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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2
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3answers
53 views

Is there a difference between $\sin^2(x)$ and $\sin(x)^2$?

Is there a difference between these? Or are they the same? If they're the same, then why does $\sin^2(x)$ seem like its used more often?
0
votes
1answer
25 views

Notation Question: Times with a subscript

What does the notation $\times_\chi$ mean in this context? Is it semidirect product? Context: $\pi_n(E)\cong \text{coker}\times_\chi\ker$, for a cohomology class $\chi\in H^2(\ker,\text{coker})$. ...
0
votes
0answers
26 views

help understanding math notation for algorithm

$Pkatz(z|x,y) =$ $P'(z|x,y), if C(x,y,z) > 0$ $α(x,y)Pkatz(z|y), else if C(x,y) > 0$ $P'(z), otherwise.$ $Pkatz(z|y) =$ $P'(z|y),ifC(y,z)>0$ $α(y)P' (z), otherwise.$ ...
0
votes
1answer
29 views

How to read the Jacobian (determinant) shorthand notation, and why is it so cryptic?

Lets say we have a function $f : \mathbb{R}^3\rightarrow \mathbb{R}^3$, as defined below, with its value being denoted as $(a, b, c)$ for convenient reference. $$f(x,y,z) = (x^2, y^2, z^2) = (a, b, ...
0
votes
0answers
29 views

Notation used for equations in finite fields

In some work I am currently writing there is a point at which I have to put values into a few different formulae. I am operating over a finite field so I aim to use values in this field. As an ...
2
votes
0answers
41 views

Does order matter when dealing with quantifiers?

Do ${\forall}x{\forall}y{\exists}z$, ${\forall}x({\forall}y{\exists}z)$ and $({\forall}x{\forall}y){\exists}z$ all mean the same thing?
0
votes
0answers
26 views

What is the use of $:$ other than “such that”?

Take this way of writing the Axiom of Pairing in the ZFC axioms, for example: ${\forall}A:{\forall}B:{\exists}x:{\forall}y:(y\,{\in}\,x{\iff}y=A\,∨ \,y=B)$ Clearly $:$ doesn't mean "such that" here. ...
0
votes
1answer
51 views

What's the conventional notation for most probable/likely value as opposed to expectation value?

Say I want to distinguish the expected value for some random variable $\mathbb{E}(\eta)$ from its most likely / probable value. Is there a conventional, succinct way to refer to the latter, other ...
0
votes
1answer
26 views

Double sigma notation case

how to write this double sigma notation? $\sum_{i=1}^n \sum_{j=1}^i 5i $ which equals to - $5\sum_{i=1}^n \frac{n(n+1)}{2} $ Thanks!
4
votes
1answer
62 views

Why are function definitions not written with the := sign

Why are function definitions not written with the $:=$ sign instead of the $=$ sign. It seems to me that $:=$ would be more intuitive and avoid a lot of unnecessary ambiguity. Consider the following ...
1
vote
0answers
20 views

mathematical notation for defining a variable inside a conditional expression

I have the following conditional expression on $f$ and I want to use a variable which is only used inside the expression. I'm wondering what would be the best typset for defining it there. Here is ...
0
votes
1answer
21 views

Iterating through the same set twice in the same equation

I have a question regarding set theory when using forall on the same set twice, in the same equation. More specifically, this is the equation I want to write: $ \forall u_i \in U : u_i \; ...
1
vote
0answers
29 views

What is this notaton in Genus Theorem called?

Recently I started studying the book "Advanced Number Theory, by Harvey Cohn". Actually I know nothing about "Quadratic Forms". There I found this theorem: Let $$Q_1=x^2+5y^2$$ and ...
0
votes
1answer
33 views

The meaning of Th(E) in default logic?

Hello I couldn't find an answer for that question anywhere. what is the meaning of Th() ? and also the meaning of the more specific Th(E)=E from Reiter's paper
0
votes
1answer
57 views

How do I write $F_1+F_3+F_5+\ldots+F_{2n-1}$ in summation notation?

How do I write $F_1+F_3+F_5+\ldots+F_{2n-1}$ in summation notation? $F_i$ represents the Fibonacci sequence. I can't figure out how to write this in summation notation. Clear steps would be ...
0
votes
1answer
55 views

What does the notation “ (2, 3] ” mean?

I know [2, 3]. But (2, 3]? The question's solution was given: The range of value of x is (2, 3]
5
votes
4answers
1k views

What does this (double absolute value like) notation mean?

