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

5
votes
4answers
62 views

How often is $x\to\infty$ used to denote ($x\to +\infty$ or $x\to -\infty$)?

How often is $x\to\infty$ used to denote ($x\to +\infty$ or $x\to -\infty$)? Both my textbook and my teacher use $x\to\infty$ as above, so e.g. it's false for us that ...
2
votes
1answer
37 views

What's the correct definition of generated ideal in a pseudo-ring?

Given a ring (with $1$) $R$, one defines what, say, a left ideal is. There's also a natural definition of ideal generated by a subset Definition A: $_R(S):=\bigcap\{I\supseteq S:I\text{ is a left ...
3
votes
1answer
53 views

What does the notation $A:B$ means for matrices $A$ and $B$?

What does the notation $A:B$ means for matrices $A$ and $B$? I saw this is an equation derived from the Navier-Stokes equation. For example, \begin{equation*} \int_{\Omega}\nabla(u):\nabla(v)dx ...
6
votes
4answers
514 views

The meaning of various equality symbols

I'm interested in knowing what is the meaning of the various equality symbols: $=,\sim, \cong,\approx,\equiv$. For example, the speed of a car $V$ in m/s: what would be the meaning of each of these ...
1
vote
0answers
31 views

Expressing the Solution to a System of Differential Equations

My professor wrote the solution to a system as $$X = C_1 \begin{bmatrix}1 \\2 \end{bmatrix} e^{\lambda_1t} + C_2 \begin{bmatrix}3 \\4 \end{bmatrix} e^{\lambda_2t}$$ Where the column vectors are the ...
2
votes
3answers
48 views

Question on $\mathbb{K}$ notation

In a lot of paper and book $\mathbb{K}$ means $\mathbb{R}$ or $\mathbb{C}$. I know that $\mathbb{R}$ comes from the word real, and $\mathbb{C}$ from the word complex. But what about $\mathbb{K}$? ...
4
votes
4answers
115 views

What does $d\log\left(\frac{y}{x}\right)$ mean mathematically?

I am used to seeing derivatives written as $$\frac{df}{dx}.$$ But my economics professor keeps using notation like $$ d\log\left(\frac{y}{x}\right)$$ and I have no idea what this means. What does ...
1
vote
1answer
49 views

What $\mathbb{C}I$ means?

I've come across this expression $$ \mathbb{C}I $$ while studying operators algebras. $C^*$-algebras and AF-algebras, concretely. In Kenneth R. Davidson's book $\boldsymbol{C^*}$**-algebras by ...
8
votes
3answers
1k views

I thought the | symbol meant “divides by”, but in set theory, does it mean something different?

I thought the | symbol meant "divides by", but in set theory it seems that it means "such that." However, I thought we wrote "such that" as ...
0
votes
0answers
11 views

How to formally describe the lowest values of a vector / sorted vector?

I have a distance matrix D and would like to describe that I am just taking the mean (or median) of the 5 lowest values for each column. The programming implementation e.g. in R is fairly easy: ...
1
vote
1answer
52 views

Index notation.

I have a very basic question concerning index notation, normally used in physic papers. I have never used index notation and it is very difficult to me to translate from index free notation, even in ...
5
votes
7answers
988 views

Notation (or Name) of the function which is 0 at x=0 and 1 otherwise

Is there a traditional notation or name of this function: $$ \epsilon (x) = \begin{cases} 0 & \textrm{ if }x = 0 \\ 1 & \textrm{ if }x \neq 0 \end{cases} $$ I know one can use Indicator ...
2
votes
2answers
61 views

Confusion with seeming lack of notational coherence between $\sin^{-1}(x)$ and $\sin^2(x)$

It seems that $\sin^2(x)$ is used to denote the square of whatever value $\sin(x)$ is, instead of the expected $(\sin(x))^2$. Based on that, I would assume that $\sin^{-1}(x) = \frac{1}{\sin(x)}$, ...
3
votes
0answers
39 views

What does $x_e$ mean in $I(x_e,y_0)$?

A book I am using has a problem which includes two points on the graph of $y=\ln x$, $M_1(x_1, y_1)$ and $M_2(x_2, y_2)$ and identifies the middle of the chord $M_1 M_2$ between them as $I(x_e, y_0)$. ...
0
votes
6answers
79 views

What does $\frac{d^2 u}{dt^2}$ mean?

When it comes to taking a derivative, what does $\displaystyle \frac{d^2 u}{dt^2}$ mean ? Does it mean taking derivative of the function twice with respect to $t$. If yes, why is then $d^2 u$ squared? ...
1
vote
2answers
48 views

What does the notation $\int_A$ mean, where $A$ is an event in a probability space?

I am used to seeing integral notation like this, which means the integral over the domain from a to b. $$ \int_{a}^{b} $$ But now I am looking at a statistics book that says "let A be an event" and ...
1
vote
2answers
31 views

Correct to write $\vec{F}:\mathbb{R}^3\rightarrow\mathbb{R}^3$?

