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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5
votes
2answers
35 views

What does the colon in the statement $T:t\to−t$ mean?

I don't understand what the colon $T:t\to−t$ means. I understand that it does something, is it a variable or just a symbol that has no significance?
1
vote
1answer
34 views

matrix inverse in tensor notation

Suppose there is a matrix $A$ that transforms vectors, $$ Y = A x $$ Now express this in some other coordinate system, with $x = B z, \,\, y = B w$, so \begin{align*} & Bw = A B z \\ ...
0
votes
3answers
69 views

What does a tilde underneath an inequality mean?

I've recently come across an expression of the form $$\Large x \lesssim y$$ What does this expression mean? Thank you.
2
votes
4answers
122 views

What does $\exp(f)$ mean?

In several posts around this site, I have encountered the expression $\exp(x)$ where $x$ is an arbitrary expression. What does this notation mean?
4
votes
4answers
479 views

A doubt in Bergman's notes

On pg. 8 of these notes, Bergman says that a group $G$ contains an inverse operation $i:G\to G$, along with $\mu:G\times G\to G$ and a "neutral element" $e$. Hence, a group should be referred to as ...
1
vote
1answer
19 views

Notation for Model-Relation of formulae with free variables

Lets assume we have a formula $\mathsf{path}(x,y)$ with free variables $x,y$, and $\mathsf{acyclic}$ with no free variables on the signature $\tau = \{E\}$ (i.e. Graphs). Informally, what the formula ...
1
vote
1answer
36 views

Is the following use of indices correct?

Is the following use of indices correct? A vector $\langle x_i, x_{i+1},...,x_{i+k}\rangle$ is given. For every such vector a function is defined through $$\mu=\frac{\sum_{j=0}^k ...
0
votes
0answers
53 views

Notation in Linear Algebra

What does $(A\mid b)$ denote in Linear Algebra? Specifically in the context of the following question: "If $(A\mid b)$ is in reduced row echelon form, prove that A is also in reduced row echelon ...
2
votes
1answer
32 views

Notation in Actuarial text

I am not very knowledgeable in Actuarial Sciences, but I was looking at a text, and found a notation, which I cannot find any references to. What does: $_{2|2}q_{1} = 0.288$ mean? I don't think it ...
1
vote
1answer
28 views

Set Theory Elementhood Notation

From How to Prove it: Given $A=\{n^2|n \in N\}$ where $N$ is the set of all natural numbers. I want to express A in terms of elementhood test notation. Velleman says $A=\{x| \exists n \in N ...
0
votes
3answers
59 views

What is this and why is it so important $(x,y) \to (y,x)$?

When doing a $y=x$ reflection the notation is $(x,y) \to (y,x)$. My teacher told us to find out what it is, what it is called, and why it is important? Please help ?
7
votes
2answers
630 views

History of notation: “!”

Does anyone know where the factorial "!" symbol came from? I can't decide if it is my favorite or least favorite notation in mathematics...
3
votes
1answer
37 views

Is there standard notation to handle “chains of functions”?

Let $f(x)=g $ $g(y)=z $ Is there standard notation to express z in terms of f(x)? Something like (f(x))(y)?
0
votes
1answer
50 views

notation used in algebraic topology [closed]

i have some confusion in notations used in my algebraic topology class. $\approx$ homeomorphic $\simeq$ homotopy $\cong$ isomorphic Please correct me for the above.
1
vote
1answer
28 views

Representing a for loop with modulus in formal notation

I have the following section of code I am writing for research. Basically I need to formally represent the mathematical notation behind a set that follows: ...
0
votes
1answer
32 views

What is the meaning of the semicolon in $h(x;\theta)$?

