Questions tagged [notation]
For questions about mathematical notation, i.e. the symbols used to represent mathematical objects and operations.
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Who invented diagrammatic algebra?
There is a strong and growing trend to do mathematics via diagrammatic algebra, which involves constructing and manipulating equations whose elements are diagrams drawn in the plane. The manipulations ...
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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.)
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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 ...
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Suggestions for good notation
I occasionally come across a new piece of notation so good that it makes life easier by giving a better way to look at something. Some examples:
Iverson introduced the notation [X] to mean 1 if X is ...
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What are the worst notations, in your opinion? [closed]
With which notation do you feel uncomfortable?
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When was the "arrow notation" for functions first introduced?
When was the "arrow notation" $f: X \to Y$ for functions first introduced? Who introduced it and with which motivation?
I ask this question in order to understand whether it was, in part, this ...
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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, ...
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Notation for the all-ones vector [closed]
What's the most common way of writing the all-ones vector, that is, the vector, when projected onto each standard basis vector of a given vector space, having length one? The zero vector is frequently ...
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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 ...
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notation for finite sequence with one element is removed [closed]
Often you need a notation for a finite sequence with one element is removed;
i.e. $$(x_1,\dots,x_{i-1},x_{i+1}\dots, x_n).$$
I know one notation
$$(x_1,\dots,\hat x_i,\dots, x_n)$$
and I hate it. It ...
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Confusing notation for sets of unordered vs ordered pairs
Given two finite sets $X$ and $Y$, one may consider the ordered pairs $(x,y)$ with $x\in X$ and $y \in Y$. Then, $(x,y) \not= (y,x)$, and $(x,x)$ exists if $x\in X$ and $x\in Y$.
One may also consider ...
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What are the benefits of writing vector inner products as $\langle u, v\rangle$ as opposed to $u^T v$?
In a lot of computational math, operations research, such as algorithm design for optimization problems and the like, authors like to use $$\langle \cdot, \cdot \rangle$$ as opposed to $$(\cdot)^T (\...
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Fraktur symbols for Lie algebras
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}$, ...
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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 ...
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What is the term for combining functions $f_1,f_2,\dots,f_n$ into a tuple $(f_1,\dots,f_n)$?
This is an embarrassingly simple question, but I was not able to find a definitive answer from literature search.
Suppose one has some collection of functions $f_1: X \to Y_1, \dots, f_n: X \to Y_n$ ...
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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 ...
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Explanation why $x,y,z$ are always variables
I heard or have read the following nice explanation for the origin of the convention that one uses (almost) always $x,y,z$ for variables. (This question was motivated by question
Origin of symbol *l* ...
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Was Jacobi the first to notice the ambiguity in the partial derivatives notation? And did anyone object to his fix?
In his 1841 article De determinantibus, Jacobi remarked that the notation $\frac{\partial z}{\partial x}$ for partial derivatives is ambiguous. He observed that when $z$ is a function of $x,y$ as well ...
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What is the standard notation for group action
Please let me know what is the standard notation for group action.
I saw the following three notations for group action.
(All the images obtained as G\acts X for ...
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What does ! above = mean [closed]
Can someone please explain what the symbol $\stackrel{!}{=}$, consisting of an exclamation mark (!) above an equals sign (=) means? Below is the example I'm trying to decipher:
The normalization ...
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notation for $(a-b)(a-qb)\dots (a-q^{n-1}b)$
I wonder whether there is a notation for such thing, which I denote $[a;b]_q^n$ for a moment:
$$
[a;b]_q^n:=(a-b)(a-qb)\dots (a-q^{n-1}b)=a^n(b/a;q)_n,
$$
this last equation uses $q$-Pochhammer symbol ...
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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 $\...
user14319
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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 ...
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When is the Siegel-Walfisz theorem non-trivial?
The following paragraph appears in Analytic Number Theory (Iwaniec, Kowalski):
The Siegel-Walfisz theorem asserts that:
$\displaystyle \hspace{5cm} \psi(x;q,a) = \frac{x}{\phi(q)} + O(x(\log x)^{-A})...
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Is there a standard notation for binary relations in category theory?
In set theory, I learned that a binary relation is simply a subset of a Cartesian product. Moving on to category theory, it seems that this definition is not enough. Just as a function is no longer ...
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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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Confusion optimal control abuse notation
I'm currently reading this paper describing a numerical scheme for the approximating optimal policy of a stochastic control problem. However, I run into a confusion directly on the first page where ...
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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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