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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21 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
26 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
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0answers
19 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
45 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
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3answers
57 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?
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0answers
31 views

Distinguish between constant function and a constant. [on hold]

The constant function $\begin{array}&y: &\mathbb{R}\to \{c\}\\&x \mapsto c\end{array}$ and the constant $y = c$ are often simply written as $y = c$ and it's not always ...
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2answers
76 views

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

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
23 views

Inverse relations notation (not a function) [on hold]

Even if $f:X\to Y$ is not a bijective function, can I still notate the inverse relation of $f$ as $g:Y\to X$?
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0answers
15 views

Is there an accepted notation for the monoid of linear polynomials?

Is there an accepted notation for the monoid of linear polynomials (with addition as the operation) with coefficients from some ring R? Like $2p+3$, where $p$ and the identity generate the monoid ...
0
votes
2answers
24 views

Closure of sets (specifically regarding the notation)

I'm new to sets and the notation is somewhat confusing to me. I just want to see if what I'm doing makes sense. For the following sets I need determine if it is open, closed, or neither. I also ...
7
votes
4answers
140 views

Confused about notation “:=” versus plain old “=” [duplicate]

Relating to sets, I find the following in a text book: "...the set S := {1, 2, 3}". The book has an extensive notation appendix, but the":=" notation is not included. What exactly does ":=" mean, and ...
0
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0answers
31 views

How to get a feel for rigor/form used in mathematics?

I'm an engineer, and while you get introduced to many concepts of mathematics, but only with a subset of the vocabulary, and none of the rigor and proofs. So while trying to read a mathematical book, ...
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4answers
64 views

I want to write “$x,y > 0$”.

I want to write "$x,y > 0$". Can I do this? Or do I have to write "$x > 0$ and $y > 0$"? Which one is the proper way to write in maths?
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1answer
13 views

Is it possible to unify these two expressions into one?

I have the following expressions $\forall n \in \Bbb N$: $E = f(n)-1$ if $n \gt 1$ $E = f(n)+1$ if $n = 0$ I would like to have only one expression like this: $E = f(n)+$(some nice notation able ...
-1
votes
1answer
60 views

Why is the notation for irrational number not mainstream? [on hold]

In everywhere you see the symbol for the set of rational number as $\mathbb{Q}$ However, to find actual symbol to denote the set of irrational number is difficult. Most people usually denote it as $\...
2
votes
3answers
44 views

Understanding notation for the sequence definition

Looking for assistance in translating this definition into more laymen terms? In other words, can someone explain it to me like I'm a 5 year old? Definition. A sequence ($s_n$) is said to diverge ...
0
votes
1answer
10 views

Does $\partial_\mu =\frac{\partial }{\partial x^\mu}$ or $\partial_\mu =\frac{\partial }{\partial x_\mu}$?

I am looking at the chain rule with covariant and contravariant vectors. I understand why we have: $$df=\frac{\partial f}{\partial x^\mu} dx^\mu$$ (Please correct me if I am wrong) since even though ...
2
votes
1answer
33 views

Understanding the notation of a paper

I am reading a paper on Algebraic Number Theory that says If $p$ divides the discriminant of polynomial $f$ $r$ times and there is the factorization into irreducibles $$f(x)\equiv g_1(x)\dots g_r(...
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0answers
37 views

How do I write a function that maps a variable to a set?

I have a function $\Gamma$ that maps elements from $N$ to a (possibly empty) subset of $N$. The number of elements in the resulting subset depends on which element of $N$ we are dealing with, i.e. $\...
2
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0answers
34 views

Why are sequences and functions notated differently?

Why do we usually write, e.g., $s_n$ for sequences, while functions are usually written as $f(x)$? Conceptually, aren't sequences just functions with a subset of the naturals, not of the reals, as ...
0
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0answers
13 views

Meaning of notation $L_{subscript}$ in ridge detection.

In the wikipedia article on ridge detection, it says "let $L_{pp}$ and $L_{qq}$ denote the eigenvalues of the Hessian matrix \begin{pmatrix} L_{xx} & L_{xy} \\ L_{xy} & L_{yy} \end{pmatrix}...
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0answers
16 views

Visualization of residual sum of squares in matrix notation

I am trying to understand how to pass from \begin{equation} RSS(\beta) = \sum_{i=1}^n (y_i - x_i^T\beta)^2 \end{equation} to \begin{equation} RSS(\beta) = (y - X \beta)^T (y - X \beta) \end{...
4
votes
2answers
63 views

Notation for “the highest power of $p$ that divides $n$”

If $p$ is a prime and $n$ an integer, is there a standard or commonly used notation for "the highest power of $p$ that divides $n$"? It's a concept that is often used repeatedly in number-theoretic ...
1
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1answer
25 views

Notation for minimum

I'm reading Huber's Robust Statistics right now, and at the beginning of Chapter 3, he writes the following notation: $\sum \rho(x_i;T_n) = \min!$ Similarly, a few lines down, he writes: $\sum \rho(...
0
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1answer
27 views

Reading set notation

I am given a question and am having a hard time understanding how to read part of a question, it reads let $ C^{1}(0,1):= \{f:(0,1) \rightarrow \mathbb{R} \mid f\text{ is differentiable and $f'$ is ...
0
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2answers
57 views

What does $\partial_p$ mean?

In the Wikipedia article on ridge detection, there is this symbol $\partial_p$. I know that $\frac{\partial f}{\partial p}$ is sometimes denoted as $\partial_p f$, but I've never seen $\partial_p$ ...
0
votes
1answer
27 views

Comparison of Cartesian and Scalar Notation in Mechanics

In his book on Engineering Mechanics - Statics, R C Hibbeler provides many force problem solutions in both scalar and Cartesian notation (e.g Example 2.5 Chapter 2). It feels like he is trying to ...
0
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2answers
33 views

Notation for apply operation to digits of a number

what is the standard notation to represent that a operation has been applied to each digits of a number for example ...
2
votes
2answers
47 views

which natural english interpretation of this symbolic statement is correct?

