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3
votes
1answer
50 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
0answers
277 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
2answers
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
1answer
288 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
0answers
111 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
1answer
80 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
1answer
150 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
0answers
245 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
1answer
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
1answer
329 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
2answers
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
2answers
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
0answers
298 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
0answers
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
1answer
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
0answers
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
1answer
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
1answer
483 views

What exactly does \gg and \ll mean?

For example, $f(T)\ll_T 1$ where $T$ is a positive number.
4
votes
1answer
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
0answers
126 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
1answer
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
1answer
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
3answers
526 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
5answers
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
1answer
386 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
2answers
271 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
3answers
554 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
1answer
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
0answers
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
1answer
353 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
1answer
151 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
0answers
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
0answers
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
1answer
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
1answer
697 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
4answers
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
1answer
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
3answers
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
1answer
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
1answer
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
0answers
294 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
3answers
517 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
1answer
556 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
4answers
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
1answer
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
4answers
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
1answer
611 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
1answer
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
2answers
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 ...
10
votes
6answers
6k views

A symbol to denote the set of prime numbers ?

It strikes me that there is no widely accepted symbol to denote the set of usual prime numbers in $\mathbb{N}$. Look: $$\zeta(s)=\prod_{p\in \mathrm{?}}\frac{1}{(1-p^{-s})}$$ Wouldn't it be nicer ...