The context is machine learning, and the full expression is $h(x;\theta) = \operatorname{sign}(\theta_1 x_1 + \cdots + \theta_d x_d)$. $x$ is a feature vector and $\theta$ parameterizes a set of ...
0
votes
1answer
20 views

Notation for the mean within a set of divided values multiplied by another value

This is my very first crack at notation and I'm very unsure about the results: With two sets with values: QTY: [4, 5, 5, m...], DOSE: [20, 10, 10, n...], and the number 30. The formula is: ((30 / ...
0
votes
2answers
39 views

Problem with symbology

I know this may be a pretty basic question, but what is the difference between $\approx , =,\cong, \text{and}\sim $ ? I had problem while changing schools and now I am confused.
2
votes
1answer
60 views

Hartshorne notation in Theorem 3.4

I have a nitpicky question about notation in Hartshorne's proof of his Theorem 3.4 in his AG book; in particular, it is in his proof of part (b). The point in contention is the line One checks ...
3
votes
1answer
84 views

Is this notation good for the chain rule derivative?

When we take this derivative, for example: $$y = \log(\sin x)$$ We call $u = \sin x$, so we have: $$\frac{dy}{dx} = \frac{d y}{du}\frac{du}{dx} = \frac{1}{u}\cos x = \frac{\cos x}{\sin x}$$ But for ...
0
votes
2answers
32 views

How to notate a vector out of a $\mathbb{R}^+$

Say you have a set $\mathbb{R}^+$, (in other words the positive real numbers), how can one express a vector with $n$ elements out of it? $\mathbb{R}^{+n}$ might by confusing and $\mathbb{R}^{n+}$ as ...
1
vote
3answers
48 views

Notation for limit approaching from above/below

Consider the equation $$f(x)=\frac{4x+8}{x-3}$$ It is known that $$\lim_{x \to \infty} f(x) = 4$$ from above and $$\lim_{x \to -\infty} f(x) = 4$$ from below. How do you write the "from above/below" ...
1
vote
2answers
33 views

Iterated self-composition of arbitrary function

Does there exist some notation that represents the iterative composition of a single-input, single-output function with itself? As in, say, $f_5(x)=f(f(f(f(f(x)))))$. In other words, going by the ...
0
votes
1answer
28 views

Should random variables be italic or roman ($X$ or $\mathrm X$)?

I just recently learned that it is good style to write constants like Euler's number $\mathrm e$ and also functions and operators in roman letters while reserving italic letters for variables. ...
2
votes
1answer
24 views

limit notation syntax validity

If you know $$\lim_{x \to \infty} f(x) = -\infty$$ and $$\lim_{x \to -\infty} f(x) = -\infty$$, is it valid syntax to write $$\lim_{x \to \pm \infty} f(x) = -\infty$$?
3
votes
1answer
46 views

Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?

Title says it all - is there an accepted mathematical way in matrix notation to show those operations on a matrix? Thanks.
2
votes
3answers
150 views

Summation Notation Confusion

I am unclear about what the following summation means given that $\lambda_i: \forall i \in \{1,2,\ldots n\}$: $\mu_{4:4} = \sum\limits_{i=1}^{4} \lambda_i + \mathop{\sum\sum}_{1\leq i_1 < i_2 \leq ...
0
votes
2answers
24 views

Standard notation for sum of vector elements?

I can think of multiple ways of writing the sum of a vector $\mathbf{v}$'s elements, but is there a standard operator for this? Using "programming" notation it is typically sum($v$), but this seems ...
-1
votes
1answer
44 views

Strange Integral Notation? [duplicate]

When reading about an certain algorithm (about parameter estimation for Kalman Filtering page 7 eq 57) I found this notation: $\int dx f(x)$ which is normally written as $\int f(x) dx$. I spent a ...
0
votes
1answer
88 views

What does $\mathbb{Z}_2$ mean?

Wich number space is ment by: $\mathbb{Z}_2$ (I know that $\mathbb{Z}$ stands for Integer)
3
votes
1answer
1k views

How do we pronounce this symbol?

I would like to know how to pronounce in english this symbol $\nabla \phi$ It is something phi ... ? thank you
3
votes
2answers
31 views

Big O-notation and series

While there are many questions regarding Big O-notation and in particular, its usage when it comes to series, none fit my question perfectly: possibly because I am so unfamiliar with the notation. ...
0
votes
0answers
62 views

What does $\dot{\mathbb{R}}$ mean?

I just run into a notation like this: $\dot{\mathbb{R}}$ $-$ any idea what could it mean? I have guesses, but I'd like to be sure. Thanks in advance! [I ran into this notation in the introductory ...
0
votes
0answers
23 views

What is the symbol ≙ most commonly used for in a mathematical or math-related context?

