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
0answers
36 views

Do we need parenthesis in lim?

Is  $\lim_{x\to 0} x+x^2=(\lim_{x\to 0} x)+x^2=0+x^2=x^2$ or $\lim_{x\to 0} x+x^2=\lim_{x\to 0} (x+x^2)=0+0^2=0$?
10
votes
1answer
156 views

Is there a reason for different nomenclature on Calculus of Variations?

While sightseeing aspects of Calculus of Variations, the following fact elludes me: there is a plethora of new definitions which seem redundant to me. This phenomenom happens, of course, with other ...
14
votes
1answer
856 views

What does this joke mean?

I saw this written on a blackboard in the math department building the other day: Gas Law: $PV=nRT$ Ideal Gas Law: $(P)(V)=(n)(R)(T)$ I know the ideal gas law is something from chemistry, but I'm ...
0
votes
0answers
37 views

Is the Period Symbol (.) Ever Used as an Operator

Are there any cases in which x.y (where x and y are both integers) would produce some kind ...
0
votes
1answer
28 views

Two-sigma notation k-means clustering

I have referred to this question: Two sigma notation, to get an understanding of how two-sigma notation works. But this is insufficient for my purposes. I am looking at a k-means clustering ...
39
votes
11answers
4k views

Does “Doing a thing to both sides of an equation” have a name?

A two part question. 1 True or False: when working with an equation or inequality, everything that you do is either: a substitution, or an operation performed on each side Note that algebraic or ...
1
vote
0answers
14 views

Notation for an expression that is true for modular arguments

I am trying to write clearly and compactly that a certain coefficient, with indices $k_1$ and $k_3$ is null unless both $k_1$ AND $k_3$ are integer multiples of the integer variable $s$. Right now I ...
1
vote
1answer
28 views

Concise way of writing $f:\mathbb{Z}\to\mathbb{Z}$ defined by $x\mapsto 2x$

I would normally see a function like this written as $f:\mathbb{Z}\to\mathbb{Z}$ $x\mapsto 2x$ or as $f:\mathbb{Z}\to\mathbb{Z}$ defined by $f(x)=2x$. Is it 'correct' (or at least, standard) to ...
1
vote
1answer
81 views

Does $\sqsubset$ have any special meaning?

What is the meaning of $\sqsubset$ and $\sqsubseteq$? Does it have any special meaning, or is it just an alternative to writing $\subset$ and $\subseteq$ respectively (for proper subsets and subsets)? ...
2
votes
1answer
16 views

Algebraic Riccati equation (DARE) stabilazability condition

I'm Trying to help in this question which involves Algebraic Ricatti equation. Honestly to say I never met this equation before. I'm struggling to understand the conditions stated in the limitations ...
0
votes
1answer
38 views

Can anyone explain relation between <> and ⌊⌋ symbols (in probability theory?)?

I see this: $\left<nx\right> = nx - ⌊xn⌋$ in one of my exercise solutions for probability theory class. I found on wikipedia that <> means average and ⌊⌋ means greatest integer with the ...
6
votes
2answers
113 views

Does $\infty$ mean $+\infty$ in “English mathematics”

My question background is the set $\mathbb R$. I often see the symbol $\infty$. Does it always mean $+\infty$ or can it has the meaning of $\pm \infty$? In particular what means that a real sequence ...
0
votes
0answers
76 views

Where does the $\int$ sign come from?

I've heard that the symbol derives from a big "S" for sum, but I'm a bit skeptical. Where did the notation come from?
2
votes
4answers
103 views

Is $(f \circ g)(x) = g(f(x))$ Common in Group Theory?

In the text Group Theory and the Rubik’s Cube by Janet Chen, definition 1.11. on page $4$ says If $f:S_1 \to S_2$ and $g:S_2 \to S_3$, then we can define a new function $f\circ g: S_1 \to S_3$ as ...
0
votes
0answers
9 views

Notation for iterative application of a function with two arguments

I have a function $f: X \times 2^C \rightarrow 2^C$. I was wondering how I would be able to show this function being applied iteratively over a sequence of elements $X_s$. For example, assuming I had ...
0
votes
2answers
107 views

Are the following sets exactly the same: $\mathbb{N}$, $\mathbb{N_{-\{0\}}}$, $\mathbb{N^+}$ and $\mathbb{Z^+}$?

At university, my Maths Analysis lecturer said that this is still debated nowadays. For example, a definition of an rational number is $\cfrac{p}{q}$ where $p\in \mathbb{Z}$ and $q\in \mathbb{N}$ (or ...
-1
votes
1answer
21 views

I know how to solve equations of $t$, but I'm not sure what $t'$ represents in this equation????

