Question on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.
9
votes
0answers
355 views
How do Greek mathematicians name variables?
I've always wondered how people in Greek name variables that other people use greek letters e.g. $\theta$. They use latin?
8
votes
0answers
118 views
Is there a collection of alternative mathematical notation? (Semi-soft Question)
I'm interested in alternative systems of notation for mathematics. I've often heard how mathematical notation is illogical, inconsistent, filled with grandfather clauses that serve no purpose, and ...
7
votes
0answers
77 views
If $H$ is a subgroup of $G$ and $x,y\in G$, what is $xHy$ called?
For a group $G$, its subgroup $H$ and $x,y\in G,$ we call $xH$ a left coset of $H,$ and we call $Hy$ a right coset of $H.$ Is there a special name for sets of the form $xHy$? Is there a name or ...
7
votes
0answers
268 views
notation for ramification index and inertial degree
For a prime $Q$ lying over a prime $P$, I have seen the ramification index of $Q$ over $P$ denoted by $e(Q|P)$ and the inertial degree of $Q$ over $P$ by $f(Q|P)$.
What is the origin of the ...
6
votes
0answers
69 views
Working with subsets, as opposed to elements.
Especially in algebraic contexts, we can often work with subsets, as opposed to elements. For instance, in a ring we can define
$$A+B = \{a+b\mid a \in A, b \in B\},\quad -A = \{-a\mid a \in A\}$$
...
6
votes
0answers
169 views
Looking for an approach to mathematical notation wherein the universe is divided into disjoint worlds.
Is there a rigorous approach to mathematical notation wherein the "universe" is divided into disjoint "worlds," and the meaning of notation is world-dependent? This would solve a few pesky problems. ...
6
votes
0answers
122 views
Articles on ideas in the history of mathematics notation?
I'm teaching a course this term on the history of scripts (writing systems) and rather than talking interminably about Semitic and Chinese and their spawn, I'd like to give students a more varied ...
5
votes
0answers
102 views
Notation for n-ary exponentiation
We have $n$-ary sums ($\sum$) and products ($\prod$). Is there an $n$-ary exponentiation operator?
$$\underset{i=1}{\overset{n}{\LARGE{\text{E}}}}\, x_i = x_1 \text{^} (x_2 \text{^} (\cdots \text{^} ...
5
votes
0answers
181 views
Where does the notation $\mathrm{Ad}(U)$ for $a\mapsto UaU^*$ come from?
I have often seen, in the context of operator theory and operator algebras, the notation $\mathrm{Ad}(U)a=UaU^*$, where $U$ is a unitary operator on a Hilbert space $H$ and $a$ is a bounded linear ...
4
votes
0answers
105 views
Is there a name or definition for this popular notation?
I'm sorry if this is a silly question. I've done quite a bit of searching and have not found any definition or name for this symbol/usage, despite immense popularity and convenience. The sources I've ...
4
votes
0answers
220 views
Is there a notation for $f(x,y) - f(y,x)$?
Suppose we have a function $f(x,y)$ in two variables. Is there an operator on the function, say, $$([]f)(x,y) = f(x,y) - f(y,x)?$$
In other words, I'm looking for a commutator in terms of function ...
4
votes
0answers
82 views
Harmonic measure or harmonic kernel
In the theory of discrete-time stochastic processes on a measurable space $(\mathscr X,\mathscr B(\mathscr X))$ one usually starts with a Markov kernel
$$
P:\mathscr X\times \mathscr B(\mathscr ...
4
votes
0answers
166 views
Where does the 'divides' sign come from?
When $a$ divides $b$ we say $a | b$. Where does the $|$ sign come from?
This is not homework, just personal interest in the history of mathematical language.
3
votes
0answers
34 views
Definition(s) for variable binding in first-order logic
The following statement made me realize that variable binding can be defined in first-order logic:
The same holds for λ terms to define functions. There is no reason that they could not be ...
3
votes
0answers
52 views
Why is the Euclidean metric called the prime at infinity?
I've been studying p-adic analysis recently and after a bit of searching on the web, I haven't found an answer as to why the Euclidean metric is referred to as the 'prime at infinity', and given the ...
3
votes
0answers
49 views
What is the name of the function that indexes Grothendieck universes?
Assume Tarski-Grothendieck set theory. Then Grothendieck universes form a well-ordered proper class, so we can let $U_\alpha$ denote the $\alpha$'th Grothendieck universe, where $\alpha$ is an ...
