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Questions tagged [notation]

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0answers
19 views

Notation for the prime-counting functions for subsets of the natural numbers

The prime-counting function is commonly denoted by $\pi(x)$, and if $b$ is a modulus and $a$ a unit in $\mathbb Z/b$, then $\pi(b,a,x)$ counts the primes in $a \mod b$. Yet suppose one wants to count ...
2
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0answers
106 views

Name for generalization of property: $f^n(x) \ne x$ for all $n > 0$

I am curious about how to specify with standard terminology that a certain function is non-periodic, in the following sense: In the simple case of a unary operation $f: X \to X$, this property would ...
1
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0answers
320 views

Why do some mathematicians believe that the notation $(x_n)_{n\in \omega}$ is better than $(x_n)_{n=0}^\infty$ or $(x_n)_{n\in \mathbb N}$ [closed]

It seems that there is a trend among certain set-theory-oriented mathematicians to prefer the notation $n\in \omega$ to $n\in \mathbb N$ even when dealing with things totally unrelated to ordinal ...
0
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1answer
79 views

Name of a matrix with one column and row removed [closed]

I am looking for the exact name of a matrix where the i-th column and rows have been removed. I cannot remember how it is called in linear algebra, does anyone got an idea? Thanks!
8
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1answer
485 views

Whence “Durchschnitt” and “Vereinigung”?

Today the set-theoretic operations of intersection $\cap$ [German: Durchschnitt] and union $\cup$ [German: Vereinigung] are standard. The modern notations are present in the first edition of van der ...
73
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5answers
11k views

Has incorrect notation ever led to a mistaken proof?

In mathematics we introduce many different kinds of notation, and sometimes even a single object or construction can be represented by many different notations. To take two very different examples, ...
0
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0answers
42 views

Notations for upward Church-Rosser and upward diamond

The following notations are sometimes used to indicate that a relation $\rightarrow$ is (strongly) confluent: $$ \rightarrow\; \vDash \Diamond; \\ \rightarrow^*\; \vDash \Diamond\ \Leftrightarrow\ \...
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0answers
46 views

Question about Notation for Spaces of $n$-ary $k$-ic Forms

Define an $n$-ary $k$-ic form to be a polynomial over the integers of homogeneous degree $k$ in $n$ variables. In Section 1 of the paper "Higher Composition Laws I" (linked below), Bhargava writes $(\...
0
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1answer
84 views

Basic question regarding notation of summation over primitive characters

This seems like a very standard notation in analytic number theory, and I see it a lot. But I was confused with it and I would greatly appreciate any clarification. When one writes sum of the shape $$...
5
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8answers
2k views

Mathematical objects whose name is a single letter

(Not research-level, but perhaps not easily answered elsewhere — you decide if MO can afford the innocent fun. If so, it should likely be “community-wiki” i.e. one object per answer.) I am seeking ...
5
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1answer
177 views

Question about denoting/designating of algebraic structures

I saw this image on Wikipedia (Template:Group-like structures, current revision): Since there are five "properties" that we can have (in this context), namely: totality, associativity, identity, ...
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1answer
150 views

Notation for the restriction map in Galois cohomology

My coauthors and I are writing a paper based on MO questions and answers: Friedrich Knop's answer, my answer 1 and my answer 2. For a linear algebraic group $G$ over a perfect field $k$, I consider a ...
3
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0answers
233 views

Grothendieck construction and coends

In category theory, both the Grothendieck construction and coends are represented by a sort of "integral sign", respectively: $$ \int F $$ for a functor $F:C\to\mathbf{Cat}$, and: $$ \int^x G(x,x) $$ ...
20
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5answers
1k views

The letter $\wp$; Name & origin?

Do you think the letter $\wp$ has a name? It may depend on community - the language, region, speciality, etc, so if you don't mind, please be specific about yours. (Mainly I'd like to know the English ...
2
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2answers
189 views

Technical term for representing object of a presheaf determined by a left-adjoint?

If $\mathcal{D}$ is a locally-small category, then a functor $F\colon\mathcal{C}\rightarrow\mathcal{D}$ has a right-adjoint if and only if for each object $d$ of $D$, the presheaf $$\mathcal{C}^{\...
2
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0answers
219 views

What does the $\pi_1(\mathsf{C})$ really mean?

