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
votes
1answer
75 views

Notation i.i.d sample

I am learning measure theory and sometimes I am not sure if I am using the correct notations, especially with respect to distributions of random variables. In the following I try to formulate the ...
2
votes
2answers
67 views

Is there any difference between $\sum_{ij}$ and $\sum_i\sum_j\;?$

I was reading Tensors by Feynman, where he said: [...]$$u_P=\tfrac{1}{2}\sum_i\sum_j\alpha_{ij}E_iE_j\;.\tag{31.7}$$ The energy density $u_P$ is a number independent of the choice of axes, so ...
0
votes
2answers
32 views

How to express that one interval is included in another interval?

Would the symbol "$\in$" work for denoting that one interval is included in another interval? Like this: $(x>2) \in (x>0)$
1
vote
2answers
30 views

Quantum group notation

I was jumping into the deep end and reading a few papers and lectures on quantum groups. My knowledge on Lie algebras is a bit thin but I was just wondering the notation used in the starting of this ...
0
votes
2answers
15 views

Name for opposing (complementary) multisets (bags)

I am looking for the accepted mathematical name for opposing multisets (or complementary multisets). I have done a Google search and a Stack Exchange search, and have come up empty. These are the ...
3
votes
2answers
47 views

What's the notation of the one-sided differential of a function?

Assume $$f(x)=\left \{\begin{matrix} x-1 & x \leq 0\\ x+1 & x > 0 \end{matrix} \right.$$ Obviously, $df(x)/dx$ do not exists at $x=0$ but the one-sided differential exists. What's the ...
0
votes
0answers
26 views

Show that $(\log(n))! = \Omega(n^3)$

I want to prove that $(\log_{2}(n))! = \Omega(n^3)$. I Think that $(\log_{2}(n))! = \Theta({\log_{2}(n)}^{\log_{2}(n)})$ But, I dont know how to continue. Someone has an idea ? Thanks
0
votes
2answers
39 views

How are these different types of notation called?

My teacher used to give questions on integrals of vector fields with different notation to get us used to seeing things in different forms. I'm just wondering what these three different forms of ...
3
votes
0answers
29 views

Origin/history of mixed number notation with misleading hyphen, e.g. 1-1/2

So there is a system of writing mixed numbers (that is, a combination of whole number and fraction, used instead of an “improper” fraction) used in cases where typing vulgar fractions (e.g. ½) ...
-1
votes
3answers
85 views

What does the mathematical symbol with an underline below the variable name mean?

I have been reading a research paper. The author has used a variable '$x$' with an underline beneath '$x$'. I know that a variable with with a line on top of it implies it's arithmetic mean. But I ...
2
votes
1answer
71 views

which odd integers $n$ divides $3^{n}+1$?

I don't understand this solution to this problem. Can anyone explain why d divides n?
-1
votes
1answer
39 views

How to represent a nested loop using mathematical formulae [closed]

Excluding the context of summation or product, how can one represent a nested loop within mathematical notation? For instance, if every element of an array X is being compared to one another as part ...
1
vote
1answer
41 views

What is the origin of PEMDAS?

While working on a compiler's grammar to follow this, It occurred to me that although it's something we are all taught to and simply follow, I don't know the origin or the reason we do it in the first ...
3
votes
2answers
66 views

What does $\mathbb{Z}/n \mathbb{Z}$ mean in abstract algebra?

If you look at this wiki page under the image on top of right hand side, you see $\mathbb{Z}/ \mathbb{8Z}$. What does it mean and give example if possible please thanks.
5
votes
2answers
87 views

Is it weird to say $A \in B \in C$?

I've just noticed that I've never seen any text say $A \in B \in C$, which is why when writing it myself it immediately looked weird. For context, I was proving a result about the topology $\mathcal{...
1
vote
1answer
29 views

Two different notations for inner product

In my linear algebra course on the faculty of mathematics, we used the following notation for the inner product: $$\langle v, w \rangle$$ On the other hand, my friends from the faculty of physics ...
0
votes
1answer
32 views

Why the separate notation for norm

One usually denotes the norm as $\|\cdot\| $, $\| v\| := \sqrt{\langle v, v \rangle}.$ However, in metric spaces, one often writes $d(x,y) \equiv \lvert x-y \rvert$. Since the norm canonically ...
11
votes
6answers
746 views

When can we not treat differentials as fractions? And when is it perfectly OK?