3
votes
0answers
51 views
Define composition of small cyles and making a big graph
I am having following sub graphs and wish to compose all and make a
one bigger graph (say G). After that, I want to select the closed path
where it is passing along the outer vertices of that ...
3
votes
0answers
96 views
What kind of matrix/tensor notation is this?
I'm hoping someone on here recognises this and has an answer, because I'm having serious memory issues.
About a year ago, I came across the following way of representing tensors of rank $n$ in matrix ...
3
votes
0answers
82 views
3
votes
0answers
163 views
Divisibility notation history
I'm writing a paper project for school about divisibility, so I'd like to include a bit of history about that subject. I'm mostly interested in notation of $|$ sign used in past, but everything else ...
3
votes
0answers
132 views
Better Tensor Notation
I am in a General Relativity class, and I am finding the usual tensor notation very difficult to think about -- it seems like there are too many names to express something simple. E.g., I think of ...
3
votes
0answers
174 views
How did Bessel functions come to be denoted by $J_n$?
The $n$th Bessel function of the first kind is usually denoted $J_n(x)$.
Where did the use of the letter $J$ to indicate the Bessel function come from?
2
votes
0answers
49 views
“Product” bundle notation.
Let $\newcommand{\Spin}{\operatorname{Spin}}M$ and $M'$ be two manifolds, equipped with a principal $\Spin_n$ and $\Spin_{n'}$ bundle called $P$ and $P'$, respectively.
Then there is an induced ...
2
votes
0answers
35 views
What does the notation $\mathbf{Lt}$ signify in a limit?
The author of a book I'm reading defines the Dirac delta-function as
$$
\delta(\omega_0-\omega) = \frac{2}{\pi}\mathbf{Lt}_{t\rightarrow \infty} \frac{\sin^2\left(\frac 1 2 ...
2
votes
0answers
29 views
Mathematical notation for formulas involving trees
I am working on document that requires me to write such things as "$T_1$ is a descendant of $T_0$", or "$N_1$ is an parent of $N_2$". For now, I've been highjacking set notation for use in formulas, ...
2
votes
0answers
43 views
Ideas for denoting parameters of a function, as opposed to variables, in the list of arguments?
In general, the list of arguments of a function includes only variables, not parameters.
In some specific cases, a parameter could be incorporated into the function name, like $y$ in $$\log_y (x)$$
...
2
votes
0answers
86 views
Writing a probability expression (Notation)
What is the best way to denote,
Probability of $n_i$ changing its value from $0$ to $1$ at time $t$.
I come up with these, any suggestions _
$$
P_{n_i,0\rightarrow1}(t) \\
P(n_i:0\rightarrow1, t)
$$
...
2
votes
0answers
75 views
Is there a common symbol for concatenating two (finite) sequences?
Say we have two finite sequences $X = (x_0,...,x_n)$ and $Y = (y_0,...,y_n)$.
Is there a more or less common notation for the concatenation of these sequences, like $\sum (X,Y) = ...
2
votes
0answers
129 views
Scientific notation and negative numbers
My daughter is learning scientific notation in school, and her textbook says something to the effect of this:
Scientific notation is a method of writing numbers as the product of
two factors ...
2
votes
0answers
134 views
What's more common? Re / Im or Fraktur-R / Fraktur-I for real / imaginary part?
Title says it all. What's more common? Is there one to prefere (maybe due to some norm)?
This:
$\operatorname{\mathfrak{R}} z, \operatorname{\mathfrak{I}} z$
or that:
$\operatorname{Re}z, ...
2
votes
0answers
65 views
Where can I find a description of math language symbols?
I am reading math articles. I meet math symbols.
For example $\exists$ or $\forall$.
For example for "For any a exist e that" can be rewriten as: $\forall a \exists e$
Where can I find full ...
2
votes
0answers
69 views
What's the equivalent to floor(x) and ceil(x) for real numbers?
Are there equivalents to the notation of $\lfloor x \rfloor$ and $\lceil x \rceil$ that don't round to the next integer, but to a specified digit of a real number?
Examples
$floorReal(2.3656, 1) = ...
2
votes
0answers
200 views
Submatrix Notation
I'm looking through some computer science papers and I see some notation that I'm just not familiar with.
Consider an 5 x 6 matrix
$$G = \begin{pmatrix}
a_{0,0} & a_{0,1} & ...
