Questions tagged [notation]
For questions about mathematical notation, i.e. the symbols used to represent mathematical objects and operations.
282
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Does $\mathsf{SVC}^\ast$ exist?
$\mathsf{SVC}(S)$ is the assertion that for all sets $X$ there is an ordinal $\eta$ and a surjection $f\colon\eta\times S\to X$. I would like to denote by $\mathsf{SVC}^\ast(S)$ the same assertion but ...
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0
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How to talk about the “shape” of the kernel of an integral transform
So I'm learning about integral transforms, and although it isn't a complete specification, the fact that the Fourier transform decomposes functions into sinusoids, the Laplace into damped sinusoids, ...
3
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1
answer
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Notation for weak derivatives
I remember that, as a student, I felt a bit uncomfortable because I had to use the same notation (say $f'$, $D^\alpha f$, $\frac{\partial f}{\partial x^j}$, $\nabla \cdot f$ etc...) for classical and ...
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Adjunction symbol
What are the reasons for the adjunction symbol $F\dashv G$ for a pair of functors $F:C\to D$ and $G:D\to C$? There is no explanation or motivation in the article of Kan where adjunctions are ...
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Notation $\le_{a,b,n,\ldots}$ in Analysis
In modern Analysis, especially Functional Analysis, one proves, or one uses inequalities of the form
$$F(X)\le_{a,\ldots,n}G(X).$$
The meaning of the subscripts in the inequality sign means that there ...
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1
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Is this single-variable function being called with two variables (and if so, how do I handle that), or am I misreading the notation? [closed]
While working on a project, I came across a paper that includes this sum on page 15 as the definition of a support function $r$ for a surface with tetrahedral symmetry:
$$
r(ξ, \bar{ξ}) = \frac{1}{\#𝒢...
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1
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Unpacking the plethystic substitution $h_n[n\mathbf{z}]$ in a paper by Aval, Bergeron and Garsia
I'm not familiar with the formalism of plethysm, so I need some help in unpacking the plethystic substitution $h_n[n\mathbf{z}]$ found in eqns. 5.6 and 5.9 of "Combinatorics of labelled ...
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3
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1
answer
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Cartesian product of $(k-2)\text{-times } [\text{Interval}_1] \times [\text{Interval}_2] \times [\text{Interval}_2]$
This is a soft question, hoping that it is still appropriate for this forum.
I need to describe twice the following region of $\mathbb{R}^k$ (i.e., we are in a $k$-dimensional Euclidean space, where $...
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0
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Definition of term functions, in universal algebra
According to the definitions in Sankappanavar's universal algebra :
Assume $p$ is a term, then $p(x_1,x_2,...,x_n)$ indicates that the variables occurring in $p$ are among $x_1,...,x_n$. But there is ...
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Notation for spectral sequences [closed]
Every single spectral sequence I have seen in my life was denoted by $E$. Even when there is more than one spectral sequence, people tend to use the same letter with some workaround (e.g. a fourth ...
- 1,954
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Merging two composable walks in a graph
Let $G$ be a graph (i.e., an undirected graph in which we allow for loops and parallel edges). Denote by $V$ the vertex set, by $E$ the edge set, and by $\psi$ the incidence function of $G$, and let $\...
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Examples of bad notation and its consequences [closed]
An example of bad mathematical notation that comes in my mind and has caused complications throughout history is the notation for imaginary numbers. The original notation used to represent imaginary ...
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0
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Minus sign inside derivative operator, notation problem
Hello fellow mathematicians. Can anybody help me understand what the minus (-) sign in this derivative means? Its the usual d/dy but with a minus added d-/dy. I can't find references, the book cited ...
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What do you call $x$ such that $\textrm{dim} f^{-1}(f(x))>0$?
Let $f:V\to W$ be a morphism between varieties, with $\dim \overline{f(V)} = \dim V$. What do you call the closed proper subvariety $S$ of $V$ consisting of points $x$ such that $\textrm{dim} f^{-1}(f(...
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1
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Notations for open and closed sets
I am wondering why a standard notation for open sets is $G$ and that for closed sets is $F$. I mean, $F$ precedes $G$ in the alphabet, whereas open sets are usually introduced before closed ones.
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