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.

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3
votes
1answer
48 views

In set theory, what does it mean for a variable to have a bar symbol above it?

Please see the image below. What does the bar symbol mean in this context?
0
votes
1answer
29 views

How do I indicate approximation by rounding when manipulating equations?

I manipulate a set of inequalities and arrive at $$\Leftrightarrow \frac{(||\nu|| - \lambda^{-1})^2}{2\tau^2} \geq 53\ln(2)$$ Note the $\Leftrightarrow$ sign, indicating that this inequality is ...
2
votes
2answers
54 views

Notation for the set of zero divisors in a ring

If $R$ is a nonzero ring with identity then I have seen the group of units denoted by $R^{\times}$ or possibly $R^*$ in some texts. In a classical ring there is a trichotomy which declares each ...
1
vote
3answers
112 views

Can functions be passed into functions and then called?

In computer science there are what are known as higher-order functions. This means pretty much nothing, really. It is a property of a programming language. I want to know if they are valid in ...
1
vote
1answer
30 views

Understanding metric tensor notation

I am trying to understand if there is a conventional way to read super- and subscript notation of metric tensors. Is there a canonical way of doing this? For instance, what is the difference between ...
0
votes
1answer
50 views

$f$ equals <fill in blanks>

Related to: Question about $x\mapsto f(x)$ notation. Is there a way to write $f = \text{some expression}$, and thus define a function without a domain or a variable? A function is too often defined ...
0
votes
0answers
19 views

Describing a function with independent variables.

The normal distribution is often written $f(x\,\rvert\,\mu,\sigma^2)$, with the independent variables on the right side of the vertical line. Is this notation common, or are alternatives? For instance,...
0
votes
0answers
20 views

$\max_y$ notation

Simple question, but googling $\max_y$ is taking me off track. What does $\min_y$ mean here? The value of $y$ that minimizes the integral? $$\mathscr{l}(b^\prime) \equiv \min_y \int_{-L}^L \mathscr{l}...
4
votes
1answer
46 views

Abuse of notation for infimum and supremum

I would like to take the infimum and supremum of two sets $(\frac{1}{2} e^{8m+4} - 1, e^{8m+4} - 1)$ and $(\frac{1}{2} e^{8m+4}, \frac{3}{2}e^{8m+4})$, but writing $\sup((\frac{1}{2} e^{8m+4}, \...
2
votes
3answers
45 views

Math symbols on vectors e.g item in, item not in, for all

I have a vector s= <1,2,3> and I want to perform various operations on it like these ones: check if an item x exists in <...
0
votes
1answer
40 views

What does $_A\backslash B$ mean?

I came across the following notation in this document $_{GL(k)}\backslash \text{Mat}^*(k,n)$ What does $_A\backslash B$ mean, where $A$ and $B$ are suitable mathematical objects?
0
votes
1answer
24 views

Notation in the stochastic derivatives in the mean square sense

The stochastic limit $X$ in the mean square sense is given the definition: For a row (sequence?) of stochastic variables $X_n$ if $\displaystyle\lim_{n\to\infty}E\{(X_n-X)^2\}$ = 0 and we write $\...
1
vote
0answers
38 views

Notational differences for integration?

I've noticed a small difference in notation for integration in British literature and American literature. (Surely both of these notations exist in other countries' literature but this is the extent ...
2
votes
3answers
56 views

Is $x$ in $ax+b$ every value, or a specific unspecified value?

Given $ax+b$, we often draw a line $y = ax+b$ and we say this is for all values of $x$ and $y$, but is it wrong to say that $x$ is every value at the same time? For instance we say $x\in \mathbb{R}$. ...
1
vote
1answer
76 views

What does the symbol := mean in mathematics? [duplicate]

What does the symbol := mean in mathematics? for example, C(continuum) := |R|
0
votes
2answers
33 views

Meaning of $F = T(E) ⊕ Ker(T^*)$? Espacially the notation $⊕$?