Part of Keith Devlin's Coursera MOOC on mathematical thinking requires the translation of this symbolic statement into natural language: $$ 5 < x < 7$$ Interpretation 1: $x$ is a single ...
1
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0answers
16 views

Are there established names and/or symbols for these orderings?

Consider the following orderings on $\mathbb{Z}^2$. Say $(a, b) \leq_1 (c, d)$ if $a \leq c$ or if $a = c$ and $b \geq d$. So for instance $$(1,3) <_1 (1,2) <_1 (1,1) <_1 (2, 3) <_1 (2,...
0
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0answers
14 views

Notation for the index of minimum value of several variables

Assume we have several variables of the form $d_c$ which namely can be $d_1$, $d_2$, ..., $d_n$. I want to use mathematical notation to show for which index $c$ the value of $d_c$ is minimal for all ...
18
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6answers
4k views

How to represent “not an empty set”?

I'm writing a academic paper and need to represent "A is not the empty set". What is usual way for professional mathematicians? My idea is: $|A| > 0$ However, using the emptyset $\emptyset$ ...
1
vote
1answer
46 views

Notation for probability: $C_n^r$, $P_n^r$, $A_n^r$?

I was told that $C^{n}_{k}$ refers to combinations or choose k elements from n elements, $\bar{C^{n}_{k}}$ refers to combinations with repetitions (i.e. $C^{n+k-1}_{k}$), and $P^{n}_{k}$ refers to ...
2
votes
1answer
57 views

$T*T$ Notation and proof

Let $T:H\to H$ be compact where $H$ is a Hilbert space and let $T^*$ be the adjoint operator of $T$. Prove that $T^*T$ is compact and self adjoint and that the eigenvalues of $T^*T$ are nonnegative. ...
4
votes
1answer
27 views

Notation: When to imply and when to express equivalence?

I have recently been trying to improve the readability of my work as I solve equations, so that I and others can easily navigate how exactly I solved them. I want to make sure I using proper notation. ...
3
votes
2answers
125 views

Is this notation mathematically-correct? $\cot\alpha\pm\tan\alpha=\frac2{{\sin\atop\tan}(2\alpha)}$

I have a question. Look at the following expression: $$\cot\alpha\pm\tan\alpha=\frac2{{\sin\atop\tan}(2\alpha)}$$ Is it written well, according to the laws of mathematical language? In that ...
0
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0answers
23 views

How to express the condition that describes at least one element is negative real numbers

As I have a different algorithm to be applied for negative number, I would like to describe the set with negative number as condition. I would like to mathematically describes the condition that ...
0
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0answers
15 views

What is the Euclidean Metric of the Right-Most Column of a Matrix called?

If I have matrix like, $$M_2=\begin{bmatrix} m_{11} & m_{12} \\ m_{21} & m_{22} \end{bmatrix}$$ and I apply an operator such that, $$r_e(M_2)=m_{12}^2+m_{22}^2$$ What is that called? For ...
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votes
1answer
12 views

Notation of discrete functions with variables that only exist for certain multiples of all natural numbers

I have a question about adding two discrete functions, one of which is an exact copy, but dilated. Imagine function x[n]. This function exists for all n in the set of natural numbers (1,2,3,etc.). ...
1
vote
2answers
27 views

notation of a real coordinate system of n dimension

I observe that books write a bold faced R, But the professors write R preceded by a bar. Is that I, denoting infinitism? I am not sure if it is I, its more of a vertical bar. Is it universal, or ...
1
vote
0answers
25 views

Notation for directed and undirected edges of a graph

Let $G$ be a directed graph. I want a way to talk about the edges of $G$ without orientation, so I defined a function $u$ for "unorient" which takes $G=(V,E)$ to $u(G)=(V,E')$ where $$E'=\{\{v,w\} \...
1
vote
3answers
81 views

Integral boundary notation $\int_0^{(1+)}dx~f(x)$?

What does the notation for the upper boundary in the following kind of integral mean? $$\int_0^{(1+)}dx ~f(x)$$ It can be seen here.
1
vote
1answer
18 views

Formula for the weighted median

I am looking for mathematical notation (not computer code) for the following simple scenario: I have three numbers: 6, 7 and 2. I wish to find the weighted median where the weights are say, 20, 10, ...
0
votes
2answers
35 views

Convert the following between octal, decimal and hexadecimal

(a) Convert $61502$ from base $8$ to decimal. (b) Convert $EB7C5$ from base $16$ to octal. My answer: a) $6\times8^4+1\times8^3+5\times8^2+\times8^1+2\times8^0=25410$ b) not sure: converting $E=14$,...
0
votes
1answer
23 views

Why do we call this 'homogeneous oscillation'?

For a pde, a solution of the form $u(x,t)=u_{*}(kx-\omega t)$ are sometimes called wavetrains. Here, $k$ is the wavenumber and $\omega$ is the frequency. Let $k=0$, then, I've heard that we are ...
0
votes
2answers
51 views

What is $\mathbb{R}^+$

Well some books refer to $\mathbb{R}^+$ to be the set of all positive real numbers while others say $\mathbb{R}^+$ is a set of non-negative real number. Is there a universally accepted definition ...
4
votes
2answers
89 views

What does $\mathbb{R}^{[0,1]}$ stand for?

What does $\mathbb{R}^{[0,1]}$ stand for in the following expression? $\Phi: C[0,1] \to \mathbb{R}^{[0,1]}$, where $C$ is the space of all the continuous function in $[0,1]$ and $\Phi$ is an operator....