Here, $$\left\lVert\frac{\partial\bf x}{\partial s}\times\frac{\partial\bf x}{\partial t}\right\rVert$$ the inside will at last be a vector. and two absolute value signs have covered it. what does ...
0
votes
0answers
17 views

Differing notation in compact Taylor series for several variables

I'm a second year mathematical physics student. Wikipedia has a compact definition for the Taylor series in several variables: $$T(\textbf{x})=\sum_{\alpha\geq ...
0
votes
0answers
11 views

Formulating the optimal sequence in a TSP

Im in the process of writing a section of a scientific paper, and im struggling a bit with the notation of the solution to a traveling salesman problem. I have a fully connected graph with a set of ...
2
votes
0answers
35 views

Dirac Notation: What Do $\langle u|v \rangle$ and $\langle u|T|v \rangle$ Represent?

I post this hoping for clarification, and particularly in a context of linear algebra without too much mention of matrices. (1) Let $V$ be a (perhaps infinite dimensional) Hilbert space and $V'$ its ...
0
votes
1answer
15 views

Understanding notation of the Multivariate Gaussian Distribution

I have a simple notation question on the multivariate gaussian formula. I don´t get what the $T$ symbol means on the exponential part. Can anyone explain this part of the formula and the correct way ...
1
vote
1answer
76 views

What justifies the differential in an indefinite integral?

I saw this question and found the accepted answer to be very satisfying. However I thought about indefinite integrals and the differential in them (eg. $dx$). And a central part of the answer's ...
2
votes
1answer
43 views

Notation for sets of unordered pairs

Let $A$ be a finite set of unordered pairs, e.g., $$A = \{\{1, 2\}, \{1, 3\}, \{2, 3\}\} \enspace .$$ Which of the following is proper notation for "the element $\{1, 2\}$ belongs to $A$"? $\{1, 2\} ...
2
votes
1answer
22 views

Variable naming in combination of minimum and set builder notation

I wonder if this notation is 100% correct, or whether it could be misunderstood in any way: $m = \min \left\{ m \in \mathbb{N} \;\middle|\; f(m) > 0 \right\}$ In my opinion, the expression of the ...
0
votes
1answer
44 views

Is this correct math notation?

Is the following correct? $$ x_{ap} = x_{ij} \quad \forall a,i \in [1,4]\ \forall p,j \in [1,5] $$ I want to write that $x_{ap}$ is equal to $x_{ij}$. And $i$ and $a$ can only be values between $1$ ...
0
votes
1answer
34 views

Symbol to represent “On the unit sphere” to laymen

I am preparing a deck of slides related to quantum computing for network-administrator and business type people which involves the following diagram: In the text I had $|\Psi> \in \{0,1\}$. I ...
0
votes
1answer
21 views

Iverson Bracket / Conditional Sum of a string

I'm trying to turn calculations that I've been using on a data set into mathematic notation to write it down in a research paper. One of my calculations creates a factor that determines how often a ...
0
votes
0answers
19 views

How to write the set of tuples of consecutive numbers in a set

I would like to write a sum iterating over 3-tuples of consecutive elements of a set (of floating-point numbers, representing timestamps). For the moment, my notation is: $\sum\limits_{(t1, t2, t3) ...
2
votes
2answers
78 views

Is the composition of the differentiating operator commutative?

First of all, can I check that $d\over dx$ can be considered an operator, or function (as it says in the title)? Is the composition of the differentiating operator commutative? In other words, if ...
1
vote
1answer
29 views

Irreducible and recurrent Markov chain - theorem notation question

In [J. R. Norris] Markov Chains (Cambridge Series in Statistical and Probabilistic Mathematics) (2009), page 35, Theorem 1.7.5 says: In (ii), does it mean $\gamma^k$ is notation for $\gamma^k_i$ ...
0
votes
1answer
19 views

Notation for all of the integer divisors of a number

What is / is there a notation for the set that consists of all of the integer divisors of an integer. For example: $$[7]=\{1, 7\}$$ $$[12]=\{1, 2, 3, 4, 6, 12\}$$ Note that I am using $[$ and $]$ in ...
1
vote
2answers
39 views

Does the colon in function notation stand for “such that”?

