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.

learn more… | top users | synonyms

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
36 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
28 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
48 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
39 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
20 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
38 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 ...
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
28 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
47 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 ...
6
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
37 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
20 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
81 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
20 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
70 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
31 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
22 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
169 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 ...
58
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
30 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
14 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
38 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 ...
1
vote
0answers
31 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
46 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
46 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?
1
vote
1answer
36 views

Is there a generic hierarchical difference in measure theory between $\LaTeX$ \mathcal and \mathscr?

I am wondering abut $\mathcal F$ perhaps denoting a $\sigma$-algebra, whereas $\mathscr F$ may be a Borel $\sigma$-algebra, or a set of sigma algebras. Also, if there a standardized, or tacit ...
1
vote
1answer
35 views

The $I$ in the smallest sigma algebra generated by collection of subsets of $\Omega$

In defining a Borel sigma algebra (and if I understand it right) you can depart from the idea that an arbitrary collection of subsets $\mathcal C$ of the sample space $\Omega$, where $\mathcal C$ will ...
0
votes
1answer
16 views

Notation: $\sum_i \dfrac{\partial A_i}{\partial x_i} \boldsymbol{e}_i$ using $\nabla$.

I would like to write $\sum_i \dfrac{\partial A_i}{\partial x_i} \boldsymbol{e}_i$ using the $\nabla$ operator if possible, where $\boldsymbol{A}=A_1\boldsymbol{e}_1 + A_2\boldsymbol{e}_2 + ...
1
vote
0answers
23 views

$ \div $ as divergence operator

I am reading Nonlinear continuum mechanics for finite element analysis by Bonet and Wood, and I encountered an operator $ \div $ I am unfamiliar with. They define it as the divergence of a second ...
0
votes
1answer
24 views

Meaning of symbol “$y\nearrow x$” in CDF Limit

Could somebody explain the meaning of "$y\nearrow x$"? $F_X$ is right continuous, that is, for any $x$, $\lim_{y \nearrow x} F_X (y) = F_X(x)$.
2
votes
0answers
26 views

use little $o$ notation.

out from apostol's book. $f(x)=o(g(x))$ if $\frac{f}{g}\rightarrow 0$ when $x\rightarrow a$ and gives some properties. 1)$o(g(x))+o(g(x))=o(g(x))$ 2)$o(cg(x))=o(g(x))$ ...
0
votes
1answer
21 views

Limit notation where variable does not approach anything

I was reading an example in my probability textbook that states a limit as $$\lim_{n}{P\left\{X \leq 3 - \frac{1}{n} \right\}}$$ where the RV $X=k$ is defined for $ k \in \mathbb{R}$ What exactly ...
2
votes
3answers
64 views

Expected value of $g(X)$.

If $\mathrm{E}(X) = \sum_{x\in I} x\,\mathrm{P}(X=x)$, how can I deduce that $E(g(X)) = \sum_{x\in ?} g(x)\,\mathrm{P}(X=x)$? I don't see why it isn't $E(g(X)) = \sum_{g(x)\in ?} ...
0
votes
1answer
14 views

Is it correct to write $argmin(x, y) \sum_i^n |p_{x_i} - x| + |p_{y_i} - y| = argmin(x) \sum_i^n |p_{x_i} - x| + argmin(y) \sum_i^n |p_{y_i} - y| $?

$argmin(x, y) \sum_i^n |p_{x_i} - x| + |p_{y_i} - y| = argmin(x) \sum_i^n |p_{x_i} - x| + argmin(y) \sum_i^n |p_{y_i} - y| $ Is it a legit way of separating argmins to show independence of $x$ and ...
-1
votes
2answers
47 views

Using the definition of $f$ is $O(g)$ proof:

I'm studying for my discrete math class and I don't understand how to prove big O notation. I understand that $f$ is $O(g)$ of another if $f(x) \le c g(x)$ holds. How would I go about proving $\sin ...
0
votes
1answer
31 views

Regarding taking powers of prime ideals in a ring

My question is simple to ask: given some prime ideal $P$ in a ring $R$, we can talk about $P^2, P^3$ etc. but can we discuss $P^0$? Is there a convention that says $P^0 = R$, or is there something ...
0
votes
1answer
13 views

Notation: square brackets with a unique scalar?

my question is purely about notation. I am reading papers in computer science and I see that people use the following notation $[x]$ to denote $\{1,2,\ldots,x\}$. Is that correct? Or does it mean ...
1
vote
1answer
26 views

How to interpret scientific notation?

I'm having a problem understanding scientific notation. What is the difference between the following: $$\text{5e2, 5e-2, -5e2, -5e-2}$$
1
vote
1answer
23 views

The sum of $V=U+W$ of a vectorspace V and subspaces $U$, and $V$

I know what the sum of two subspaces is and how we notate but is it ok to write a minus to denote what I hope should be obvious is meant. So we have $V=U+W+Y$ where $V$ is a v.space and $U,W,Y$ ...
0
votes
0answers
43 views

Is the notation $\mathbb{P}(X \cap Y) = \mathbb{P}(X,Y)$ common?

For two random variables $X,Y$, is the notation $\mathbb{P}(X \cap Y) = \mathbb{P}(X,Y)$ common? In a probability class last year we had always used $\mathbb{P}(X \cap Y)$. This year in a stochastic ...
0
votes
1answer
14 views

Clarification of Direct sum meaning with $\geq 3$ subspaces

Let $V$ be a vectorspace and $U_i$ subspaces of V. In the definition of $\oplus_{i \in I} U_i$ it is said that is does not suffice for $U_i$ to be pairwise disjoint. Instead we must have the stronger ...
1
vote
1answer
18 views

Explanation Notation Union Probability

Could somebody explain how to create intuition for the probability/union notation below? I don't know how to read it. And is this a situation where events are disjoint, but dependent?
1
vote
0answers
55 views

On a Probability notation - $\mathbb{E}[X(.)|\mathcal{F}]_G$

What could mean this notation : $\mathbb{E}[X(.)|\mathcal{F}]_G$ ? where G : $\Omega \rightarrow \mathbb{R}$ is a random variable on a probability space $(\Omega,P, \mathcal{F})$. X could be a ...
0
votes
0answers
19 views

Topology; difference between open subsets of $X$ containing $x$ and open neightborhood od $x$?

I see my lecture notes and some texts alternate between the two. What is the difference in saying that "an open subset of $X$ containing $x \in X$" and an "open neighborhood of $x \in X$"?