I am a first year calculus student so I would prefer if answers remained in Layman's terms. It is common knowledge and seems to me a mantra that I keep hearing over and over again to "not treat ...
0
votes
0answers
55 views

What does this notation mean? $∂df^2 / ∂x$

I am given variance $\sigma_x$ and function $y=f(x)$ According to my book, the following equation gives the new variance of $y=f(x)$. But I'm not sure what this notation means, as in what this ...
0
votes
1answer
21 views

Is this notation equivalent $(\Bbb{Z}_p)^n=\Bbb{Z}_{p}^n$?

A pretty straightforward , and somewhat embarrasing question concerning notations because I am a bit confused here (trying to study by myself some Abstract Algebra). We consider the finite field $\...
1
vote
1answer
41 views

What is the correct notation for $\frac{du}{dx} * dx$?

first post on stackexchange here, so please excuse any incorrect formatting or wording, etc. I'm currently studying intermediate integration, especially integration by parts and u-substitution. I am ...
0
votes
0answers
29 views

Mathematical notation for a number to contain all of the digits from a set

Recently I was thinking about "interesting" numbers with the property of containing all of the digits 0 through 9 and being divisible by all of the numbers 1 through 9. The second part of that is ...
0
votes
0answers
18 views

What is the correct notation for the conjugacy function?

Let say I have two mappings which are $f:\mathbb{Z} \times \mathbb{Z}$ $\rightarrow\mathbb{Z} \times \mathbb{Z}$ and $g:d\mathbb{Z}\times \mathbb{Z} \rightarrow d \mathbb{Z} \times \mathbb{Z}$. If I ...
0
votes
2answers
49 views

Meaning of curly brackets with numbers around: $\{\log\lambda_i\}_1^n$

I am studying for an exam and found this in the solutions: "... with canonical parameters $\{\log\lambda_i\}^n_1$". Index $I=1,2,\ldots,n$. The professor that wrote the exam has retired. Does ...
0
votes
2answers
41 views

A matrix of a single 1 in each row and 0 elsewhere

Is there a particular name given to a matrix of m rows and n columns such that it must have one and only one 1 in each row and 0 elsewhere? For instance: ...
1
vote
1answer
21 views

What is the notation $PQ$ supposed to mean for subgroups?

My notes just jumps to it without prior explanation like I am supposed to know it. I don't. It's talking about Sylow p-groups and such, $A$ is a group and let $P,Q$ be sylow $p,q$-groups ...
0
votes
2answers
39 views

What Does a Subscript Do to a Number? [closed]

So I had a math question that had a formula for that said Tn= arn-1 Where a is the first sequence and r is the common ratio. For example, in the sequence 10,40,160,640,..., a=10, and r=40/10=160/40=...
0
votes
3answers
55 views

Linear Algebra: How to notate vectors?

In my paper, I want to write that the $(x,y)$ coordinate could be transformed into a $(u,v)$ coordinate. $$\begin{bmatrix}x\\y\end{bmatrix}=P\begin{bmatrix}u\\v\end{bmatrix}$$ I would like to say ...
1
vote
0answers
29 views

Series with Markov Chains Probabilities

Notation For each $t \in \mathbb{N}$, let $h_t \in H$ be a random variable that follows a Markov chain, and $h^t \equiv \{h_0,h_1,\dots,h_t\} \in H^t$. Let $\Pi(h^{t})$ be the probability that a ...
4
votes
1answer
49 views

Applying equivalence of norms on $\mathbb R^n$ .

Let $\|\cdot\|$ be any norm on $\mathbb R^n$. Prove that a sequance on $\mathbb R^n$ converges to an element $x \in \mathbb R^n$ under the $\|\cdot\|_2$ norm if and only if the sequance converges to $...
1
vote
0answers
28 views

When is it appropriate to use set notation outside measure theory?

Soft question and just starting to learn measure theory. So please be kind, and if you want the question gone, just place a comment. I got stuck in trying to write on a problem of combinations with ...
7
votes
4answers
2k views

Is there a mathematical notation of indexing a matrix?

Do matrices in linear algebra support an operation of indexing them analogous to array indexing? For example: $$ A = \left [\begin{array}{cc} 1 & 2 \\ 3 & 4 \end{array}\right] $$ In ...
0
votes
4answers
39 views

Scientific notation (counting digits)

How many digits are there when $7.30\times10^{28}$ is expressed in ordinary numeral? I thought there should be $30$ digits, but I'm wrong, why?
1
vote
1answer
21 views

How to notate the restriction of an inverse of a function?