Assume that $\mathsf{C}$ is a small category (in my case with finitely many objects but this is probably irrelevant). In a paper I'm studying at the moment there is a notion used constantly, this of $\...
3
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0answers
559 views

Affine line with a double origin

Is there a standard short notation for the affine line with a double origin $\mathbb{A}^1 \sqcup_{\mathbb{A}^1 \setminus \{0\}} \mathbb{A}^1$? More generally for $X \sqcup_{X \setminus \{p\}} X$ for a ...
2
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0answers
62 views

Spectral multiplier and Littlewood-Paley projection

I am trying to understand this paper, and have some basic question, and hope this is OK for the MO. Let $f\in \mathcal{S}(\mathbb R^d)$ (Schwartz Space). We know that $\widehat{\nabla f}(\xi)= 2 \...
3
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0answers
111 views

Local system corresponding to induced representation

Let $p\colon Y\to X$ be a finite covering map of path-connected "good" spaces (e.g. manifolds), and let $L$ be a local system on $Y$, and let $V$ be the corresponding representation of $\pi_1(Y)$. ...
5
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1answer
340 views

Generalizing Big O notation to arbitrary vector spaces

I'm constructing a Coq library for Big-O notation. Naturally, I'd like it to be as general as possible. The Wikipedia page on Big-O notation says The generalization to functions taking values in ...
6
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0answers
196 views

Notation: Why Ω for the based loop functor?

This is just a question about notation - probably useless, but it's always baffled me: Why was $\Omega$ chosen to denote the based loop functor? I once heard someone speculate: "It's because $\Omega$...
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1answer
119 views

Typed Values in Formulas

Question: are there any "standard" ways of indicating the meaning of numerical values in formulas, resp. general mathematical texts (theorems, proofs, etc.)? I am especially looking for ...
2
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0answers
163 views

Is there standard notation for restriction partial functions?

Given a partial function $f : A \rightarrow B$, and a subset $S \subseteq A$, we get a new partial function $$f \restriction_S : A \rightarrow B$$ by restriction. However, I prefer to analyse $f \...
10
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1answer
590 views

History of the pullback corner notation

Where/when did the convention originate of marking pullback (and/or pushout) squares by that little right-angle symbol in the corner? The earliest instance I’ve been able to find is in Paul Taylor’s ...
2
votes
1answer
185 views

Notation for the automorphisms of a $S$-scheme over automorphisms of $S$

Here is a slightly anecdotical notational question. Let $S$ be a scheme and let $X$ be a scheme over $S$, with structural morphism $s\colon X\to S$. Is there a good suggestive notation for the group $...
1
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0answers
102 views

Notations - Hardy and Sobolev Spaces [duplicate]

After some confusion on my part, I wanted to know is there a profound mathematical reason why both Hardy spaces and Sobolev spaces are denoted by $H^p$(1). Is it just coincidence? Does it have any ...
7
votes
3answers
288 views

Notations for dual spaces and dual operators

I'm asking for opinions about the 'best' notations for: 1. the algebraic dual of a vector space $X$; 2. the continuous dual of a TVS; 3. the algebraic dual (transpose) of an operator $T$ between ...
1
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0answers
122 views

Does the LaTeX $\eqslantless$ symbol, or the comparable Unicode ⋜, have a well defined meaning for binary numerical relationships? [closed]

At first this appeared a simple question; Unicode defines the symbol as "equal to or less-than", which would appear to be the same as "less-than or equal to". But on investigating a bit, I found very ...
5
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0answers
136 views

Notation for calculus with measures?

One of the strengths of ordinary multivariable calculus is that you can use notation where functions are expressed pointwise (e.g. $\int_a^b x^2 \, \mathrm{d}x$ rather than merely $\int_a^b f$), and ...
1
vote
1answer
121 views

Using Ordinal Notations in Computability Theory Is There A Standard Notation For The Notations Below $\alpha$

I find I frequently have to refer to the set of ordinal notations below some given notation. For instance given a notation $\alpha$ I often need to refer to the set $\lbrace \beta \mid \beta <^{\...
5
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2answers
748 views

What is the standard notation for reversing the order of vector's components? [closed]

If we have a vector $x=(x_1,x_2,\ldots,x_n)$, is there any standard way to denote the vector $(x_n,x_{n-1},\ldots,x_1)$?. I think that $x^{-1}$ could be a good option.
2
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1answer
215 views

Stochastic Process Notation

Note: I'm not an expert on stochastic processes. Please use small words and speak real slow. I'm reading a paper [1], which uses a notation for stochastic processes that doesn't seem to be standard. ...
1
vote
1answer
114 views

Notation and reference for polynomials with coefficients not commuting with the indeterminates

Let $R$ be a noncommutative ring (with unit). Then a "fully noncommutative" (for a lack of better wording) monomial over $R$ in the single noncommutative indeterminate $X$ of degree $d$ is given by a ...
12
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3answers
845 views

Where does the name “R-matrix” come from?