What is the symbol most commonly used for in a mathematical or math-related context? LaTeX produces the symbol with \hateq. ...
0
votes
0answers
28 views

'monotone in (x,y)' vs 'monotone in x and y'

What's the difference between function being 'monotone in (x,y)' and 'monotone in x and y'? Or they denote the same?
1
vote
0answers
23 views

Correct notation for variable substitution?

Is this notation conventional to indicate that $M$ should be replaced with 2? $$ \left. \frac{(D + M - 1)!}{(D - 1)!M!} \right|_{M = 2} $$
1
vote
0answers
36 views

problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\ $ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\ $ is ...
0
votes
1answer
22 views

Y-Coordinate of a Point - Notation

Given point $P$ on curve $\omega$, what expression is generally use to denote the $y$-coordinate of point $P$, also, the $x$-coordinate. Would it be $P_y$? Also, let $\omega$ be in $\mathbb{R}^2$, not ...
3
votes
0answers
73 views

A name for something like a CW complex?

The class $\mathcal{CW}_n$ of finite $n$-dimensional CW complexes can be defined recursively: $\mathcal{CW}_0$ consists of finite sets; If $X \in \mathcal{CW}_n$, $\phi:S^n \amalg \cdots \amalg S^n ...
2
votes
1answer
84 views

Which is the best notation for a sequence?

In a set, the order of its elements is (as far as I know) not important; in a sequence, the order of its elements is important. Which is the notation I should use in order to define a sequence? I ...
1
vote
2answers
71 views

Difference between limits $\infty$ and $+\infty$

Is there a difference between these two limits? $$\lim_{x\rightarrow\infty}f(x)=+\infty\text{ and }\lim_{x\rightarrow+\infty}f(x)=\infty$$
1
vote
1answer
52 views

Can someone explain this notation of a limit?

What is the explanation/motivation for this notation? tiontion $$\lim_{x\rightarrow a+0}f(x)$$ I understand it should be equivalent to this notation, which seems much more logical (and simpler): ...
1
vote
0answers
22 views

Notation for appending 2 submatrices

I have a matrix $M$ with $i$ rows and $(e+n)$ columns: $M_{i,e+n}$ I would like to express that $M_{i,e+n}$ is the result of appending $M_{i,e}$ and $M_{i,n}$ What is the algebraic notation to ...
1
vote
2answers
92 views

Can I use “: ,” instead of “, implies” for this example?

I've to write this statement in a formal manner: if $x>1$ then $x^{2}>1$. Writing the result of the exercise I face this problem, I wonder if these two statements are equivalent: ...
0
votes
0answers
50 views

Why is real part written first in complex numbers?

While expressing complex numbers as $a + \iota b$, is there a specific reason for writing the real part before the imaginary part? Who introduced this notation first? Is it a case where it just hung ...
1
vote
1answer
95 views

Notation: what is “arg min”

there is a function that says j=arg_min{ f(x),g(y) } What does that mean? As noted by the comment, arg_min(f(x)) is the x that gives smalles f. But what happens when arg_min takes two function, ...
1
vote
1answer
44 views

Strange notation for a decimal expansion of a transcendental number

I am checking page proofs for one of my papers right now and an editor changed $\zeta(3)=1.202$$\ldots$ to: $\zeta(3) = 1.202,...,$ I find this latter notation very strange and think it ...
0
votes
1answer
28 views

Notation: need help to understand the notation in the following formula

E is just a function such that E1=1, E2=2 and so on. But my question is the part of on "arg" and "min". 1) so "arg" stands for the angle of complex number? this doesn't make any sense. 2)If I ...
5
votes
1answer
73 views

Intuition for Integration of Differential Forms

In mathematics, we define $dx^i$ as linear functionals, when speaking of integration. However, in physics, we interpret $dx^i$ as very small quantities. There is nothing inherently small about a ...
0
votes
0answers
11 views

Coordinatewise vector operation notation

I have seen questions on Math.SE what is the typical notation for coordinatewise vector multiplication (Hadamard product), but I haven't found an answer to case of exponentiation. Given a vector ...