I am not get used to with the notation $⊕$. I met this notation in the document SPHERICAL HARMONICS AND HOMOGENEOUS HARMONIC POLYNOMIALS with ($*$) $F = T(E) ⊕ Ker(T^*)$ page $3$. Could anyone be able ...
0
votes
2answers
66 views

Definition of $\Bbb{Z}[\sqrt{n}]$

What is the ring $\Bbb{Z}[\sqrt{n}]$? What does this notation mean?
0
votes
0answers
19 views

Meaning of $\lfloor nt \rfloor$ in $S_{\lfloor nt \rfloor}$

Let $S_n$ be the position of simple random walk at time $n$, with $n \in \mathbb{N}$. What does $\lfloor nt \rfloor$ mean in $S_{\lfloor nt \rfloor}$ for $0 \leq t \leq 1$? More general, what does ...
0
votes
2answers
20 views

Translate the following argument into symbolic form

Translate the following argument into symbolic form. State clearly what each of the propositions are I walk and I cycle and I run. If I do not stay at home I cycle or I run. I do not cycle ...
0
votes
0answers
24 views

What is the meaning of the notation: $dx_\alpha\wedge dy_\alpha$,$dzd\bar{z}$, $dwd\bar{w}=du^2+dv^2$

I am studying some notes on introduction to Riemann Surfaces and the notation $dx_\alpha\wedge dy_\alpha$,$dzdd\bar{z}$, $dwd\bar{w}=du^2+dv^2$ keeps popping up everywhere and I have never seen it and ...
3
votes
2answers
50 views

Can a simple (atomic) proposition be a tautology?

Definition: "A tautology is a propositional formula that is true under any truth assignment to each of the atomic propositions in the domain of propositional function." Let $p$ be a simple (or atomic)...
-4
votes
1answer
56 views

What does this notation mean? Sets

The $()^c$ means the complement of whatever there's in the bracket in respect to $\Omega$ i just want to know what this big U and the flipped U means. Also what's the Latex-Symbol?
0
votes
1answer
40 views

Where to draw the line in scientific papers in respect to definitions

Now, a science paper about i.e. "the decrease of sunken pirateships as a function" would look (despite the title) very silly if it would define addition, multiplication, heck even exponentiation or ...
0
votes
2answers
49 views

What kind of operation is this? [closed]

$3\circ 7=37$ $7\circ 4=74$ $a\circ b=10*a+b$ This question came me from a mathpuzzle here. Basicly we multiply the first number by 10 and add the second number, but would this be a operation by ...
1
vote
1answer
39 views

How to correctly write this in set notation?

I have defined the following set $$\{\mathrm{skill}_i^j\mid 1\leq i\leq 100\text{ and }1\leq j\leq n\}$$ I'm unsure if this notation is correct. My intention is to say that the set contains $n$ ...
1
vote
0answers
16 views

Notation for arguments that maximize functions with priority

Suppose we have some functions $f_1(x), f_2(x), \ldots, f_n(x)$ with $x \in \mathbb{Z}^n$. We can denote the subset $X_1$ of $\mathbb{Z}^n$ that maximizes $f_1(x)$ as: $$X_1 = \underset{x \in \...
1
vote
0answers
67 views

In mathematics, what is a placeholder?

Google defines the word placeholder in the following image: My question is: Is this the only definition of the word placeholder in mathematics? I am thinking along the lines: If $M = p^k m^2$ ...
1
vote
1answer
11 views

Sampling Distribution Notations

I'm reading a chapter on sampling distributions of a statistic and I don't seem to have an understanding of the notations used. From probability theory, a random variable is usually denoted by a ...
2
votes
3answers
127 views

What are the differences between: $\sqrt{(-3)^2}$, $\sqrt{-3^2}$ and $(\sqrt{-3})^2$. [closed]

First, is $\sqrt{-3}$ is equal to $-3$ or is it imaginary? What is the difference between: $\sqrt{(-3)^2}$ $\sqrt{-3^2}$ $(\sqrt{-3})^2$ Can I write $(\sqrt{-3})^2 = -3$? And, given the rule ...
2
votes
0answers
22 views

The definition of the operator $\Delta_{\bar\partial}$

Preliminaries: Let $(X,h)$ be a Kahler manifold of complex dimension $d=2n$. Lets denote with $\mathscr A^{p,q}_X$ the sheaf of $C^\infty$ (complex) $(p,q)$-forms over $X$ and let $A^{p,q}(X):=\Gamma(...
4
votes
6answers
74 views

Is there a difference between $y(x)$ and $f(x)$

Oftentimes functions described by $f(x) = 2x+4$, and when this is mapped to the Cartesian plane, $f(x) = y$. This surely implies that $y = 2x+4$. Is there a difference between this and $y(x) = 2x+4$?
3
votes
0answers
45 views

What does $x$ represent? [closed]

$x$ can mean: A defined value in $x = 5$ An unknown, TBD. value, in $3x = 2+4$ A variable in $y(x) = x+4$ A sum of numbers in $\int_0^2 \mathrm{d}x$ Are there any other examples?
2
votes
0answers
99 views

Is this notation common in Calculus?