I am investigating the Wilson Cowan neuron population model, and I can follow most of it, but I'm not sure what is meant by $t'$ in the equation for proportion of neurons in the refractory period. ...
0
votes
2answers
67 views

Is there any difference in mathematical notations between French and English?

I studied Mathematics mainly in French and now I am going to write research articles in English. I would like to know if there are some important differences in mathematical notations between French ...
-2
votes
3answers
60 views

Notation in set thory. [closed]

Will someone please describe the following set in words.
1
vote
0answers
33 views

Einstein notation - Diagonal matrix

This may be very easy, but I'm not seeing it. I am using Einstein notation to write a proof of a theorem in classical mechanics. I have a $3\times 3$ matrix $I$. After a diagonalisation process I ...
0
votes
1answer
37 views

Is it ok to make an operation over some definition at very the first time you are defining it?

Suppose we have an expression and want refer to it with some symbol. Usually one can write something like "$X:= \text{Expression}$" to mean the symbol $X$ is defined to be the expression after the ...
0
votes
1answer
28 views

Terminology request: operations on graph adjacency matrices

I have a physics/computer science background. I'm writing up some research, and I keep hesitating and second-guessing myself when it comes to the formal definitions. I would like to settle my mind and ...
2
votes
3answers
43 views

Notational Definition: $A \subset B$

Suppose $A$ and $B$ are two sets and suppose $A \subset B$, then from the definition of subset, it implicitly follows that $A$ might also be equal to $B$. Then why do we need $A \subseteq B$ where we ...
3
votes
2answers
43 views

Understanding mathematical notation for coding problems.

The majority of my questions revolve around code (thus my activity on stackoverflow), but I've been going over interview question that assume a good understanding of mathematical notation. I don't ...
1
vote
1answer
40 views

Evaluation of a Christoffel Symbol

I am a bit confused on the notation for a certain evaluation of a Christoffel symbol. In particular, I am confused about the following formula: $$\Gamma_{ij}^k = \frac{1}{2}g^{kl}(\partial_i g_{jl} - ...
0
votes
1answer
23 views

Closed form expressions for a sum

I was given a sum s, then I expressed it using sigma notation as you can see below. Now, I am supposed to find the closed form values for the said sum as shown in eq.2, but I am stuck at eq.1. I don't ...
1
vote
1answer
21 views

What is the proper notation for the “average of the last N elements of a sequence”?

I use sliding window average in my calculations: average for the last N elements and average for the N elements before that. What would be the correct mathematical notation to describe this?
3
votes
1answer
99 views

What does algebra $A \rtimes G$ stand for?

Let $k$ be an algebraically closed field, $A$ a finite dimensional (unital associative) $k$-algebra of finite dimension, and $G$ a torus over $k$ acting on $A$. What does $k$-algebra $A \rtimes G$ ...
0
votes
1answer
22 views

Meaning of commas in set notation

Let $X=\{ x\in X: x \text{ satisfies condition } A, x \text{ satisfies condition } B\}$. Does the comma in above set notation mean that $x$ has to statisfy $A$ and $B$ at the same time or only one of ...
1
vote
1answer
44 views

Relationship among the function spaces $C_c^\infty(\Omega)$, $C_c^\infty(\overline{\Omega})$ and $C_c^\infty(\Bbb{R}^d)$

I have seen the spaces $C_c^\infty(\Omega)$, $C_c^\infty(\overline{\Omega})$ and $C_c^\infty(\Bbb{R}^d)$ a lot in theorems regarding PDE where $\Omega$ denotes some open subset of $\Bbb{R}^d$. There ...
1
vote
1answer
44 views

What does the gradient of the gradient ($\nabla\nabla u$) mean?

For a scalar function $u$ defined on $\mathbb{R}^n$ we have this equality: $$\nabla(|\nabla u|^{p-2})=(p-2)|\nabla u|^{p-4}\nabla u\nabla\nabla u$$ My question is : what does $\nabla\nabla u$ mean? I ...
0
votes
2answers
43 views

What is the term for an asterisk in combination with a variable?

This question could likely be phrased better, but I'm not sure how to better describe it. In calculus, when studying sigma notation, especially with Riemann sums, you often see something like this: ...
1
vote
1answer
28 views

Notation in infinite sums and infinite unions, some questions

Yesterday I see this expression: $$(a, b)= \bigcup_{n=1}^\infty [a + 1/n, b - 1/n]$$ The first thing that I thought was "why this expression represent an open interval and not a closed one?" Then I ...
0
votes
1answer
23 views

How do I interpret this notation systems of diff eq course I'm taking?