2
votes
0answers
112 views
Understanding notation (linear continuous functional on $C[a,b]$)
Let $C = C([a,b],\mathbb{R}^n)$ be a space of continuous vectorvalued functions on $[a,b]$. Let $y \in C$, $\Phi \in C^*$ and $f \in C(\mathbb{R}^n, \mathbb{R}^n)$. What does mean a notation
$$
A = ...
2
votes
0answers
90 views
Summation notation and a negative sign of some elements
Having sequence like
$$ \beta_1 \cos\theta_1 + \beta_2 \cos\theta_2 + \beta_3 \cos\theta_3 + \dots + \beta_n \cos\theta_n$$ it is possible to present it using summation notation as follows:
$$ ...
2
votes
0answers
166 views
Confused about notation and derivatives inside integrals
EDIT: To make what I am asking more clear. I've simplified it and have a more direct question.
Let's say I am writing out an expression, and I want to write:
$$\int_0^xF'(y)\,dy$$
However, for ...
2
votes
0answers
133 views
Mathematical Notation questions reading SLAM papers
I'm working through a pair of papers on Simultaneous Localization and Mapping and I'm having trouble with some of the notation as I lack some formal math education.
The papers can be found
here: ...
2
votes
0answers
200 views
Why are superscripts used instead of subscripts in this example?
A snippet from Marcus du Sautoy's The Number Mysteries, Chapter 3, in the section called HOW GOOD ARE YOU AT RANDOMNESS is shown below. My question is, why does the author use superscripts instead of ...
2
votes
0answers
99 views
What does it mean if a sequence is indexed beyond its bounds?
I'm looking at a paper (On Base and Turyn Sequences by C. Koukouvinos, S. Kounias and K. Sotirakoglou) that describes an algorithm for finding specific sequences.
Part of the algorithm involves ...
2
votes
0answers
208 views
Notation for sampling random variate
Is there standard notation for sampling a value from a probability distribution? Like, if I had a random variable $X$, setting $x$ to whatever value I happened to sample from $X$ on this occasion? I ...
2
votes
0answers
119 views
bar index notation
For complex manifolds , people usually write the first fundamental form as $ds^2=g_{a\bar{b}}dz^ad\bar{z}^b$ (at least physicists) with a bar over the second index of the metric, but don't usually ...
1
vote
0answers
27 views
What's the need of $^{S}_{T}$ in $f^{S}_{T}:S\rightarrow T$?
I'm reading Lang's Undergraduate Analysis:
In the chapter about mappings, he says that we should denote the set of arrival and the set of departure with the following notation:
...
1
vote
0answers
56 views
What's the difference between $\frac{\delta}{dt}$ and $\frac{d}{dt}$?
I have read the few questions on calculi notation, particularly the notations on partial and total derivatives. My question seems to have not been answered, or at least not brought to my attention. If ...
1
vote
0answers
60 views
French notational differences
I wish to read some French probability / measure theory papers. I do not wish to be caught out with different notations. For example if "compact" in French has a weaker meaning than in English ...
1
vote
0answers
32 views
Is there a common notation for the labelled degree of a vertex?
Let $G$ be an undirected graph with labelled edges. The labelled degree of a vertex $v \in V(G)$ is the number of edges incident to $v$ with distinct labels.
The definition of the labelled degree ...
1
vote
0answers
24 views
Notation for Restriction of Permutation
Suppose $\sigma$ and $\tau$ are permutations such that $\sigma(x)\not=x\implies \sigma(x)=\tau(x)$. Intuitively, I would like to think of $\sigma$ as a restriction (or projection) of $\tau$ onto a ...
1
vote
0answers
51 views
Is $\langle f \rangle $ an “inner product”?
Let $$\langle f(x,y)\rangle = \iint_S f(x,y)\,\mathrm{d}x\,\mathrm{d}y$$
I have seen the above in multiple papers as the definition of $\langle f(x,y)\rangle$. I would normally associate angle ...
1
vote
0answers
26 views
Enumeration of symbols in grammatical expressions or vertices in tree graphs
I have expressions (type of a function) like e.g.
$$f:(A\to B)\to C \to (D\to E)\to F.$$
(Where I understand $A\to B\to C$ as $A\to (B\to C)$, in case that is relevant.)
There might be information ...
1
vote
0answers
43 views
What's a good notation for an endomorphism induced on the quotient?
For example, suppose that $V$ is a vector space, $A \in \operatorname{End}V$, and $U \subset V$ is an $A$-invariant subspace, and $\pi_{V/U}: V \to V/U$ the natural projection. Then $A$ induces a ...
1
vote
0answers
113 views