Suppose I have some vector field \begin{align} \vec{F}\left(x\left(t\right),y\left(t\right),z\left(t\right)\right)&=G\textbf{i}+H\textbf{j}+T\textbf{k}.\tag{1} \end{align} Would it be correct for ...
1
vote
2answers
38 views

What does $\sim$ in $X\sim \mathcal{N}(\mu,\sigma^{2})$ really mean?

This is a bit of a silly question, but I can't seem to find the answer anywhere. I feel like $X\sim \mathcal{N}(\mu,\sigma^{2})$ means that $\sim$ is a relation, but if it is a relation, what ...
0
votes
0answers
13 views

What does ${\min_{r,s}}{}_{+}$ means? Is it different to ${\min_{r,s}}$?

During my study, I came across these mathematical symbols: $$\delta={\min_{r,s}}{}_{+}\|x_{r}-x_{s}\|, \quad \tau=\min_{r,s}{}_{+}\|\lambda_r-\lambda_s\|,$$ What does $${\min_{r,s}}{}_{+}$$ means? Is ...
0
votes
0answers
16 views

What do these variables in the generic BBP formula mean?

$$P(s,b,n,A)=\sum_{k=0}^\infty \frac1{b^k}\sum_{j=1}^n \frac{a_j}{(nk+j)^s}$$ I would like to understand how this generic type of BBP formula relates to the famous BBP formula: ...
-1
votes
1answer
47 views

Why do people use scientific notation to write very large/very small numbers? [closed]

I've seen numbers like these and 10 to the power of any some numbers is used sometimes for very large/very small numbers. Any reason this is used?
0
votes
0answers
39 views

I need a list of conventional symbols for spaces

I often times want to refer to a certain mathematical space, say the space of random variables on $(\Omega,\mathcal A)$ that have a variance, but cannot remember the exact conventional symbol. For ...
0
votes
0answers
29 views

Understanding notation - strange use of the del operator

I'm currently reading a paper with the following notation with the del operator which i have never encountered before: Does $\nabla _m$ just mean $\frac{\delta}{\delta \mathbf m} $ ? Furthermore, I ...
7
votes
3answers
81 views

Pedantic question on function notation and the meaning of domain

Suppose we have a function $f: A\to B$. Then we know, without specifying what $f$ is, that $f$ may or may not map to every element $b\in B$. If $f$ does map to every element $b\in B$ then it's ...
2
votes
2answers
66 views

Is it ok to do this change of variable in integration: let $x = x - 1$

In integrals like $\int \sqrt{x-1}\,dx$, is it ok to make this change of variable in integration: "let $x = x - 1$"? It looks sketchy — like saying, let 5 = 4.
4
votes
2answers
27 views

When does one use 'succeeds' and when does one use 'greater than'?

I am reading a text on convex optimisation, and there is a line: $f_i(\tilde{x})\leq0$ and $h_i(\tilde{x})=0$, and $\lambda \succeq 0$ and I was just wondering why for one term, $\leq$ is used and ...
1
vote
1answer
33 views

Help understanding a proof about cardinal numbers

I was reading a proof about cardinal numbers, but I do not understand one step. The proof goes as follows: "Let $\beta$ be any ordinal, and for each ordinal $\alpha \lt \beta$, let $\kappa_{\alpha}, ...
2
votes
6answers
60 views

When to use the $\equiv$ symbol (such as in $5^{6}$ $\equiv$ 1 mod 7) vs =

Can anybody explain why we would use the $\equiv$ symbol in the statement $5^{6}$ $\equiv$ 1 mod 7 ? I understand the $\equiv$ symbol means equivalence, but it seems like it would be more appropriate ...
84
votes
6answers
10k views

What did Alan Turing mean when he said he didn't fully understand dy/dx?

Alan Turing's notebook has recently been sold at an auction house in London. In it he says this: Written out: The Leibniz notation $\frac{\mathrm{d}y}{\mathrm{d}x}$ I find extremely difficult ...
0
votes
4answers
52 views

what does this symbol mean: [] but without the top bars?

What does the highlighted symbol mean? What are the details of this method?
1
vote
1answer
56 views

Why sum of two little “o” notation is equal little “o” notation from sum?

Why sum of two little "o" notation is equal little "o" notation from sum? o( f(n) ) + o( g(n) ) = o( f(n) + g(n) ) ? For example: f(n) = n^3 g(n) = 1/n so o(f(n)) = n^2 o(g(n)) = 1/n^2 ...
0
votes
1answer
49 views

What does $k^*/k^{*^2}$ mean?

