Questions tagged [notation]
The notation tag has no usage guidance.
0
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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
votes
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
vote
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
votes
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
votes
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
votes
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
votes
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:
$$
\rightarrow\; \vDash \Diamond; \\
\rightarrow^*\; \vDash \Diamond\ \Leftrightarrow\ \...
1
vote
0answers
46 views
Question about Notation for Spaces of $n$-ary $k$-ic Forms
Define an $n$-ary $k$-ic form to be a polynomial over the integers of homogeneous degree $k$ in $n$ variables. In Section 1 of the paper "Higher Composition Laws I" (linked below), Bhargava writes $(\...
0
votes
1answer
84 views
Basic question regarding notation of summation over primitive characters
This seems like a very standard notation in analytic number theory, and I see it a lot. But I was confused with it and I would greatly appreciate any clarification.
When one writes sum of the shape
$$...
5
votes
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
votes
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, ...
1
vote
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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$...
-1
votes
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
votes
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
votes
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
vote
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
vote
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
votes
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
vote
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
votes
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
$$K:E \times \mathcal{F} \...
4
votes
1answer
258 views
What countable ordinals are called $\kappa_\alpha$?
Jervell has a notation for countable ordinals up to the small Veblen ordinal using trees:
• Herman Ruge Jervell, How to wellorder finite trees
and get good ordinal notations, Berkeley Logic ...
4
votes
0answers
98 views
Is there a name for groups of the form $Sp(1)^n$?
A (compact) torus is a Lie group isomorphic to the product of finitely many circles: $T^n = S^1 \times \cdots \times S^1$. Such groups are extremely important in Lie theory, Differential Geometry, ...
12
votes
3answers
1k views
History of the notation for substitution
One of the very common notations for syntactic substitution is $[\ /\ ]$.
However, there seems to be an inconsistency in the literature about its usage.
Many write $[t/x]$ for "substitute $t$ for $x$...
1
vote
0answers
134 views
Name for the Quotient $SU(m+1)/(SU(k) \times SU(m-k))$
The sphere $S^{2m-1} \simeq SU(m+1)/SU(m)$ has a canonical $U(1)$-action, and quotienting by this action give complex projective space $CP^m$. We can generalise the family of sphere to the family of ...
0
votes
0answers
243 views
Notation for iterated summation
Is there a more compact way to write
$$
\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}
$$
as something like
...
0
votes
2answers
405 views
Use of ternary operator in formal writing
I would like to write
$$
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
votes
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
vote
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
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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
votes
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) = \...
-2
votes
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 ...
