 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 ...

**0**

votes

**0**answers

150 views

### 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 ...

**2**

votes

**1**answer

278 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 ...

**10**

votes

**1**answer

691 views

### 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 ...

**12**

votes

**4**answers

3k views

### Fraktur symbols for Lie algebras: $\mathfrak{g}$, etc.

Does anyone know when and why the Fraktur script was introduced for Lie and other algebras—$\mathfrak{g}$, $\mathfrak{gl}_n$, $X/\mathfrak{g}$,
$\mathfrak{g}\oplus\mathfrak{g}$, $\mathfrak{su}$, ...

**6**

votes

**1**answer

482 views

### What does the t in t-category stand for?

To my knowledge the notion of a t-category was first introduced Beilinson, Bernstein and Deligne's Faiseaux Pervers. But while they explain the name "perverse sheaf", they don't give any indication ...

**7**

votes

**3**answers

647 views

### Origin of the notation s=\sigma+it in analytic number theory

I was wondering if the standard notation of denoting a complex variable by "$s$" had an interesting origin, or if it dates back to Riemann or Weierstrass. Almost every book in analytic number theory ...

**5**

votes

**1**answer

343 views

### Is there a standard notation for a “shift space” in functional analysis?

I'm writing up some notes on the nLab about things like embedding spaces and infinite spheres and similar things (can't link to them yet as I haven't put them up yet). One aspect that crops up time ...

**1**

vote

**1**answer

223 views

### proofs of stochastic boundedness

I'm looking at some statistical literature and trying to compare the results given there in probabilistic big-Oh notation with statements I'm more familiar with.
In particular, I'm trying to ...

**0**

votes

**0**answers

289 views

### Notation for isometric spaces?

Metric spaces are isometric if there exists a bijective isometry between them.
Is there a standard notation for this, along the same lines as $X\approx Y$ for homeomorphic spaces and $X\simeq Y$ for ...

**13**

votes

**3**answers

516 views

### Certain notations in Cayley's work

Two quick questions on notation, motivated by my being reading Cayley at the moment (I stumbled across a random volume of his Collected Works and now I am unable to do anything else but read it ...

**3**

votes

**1**answer

554 views

### Is $O(10^{-6})$ an acceptable notation in numerical analysis? [closed]

The following question has been on math.SE for several days. Without having a satisfying answer, I'd like to ask the experts here.
In mathematics, the big $O$ notation is used to describe the ...

**12**

votes

**4**answers

1k views

### Notation in Frege's Grundgesetze der Arithmetik: The U with a flourish

In the Grundgesetze der Arithmetik, Frege used a number of strange characters for notation. I would be most interested to know anything about the typography (origin, usage and so on) of the strange U ...

**15**

votes

**1**answer

2k views

### What does the σ in σ-algebra stand for?

I was tutoring someone in analysis and realized I have no idea where this notation comes from (or analogous terms: σ-additive, σ-ring, etc). I would like to know why the letter σ was chosen. I can't ...

**3**

votes

**4**answers

396 views

### Better terminology than “equivalence class of functions”

Let $X = C(\mathbb R)$ be the Fréchet space of real-valued continuous functions. For each $f \in X$ and each compact set $D \subseteq \mathbb R$, let $$[f]_D = \{ g \in X : \mbox{$g(t) = f(t)$ for ...

**4**

votes

**1**answer

609 views

### What does $L^\infty_\varepsilon$ mean?

In Volume 4 of Reed and Simon on page 83 the authors refer to the space $(L^\infty(\mathbb{R}^3))_\varepsilon$,
and later on page 119 they use $L^\\infty_\varepsilon$.
Are these two spaces the same? ...

**1**

vote

**1**answer

696 views

### What does $\mathcal{N}$ mean? [closed]

I'm reading a paper that refers to a set $\mathcal{N}$, without defining it. It's a CS paper so it's not complicated maths. Is this the set of natural numbers? I don't get why they're using this style ...

**3**

votes

**2**answers

424 views

### What are some resources discussing mathematical notation?

I'm looking for resources discussing mathematical notation, the theory, the philosophy, the distinct advantages of various notations. Stuff about notation for computer algebra systems is interesting ...