Let $f$ be a function, which is defined on $E\subset\mathbb{R}^n$, and which is mapping to an extended real numbers. That is, $$f:E\longrightarrow\overline{\mathbb{R}}$$ Then, for a subset $A$ of $E$ ...
5
votes
1answer
84 views

Unusual integral notation

When I was learning analysis, I often wondered why I couldn't seem to find anything like $$\iint f(x) (dx)^2$$ in a standard calculus text, and concluded that it should be meaningless – even though, ...
0
votes
0answers
25 views

Unfamiliar notation in an AQA Core 4 Mark Scheme $p\frac{dx}{dt}=q$ where $p$ and $q$ are functions

I'm told that after $t$ years there are $x$ fish in a lake where the number of fish is decreasing. The rate of decrease of the number of fish is proportional to the number of fish currently in the ...
-1
votes
1answer
73 views

Symbol for “greater than and possibly equal” [closed]

How would I say, in mathematical notation that $x$ is greater than or possibly equal to something? If I was checking an equality, I might suppose it like $$x \stackrel{?}{=}4$$ Or if I was uncertain ...
3
votes
1answer
32 views

Interval notation: infinity, -infinity in closed interval

I was watching a video stream a little bit ago and noticed on an equation without context that had the interval $\left[{-\infty, \infty}\right]$. This was preculiar to me as I've never seen the ...
1
vote
1answer
24 views

What does $p_b \propto ρ^n _b $ mean

$p_b \propto ρ^n _b $, in fluid mechanics, where $p_b$ is the pressure inside a bubble and $\rho$ is the density. What does that symbol looking like alpha mean?
4
votes
2answers
174 views

What is the notation for the empty matrix?

My question: What is a notation for an empty 0x0 matrix (i.e. the matrix for the only linear map $f:\{0\}\to\{0\}$)? Is it written $()$? How can I distinguish the 0x0 matrix with for example the 0x3 ...
60
votes
7answers
5k views

What is “Bra” and “Ket” notation and how does it relate to Hilbert spaces?

This is my first semester of quantum mechanics and higher mathematics and I am completely lost. I have tried to find help at my university, browsed similar questions on this site, looked at my ...
0
votes
1answer
16 views

double summation notation

In a paper I am studying, the author writes $$\sum_{{i=1}\atop {k=1}}^{N+1} C_i \eta_k$$ How are the two indices to be interpreted? In other words, how would this expression be written using sigma ...
0
votes
2answers
41 views

Name of the notation where number is expressed as a sum

I have the following general form of a number: Does this notation have a name? Here is the example of using the form:
0
votes
1answer
31 views

Meaning of this expression

I found a relation while studying elliptic curves, I could not understand its' meaning. $E[n]$ is a $n$-torsion subgroup then $E[n]\cong Z/nZ \oplus Z/nZ$, What does this $\oplus$ symbol mean? Thanks ...
0
votes
0answers
15 views

Acceptable notation? $\lesssim_{n} n^{-\beta}$ for constants NOT depending on $n$

I am preparing a paper and found it convenient to write things like $$ |\text{Expression of a lot of variables}|\lesssim_{n} n^{-\beta} $$ when an inequality is true up to a multiplicative factor that ...
2
votes
1answer
22 views

Use of $\arg$ function [closed]

I know that $\underset{x}{\operatorname{argmax}}f(x)$ is defined as the value at which $f(x)$ has its maximum. There is also $\underset{x}{\operatorname{argmin}}$. However, in statistics, I often ...
4
votes
1answer
40 views

What is “non-simple applied first-order functional calculus” (60's set theory)

Azriel Lévy says in his 1960 paper Axiom Schemata of Strong Infinity in Axiomatic Set Theory, that the $\sf{ZF}$ set theory is formalized with a finite number of axioms in "non-simple applied first-...
1
vote
0answers
32 views

What notation is usually used to denote the category of $R,S$-bimodules

I came across the notation: $\mathbf{Mod}_{(R,S)}$. But generally, when handwritten, long superscripts/subscripts are becoming clumsy. So I'm wondering whether there's an adopted alternative. Is ...
4
votes
1answer
47 views

U-substitution in disguise (notation) — what is $d(2x+1)$?

I would like to know if there is a name for this notation here, which I've seen many times. $$\int \frac{1}{2x+1} \ dx= \frac{1}{2} \int \frac{1}{2x+1} \ d(2x+1)=\frac{1}{2} \ln|2x+1|+c$$ Thanks
0
votes
3answers
48 views

Is there a general operator symbol?

I want to write the expression a + b for +, - and * at once. Can it be done? Is there an operator that represents a general operator?