The colon mark sometimes stands for "such that". When writing functions, it is customary to write, for example: $f:[0,1]\rightarrow[0,1]$. Can the colon in this context be interpreted as "such ...
1
vote
1answer
18 views

Notation power functions and Neyman-Pearson Lemma part

Thanks for your attention. I have a question about notation. The way we define the power function is $B(\theta)=P_{\theta} (X \in R)$ where $X$ is a random VECTOR, and $R$ is a rejection region. I ...
0
votes
1answer
33 views

What is the symbol that is used for the universal set in these two textbooks? [closed]

From this textbook: And this textbook: It looks like a squiggly E (\mathcal{E}) or perhaps it is the Greek letter xi (ξ). But I am not sure.
1
vote
1answer
18 views

A question about convention of writing identities and formulas

I'm only a third year undergraduate math student, but I've seen a decent amount of formulas, identities, and equations (at least enough to formulate such a question). However, I haven't actually ...
1
vote
1answer
25 views

Symmetric Simple Random Walk - Definition Clarification

I'm finding conflicting answers everywhere, including in my own notes. In the phrase "symmetric simple random walk", which part, "symmetric" or "simple" refers to having a probability of $0.5$ to go ...
1
vote
2answers
28 views

Notation for sets that do not overlap

Is there notation to describe, say a set that consists entirely of two mutually exclusive subsets? Say $ D = D_1 \cup D_2 $, how to indicate that $D_1$ and $D_2$ do not overlap?
0
votes
0answers
56 views

Is it okay to say $\cos(a)$ where $a$ is a vector?

Assume you have vectors $a$ and $b$. They are not precisely defined but in the text mentioned as vectors. Can I use the following notation to mean element-wise product of $a_k$ and $\cos(b_k)$? ...
1
vote
2answers
43 views

Should I write $x (f(x))^{-1}$ with less parenthesis.

In this case, $x$ and $f(x)$ belong to a multiplicative group. I would like to write $x f(x)^{-1}$ instead of $x(f(x))^{-1}$. I figured that I could explain once what I mean by $x f(x)^{-1}$ and then ...
6
votes
4answers
128 views

Why is $\cos(x)^2$ written as $\cos^2(x)$?

I'm just wondering why the square of $\cos(x)$ (i.e.: $(\cos(x))*(\cos(x))$) is almost universally written in the form $\cos^2(x)$ rather than $\cos(x)^2$. This seems particularly bizarre when one ...
5
votes
2answers
119 views

What will mathematicians do when they run out of letters in the Greek and English alphabets? [closed]

Like x,y,z are commonly understood to be dimensions and theta is an angle and Pi is a specific irrational constant, and Tau is half of Pi, etc. etc. etc. They must be running out of letters by now. ...
4
votes
4answers
71 views

Why do univariate indefinite integrals carry the $\mathrm {d}x$?

I understand that the $\mathrm {d}x$ sort of comes from the $(x_i-x_{i-1})$ term in the Riemann sums of the integrals (just like the $\mathrm dg$ for Riemann-Stieltjes integrals), but when working ...
2
votes
1answer
46 views

Is “the reals” a slang term for $\mathbb{R}^d$ where $d = 1$?

Often times I see people referring to certain functions as a mapping from $\mathbb{R}^d$ to "the reals", are they referring to $\mathbb{R}^d$ where $d = 1$? Sorry for the potentially trivial ...
0
votes
1answer
21 views

Einstein Summation Convention Minkowski Metric

Picked up a book on General Relativity for Mathematicians, but I'm a bit unclear on some of the tensor notation. For example, the Minkowski Metric $$\eta_{\mu \nu} (\Delta x^\mu)(\Delta x^\nu)$$ ...
0
votes
2answers
50 views

Integrals without terms possible?

Is an integral without a term possible? I don't know the specific name for the term at the end but here is an example: $\int x $ vs $\int$$ (x) dx$ And does $\int$$ ((x) dx) \Rightarrow ...
12
votes
4answers
558 views

Is Sigma $\Sigma$ a mathematical way of doing a for loop?

I've been a programmer for ten years, and once upon a time I was pretty good at math. Those days are long gone. I'm taking some online classes and now I find myself needing to remember the math I ...
0
votes
0answers
12 views

Notation for “vectorized” function

Is there a notation for expressing vectorization of a function as implemented by Mathematica's Map ...
1
vote
1answer
33 views

Is interval a set?

Given a function $f$; $$ f(x) = \frac{x}{1+x^2} $$ the support of $f$ is $$ \mbox{supp}f=\begin{cases} \overline{\{(-\infty, 0), (0, \infty)\}}=(-\infty, \infty)=\mathbb{R}&&(1)\\ ...
2
votes
2answers
114 views

How to write this statement in mathematical notation?

No integer bigger than 70 can be expressed as a sum of 3 integers smaller than 30 My attempt: $U_1 = {x∈Z∶x>70 }$ $U_2 = {y∈Z∶y<30 }$ $∄x ∈ U_1 , ∀y ∈ U_2 , x = y_1+y_2+y_3$ I understand that ...
1
vote
1answer
18 views

Why aren't the degrees of freedom included in the confidence interval formula?

I have one question. In the formula for calculating the confidence interval, I don't see the degrees of freedom in the formula. In my book, the formula is : $$\text{Confidence interval:} \qquad \mu ...