I'm trying to get a more concrete understanding of what these elements 'look like.' Here $k$ is a field, $k^*$ is multiplicative group, and $(k^*)^2$ consists of the squares in $k^*$.
0
votes
3answers
27 views

Summations and integrals with no upper limits

I've seen expressions like: $$\sum\limits_{i} f(x)$$ And $$ \int\limits_\mathbb{R}f(x)dx $$ What does it mean that they have no upper limits?
0
votes
1answer
16 views

Especifying domain in expressions

When we write things like $\forall x$ does it need to be followed by an $\in \mathbb{A}$ for some set $\mathbb{A}$? Also, sometimes people write things like $\text{for some }x\in(0,3)$: 1)By ...
2
votes
1answer
24 views

Elliptic curve notation

This might be kind of a silly question about notation. I know: $E$: an elliptic curve $\mathbb{F_q}$: finite field But I recently ran across the notation $E/\mathbb{F_q}$ for the first time, so ...
6
votes
2answers
108 views

Is $x_1\cdot x_2\cdots x_n$ proper notation?

In a textbook I recently saw the notation $$x_1\cdot x_2\cdots x_n$$ which was intended to mean $\prod\limits_{i=1}^nx_i$. This is unappetizing to me because for example one wouldn't write ...
0
votes
2answers
65 views

What mathematical idea is the Leibniz notation for derivatives meant to convey?

I know that mathematical notation is often designed to convey some of the mathematical ideas that it expresses -- but I am having trouble getting an intuition for the leibnitz notation like this ...
6
votes
4answers
109 views

What does $\sum_{i=1}^{10} 2$ mean exactly?

Suppose I have $$ \large\sum_{i=1}^{10} 2. $$ Do I just add $2$ to itself $10$ times? I have worked on more complex ones with $n$ and such in the place where the $2$ is, but I have never done it when ...
1
vote
1answer
78 views

Is there a symbol with values 0 and 1 depending on parity of a parameter

Is there a reasonably standard symbol depending on a parameter, like $\delta_i$ or something, that takes the value $1$ when $i$ is even and $0$ when $i$ is odd? or the other way around? $$ \frac{1 + ...
1
vote
1answer
23 views

How should I describe this limiting operation in an equation

In the code I've written, I receive a delta between two position vectors, I then limit this delta by a maximum delta and return the value. To be clear: the direction of the vector remains the same, ...
6
votes
1answer
44 views

Is there a standard notation for the product from right to left?

I am considering a product of the matrices $(A_i)_{1\leq i\leq n}$ in reverse order $$P=A_nA_{n-1}\dots A_1,$$ and I was wondering if there was a standard notation for it, like ...
8
votes
1answer
297 views

Bourbaki and set inclusion

Which notation ($\subset$ or $\subseteq$) was preferred by Bourbaki for set inclusion (not proper)? A side question: Was the notation for subset one of the many notations invented by Bourbaki?
8
votes
2answers
152 views

What is the meaning of $\mathbb{R}\setminus\{0\}$?

This is used in many posts related to functions and googling it doesn't help. What does this mean? $\mathbb{R}$ should stand for all Real numbers.
2
votes
1answer
49 views

In set theory, what do the subscripts $A_1,A_2,\dotsc,A_n$ mean? [closed]

How are subscripts used in set theory, for example, In set theory, what do the subscripts $A_1,A_2,\dotsc,A_n$ mean?
0
votes
0answers
28 views

Notation: column/row projection function for matrix-like objects

If we have a $n$-tuple $\mathscr x$ $$\mathbf{x} := (x_i)_{i\in n}=(x_0,x_1,\ldots,x_{n-1})\in \prod_{i\in n}X_i$$ where $(X_i)_{i\in n}$ is an indexed family of sets and $x_i\in X_i$. We can ...
0
votes
0answers
25 views

Question about bilinear and quadratics form

I'm reading this book: Geometry of algebraic curves by Cornalba, Harris etc. At page 289 there is an excercise where the authors define a quadratic form $Q:V \times V \rightarrow \mathbb{C}$ taking ...
0
votes
1answer
42 views

Math notation clarification

I'm working on learning more about logistic regression and I came across an equation with some confusing notation that I've never seen before: $$ \frac{\delta}{\delta \theta_{y'}^{(j)}} l(\theta) = ...
0
votes
0answers
12 views

Alternative single-letter notations in statistics

I'm learning about statistics, and a thing that is difficult for me is the common use of multi-lettered variables and functions. For instance Standard Error of $\beta$ is written $SE(\beta)$ and the ...
11
votes
7answers
1k views

Is an empty parenthesis a valid mathematical expression? [closed]

Is using an empty parenthesis valid? For example, $15+()=15$. What is the meaning if it is valid? I need an academic reference to validate this.
0
votes
1answer
31 views

Vector notation for shifting the elements of a vector

I'm looking for a suitable notation to express a "shift operator" which shifts all elements of a vector forward and sets the first element to zero, e.g., $$\begin{eqnarray*} (1,1,0,1) & ...