In quantum integrability and related topics a lot of not-so imaginative terminology is used. One may hear people talk about "Q-operators", "R-matrices", "S-matrices", "T-operators", as well as "L-...
12
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5answers
2k views

When did the abuse of notation $y=y(x)$ start?

It's quite common nowadays to name a function and the application of the function to its input with the same letter. (Possibly more so in applied areas. Certainly many calculus textbooks do this.) ...
3
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2answers
239 views

Two different kinds of definitions of $C^k(\overline{\Omega})$ — extension and restriction

This is cross-posted in MSE. I have seen two different kinds of definitions of the notation $C^k(\overline{\Omega})$ — by "extension" of functions on $\Omega$ or by "restriction" of functions on $\...
4
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0answers
128 views

Pairing in Group Cohomology [closed]

I am following Ararat Babakhanian's Cohomological Methods in Group theory. Let $A,B,C$ be $G$ modules then we have a $G$ module structre on $\text{Hom}_{\mathbb{Z}}(B,C)$ with $$\sigma.f(x)=\sigma(f\...
1
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0answers
55 views

Notation for largest universal subclass and class of arrows “locally in” a given class of arrows

Let $\mathcal M$ be a class of arrows in a category $\mathsf C$. I would like suggestions for good notation for the following two classes. The smallest universal (pullback stable) subclass $\mathcal ...
0
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1answer
71 views

Theory of integration of Kernel in çinlar probability and stochastic

I'm reading the probabilistic book write by çinlar, but I don't understand the Kernel theory, in details: $ (E,\mathcal{E}),(F,\mathcal{F})$ are two measurable space $$K:E \times \mathcal{F} \...
4
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1answer
258 views

What countable ordinals are called $\kappa_\alpha$?

Jervell has a notation for countable ordinals up to the small Veblen ordinal using trees: • Herman Ruge Jervell, How to wellorder finite trees and get good ordinal notations, Berkeley Logic ...
4
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0answers
98 views

Is there a name for groups of the form $Sp(1)^n$?

A (compact) torus is a Lie group isomorphic to the product of finitely many circles: $T^n = S^1 \times \cdots \times S^1$. Such groups are extremely important in Lie theory, Differential Geometry, ...
12
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3answers
1k views

History of the notation for substitution

One of the very common notations for syntactic substitution is $[\ /\ ]$. However, there seems to be an inconsistency in the literature about its usage. Many write $[t/x]$ for "substitute $t$ for $x$...
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0answers
134 views

Name for the Quotient $SU(m+1)/(SU(k) \times SU(m-k))$

The sphere $S^{2m-1} \simeq SU(m+1)/SU(m)$ has a canonical $U(1)$-action, and quotienting by this action give complex projective space $CP^m$. We can generalise the family of sphere to the family of ...
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0answers
243 views

Notation for iterated summation

Is there a more compact way to write $$ \sum_{i_1=0}^{N} \sum_{i_2=0}^{N-i_1} \sum_{i_3=0}^{N-i_1-i_2} \cdots \sum_{i_{K}=0}^{N-i_1-i_2-i_3-\ldots-i_{K-1}} a_{i_1i_2i_3\ldots i_K} $$ as something like ...
0
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2answers
405 views

Use of ternary operator in formal writing

I would like to write $$ f(x) = \begin{cases}1&\mbox{if }x = 1\\ 0&\mbox{otherwise.}\end{cases} $$ However, this eats up a lot of vertical space for a very simple statement. Is there agreed ...
0
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1answer
95 views

Comparing vectors with numbers? [closed]

My question pertains to the paper "A Simplified Proof of the Divergence Theorem" by Djairo Guedes de Figueiredo. It's not a big question, actually, but it's confusing me a lot: In the statement of ...
1
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0answers
31 views

Notation to denote substitution of vector elements [duplicate]

I'm looking for notation to denote vector substitution and elimination of elements. This is possible using set notation, but I am looking for shorthand notation that is perhaps already in use. ...
1
vote
0answers
91 views

Notation clash between a representation and spectral radius

I am currently writing a paper where I need talk both about a representation of a semisimple Lie group (usually denoted by $\rho$), and about spectral radii of linear maps (also usually denoted by $\...
2
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0answers
90 views

What does the square root sign tells us in the wave equation? [closed]

I have been reading the paper on wave equations, and I have some confusion in notations. Consider the initial value problem(IVP)(Wave equation): $\frac{\partial ^2 u } {\partial t^2}(x,t) = \...
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1answer
286 views

Correction symbols used for mathematical texts [closed]

When proof reading and correcting a mathematical text, I sometimes see people use special notation symbols in the margin to indicate correction, deletion, replacement and so on. Is there any standard ...