I'm a college sophomore taking differential equations and I'm having trouble understanding the notation in the part of the course involving systems of differential equations. All the notation for the ...
0
votes
1answer
27 views

Writing a function of many variables as a function of a vector?

I have a function that looks like this $$f(x,y,z_1,z_2,z_3,\dots ,z_k) \tag{1}$$ and I figured I could write it compactly as $$f'(x,y,Z) \tag{2}$$ where $Z = [z_1,z_2,z_3,\dots,z_k]$, and $f'$ denotes ...
1
vote
1answer
33 views

Need help interpreting this symbol

I came across this symbol while reading about number theory what does it mean? Thanks for any help.
0
votes
1answer
47 views

Null Set Symbol [closed]

My professor pitched me a problem like so, 2∅(25) mod 25 ≡ ? The answer is 1. However, after much browsing of the internet, I couldn't find anything to justify this answer. I was wondering exactly ...
0
votes
0answers
18 views

Terminology and Notation: “Sphere” in a Metric Sapce

I see sphere used interchangeably with "ball" in the sense of "open ball", "closed ball", with notation like $B_r(x), B_r[x]$. I also see sphere used to refer to the boundary of a closed ball, e.g. ...
0
votes
4answers
40 views

What exactly is this equation?

Thank you for assistance, I'm just having issues remembering what this is called? For example, the equation would go like this |x+1| = 4 What is this type of equation called, with the two | | ? ...
1
vote
2answers
31 views

If $E$ and $F$ are field, what is $E\vee F$?

If $E$ and $F$ are field, what is $E\vee F$ ? Let take for exemple $E=\mathbb Q(a)$ and $\mathbb Q(b)$. Do we have $$E\vee F=\mathbb Q(a,b) \ \ ?$$
2
votes
11answers
210 views

Why is $e$ the number that it is? [closed]

Why is $e$ the number that it is? Most of the irrational number that we learn about in school have something to do with geometry, like $\pi$ is the ratio of a circle's diameter to its circumference. ...
1
vote
1answer
30 views

What does the hat symbol mean with reference to an undirected graph?

If I have a graph called $G$, what does $\widehat{G}$ mean? Is it a reference to a subgraph of $G$? Here is the full statement, for clarity. "Let $x_i$ be an endpoint of edge $e_i$ (in graph ...
0
votes
2answers
53 views

Notation with a colon that looks like set notation - what is it?

I've come across this notation in a task, it says: $f(x)=\sin^{-1}x$ and $g(x)=\cos^{-1}x$. Show that $$\lbrace{x : \cos^{-1}x = \sin^{-1}x}\rbrace = \lbrace x : x= \sqrt{1-x^2} \rbrace$$ . I have ...
0
votes
2answers
55 views

What is the mathematical notation for Convex Hull?

I've been scanning through scientific papers, this site and just googling for it, but I can't find a commonly accepted notation for the convex hull. So my question is; if there is, what is the ...
0
votes
1answer
15 views

Notation confusion for joint pdf expected value

I have a pdf for continuous random variables $X$ and $Y$ such that $f_{xy}(x,y) = 2(x+y)$ for all $0<x<y<1$ and $0$ elsewhere I'm not sure how to break up the inequality to determine my ...
2
votes
2answers
51 views

How to write “There is v in set W and P, such that v is in set P”?

How to write "There is v in set W and P, such that v is in P"? I thought of the following possibilities: ∃ v ∈ W : ( ∃ P : v ∈ P) or ...
1
vote
0answers
27 views

What does the notation $f(x) = max (1-t \mid, 0)$ mean?

I don't understand that vertical bar?
0
votes
1answer
46 views

Why do we use a single 'dash' for difference : $-$ and a double 'dash' for sum: $+$? [closed]

Why do we use a single 'dash' for difference : $-$ and a double 'dash' for sum: $+$? Just a shower thought: Who came up with this notation? It kind of makes it look like the difference is simpler ...
0
votes
0answers
40 views

Is there a standard notation for the sets of incoming and outgoing edges from a vertex?

I'm writing up an algorithm involving some graph theory and am looking for a standard way of denoting the set of incoming and outgoing edges from a vertex. If my vertex is called $v$ and graph is $G$, ...
2
votes
1answer
30 views

Quotient Space Notation

Quick question, mostly just for my knowledge, but I'm working on a problem: Determine whether the indicated set $A$ is an ideal in the indicated ring $R$: $$A = \{0,2,4,6,8\},~~R = ...