Okay this is going to be quite a stupid question, but to me this seems... wrong, or at the very least not completely correct. In the material I'm reading there's a part that states that $y$ evolves ...
62
votes
7answers
5k views

Why does the symbol for the multiplication operation change shape?

Why does the "$\times$" used in arithmetic change to a "$\cdot$" as we progress through education? The symbol seems to only be ambiguous because of the variable $x$; however, we wouldn't have chosen ...
0
votes
1answer
32 views

Notation for set of unit vectors

Is there a standard notation for the set of unit vectors $\{\vec v\ :\ |\vec v|=1\}$?
0
votes
3answers
28 views

How to read this ArgMax definition in plain english

I was reading on Wikipedia about Argmax (https://en.wikipedia.org/wiki/Arg_max) and they gave the following equation. While I get most of this line, how would you read the following in plain English? ...
1
vote
2answers
29 views

Summation Notation Question in McMillan's Theorem Proof

Let me preface by saying that this question does not pertain as much to coding theory, as it does to mathematical notation. Every symbol in this question is a natural number. Anyhow, I am currently ...
1
vote
3answers
45 views

How to write a set with an index

I'd like to write a set $\{x_1, x_2, ..., x_n\}$ in a simple way. What is a popular way? In my high school, I wrote it as $\{x_i\}_{i=1}^{n}$. Is it a correct way?
-1
votes
1answer
44 views

If $G$ and $H$ are two graphs, then what does $G \Delta H$ indicate in graph theory?

I came across this notation in a book titled "Combinatorial Optimization Theory and Algorithms" by Bernhard Korte and Jens Vygen.
19
votes
10answers
2k views

What does it mean when dx is put on the start in an integral? [duplicate]

I have seen something like this before: $\int \frac{dx}{(e+1)^2}$. This is apparently another way to write $\int \frac{1}{(e+1)^2}dx$. However, considering this statement: $\int\frac{du}{(u-1)u^2} = \...
1
vote
2answers
43 views

Notation for a sum over a set of variables

I have a vector of variables $y=(y_1, \ldots, y_n)$ whose elements are either zero or one. I would like to express the sum over all variables belonging to a subset $S$. For example, if $n=4$ and $S=\{...
3
votes
1answer
14 views

Function/Measure Notation in Geometric Measure Theory

I'm trying to understand a formula of this kind $$ ...=\phi_\sharp \left ( f \mathcal{H}^n \right ) $$ where $\mathcal{H}^n$ is the n-dimensional Hausdorff measure on a measure space $X$, $\phi : X ...
0
votes
2answers
34 views

Set notation for unordered cartesian product

In the question unordered cartesian product an shorthand notation for the unordered cartesian product was discussed but without any standard notation. So my question is what would be the explicit ...
0
votes
0answers
36 views

What does the '#' sign mean in elliptic curves?

My question is regarding specifically elliptic curves. I have seen the notation $\#E(\mathbb{F}_{q})$ used over and over again (especially in the description of Hasse's theorem). I know that sometimes ...
0
votes
1answer
33 views

Proper notation for motion integration

Say you have a projectile where at $t=0$, $ v = 0 $ and $ x = 0 $. Given $ \ddot x = -4$, in order to find $ \dot x $, we must integrate $ \frac{dv}{dt} $ as follows: $$ \frac{dv}{dt} = -4 \...
1
vote
0answers
23 views

derivative and curl vector notational difference

This must be a really trivial question, and I am not sure I am allowed to post these here. Just wanted to know but didn't know what to search. What is the difference between $\overrightarrow {dr}$ and ...
3
votes
3answers
56 views

What is common notation for “disjoint union of copies of $\mathbb{R}$”?

I'm looking at a question out of Lee's Smooth Manifolds: Show that a disjoint union of uncountably many copies of $\Bbb{R}$ is locally Euclidian and Hausdorff but not second countable. My ...
2
votes
3answers
64 views

How $f:[a,b]\rightarrow[c,d]$ should be read?

I found it in a book but I don't know what the ":" means. What does this expression mean?
-3
votes
2answers
97 views

Why is $\wedge$ a minimum and $\vee$ a maximum? [closed]

Why does $\wedge$ denote a minimum and $\vee$ a maximum? Where did this notation come from? I keep getting them mixed up because to me, $\wedge$ should be a maximum: it's a hill, or a curve reaching ...
2
votes
1answer
24 views

Inverse relations notation (not a function) [closed]

Even if $f:X\to Y$ is not a bijective function, can I still notate the inverse relation of $f$ as $g:Y\to X$?