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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3
votes
0answers
96 views

What “double bracket” means? [duplicate]

What does this symbol mean? Please i need help: Its the symbol just before "$H^{t-1}$". Thanks for help
1
vote
4answers
4k views

What is the double bracket notation used here?

Its kind of a bracket but I'm not sure what it means. I have two ideas about it: It means the number of times the expression in satisfied or it changes for $1$ or $0$ depending on the result every ...
6
votes
4answers
753 views

Notation: What does this summation mean?

I need to understand what the summation below mean. I specifically do not understand the $i<j$ below the summation. $$\sum_{\substack{ i<j}}^{N} d_{ij}$$ Insight about the equation There ...
0
votes
2answers
68 views

Notation for where two variables cannot both simultaneously take a specific value

I am building a set of values A, containing coordinates ($B_{x,y}$), where $x$ and $y$ take any of the following values: $x$ := {-2,-1,0,1,2} and $y$ := {-1,0,1} The catch is that both $x$ and $y$ ...
2
votes
1answer
63 views

Mathematical notation for redefined set?

I have a set of numbers (W), from which I am only keeping those greater than 5. I want to state that the set W has been redefined to only include the subset of values greater than 5, but want to ...
1
vote
2answers
395 views

Random math questions (modular arithmetic & notation)

I found this amazing wall clock picture on the internet but I really don't know a few things. I don't know what's $B'_L$, &#x33;, why $2^{-1}\equiv 4[7]$ and ...
2
votes
1answer
75 views

Is there a symbol for a repeated logical and operation?

For example, given a predicate $P$ and a set of variables: $\{x_1,x_2,x_3,x_4,...\}$, is there a single symbol similar to $\sum_{k=1}^n$ or $\bigcap_{k=1}^n$ to denote the following? $$P(x_1)\land{P}(...
5
votes
1answer
86 views

The use of = vs := for definitions

I have seen the following conventions, e.g. We define $K=\mathbb C$ ... We define $K$ to be $\mathbb C$ ... We define $K:=\mathbb C$ ... I prefer number 3, because it is concise and it is clear ...
1
vote
2answers
148 views

How to denote $\underbrace{(1+n(1+n(1+\cdots)))}_{x-1 \text{times}}$ in a single expression?

I learnt that, $$ n + n^2 + n^3 + n^4 +. . . + n^x = n\underbrace{(1+n(1+n(1+\cdots)))}_{x-1 \text{times}} $$ So,I want to denote RHS in a single expression.
0
votes
1answer
176 views

Notation in Geometry

I have this problem to solve: The translation is: Been the next angles: $\angle ABC$, $\angle DEF$ and $\angle GHI$, if $\angle ABC$ is "Parallel?" to $\angle DEF$ and $\angle GHI$ is parallel (...
1
vote
0answers
148 views

What is the difference between black and white square in notation?

I'm reading a book on description logic and I found white and black squares at the end of some paragraphs. I would think they stand for Q.E.D., but since there are two types used in one book, I ...
2
votes
0answers
47 views

Notation Problem

I'm reading a paper that uses the notation $[f]^+_-$ for a function f. Anyone know that this means? More explicitly it appears as $$ \frac{1}{{[U_0]}^+_-} \int^{\infty}_{-\infty}U_{0z}^2 \, \mathrm{...
2
votes
1answer
51 views

$O_{\mathcal{S}'\rightarrow \mathcal{S}}(h^\infty)$

What does the notation: $$O_{\mathcal{S}'\rightarrow \mathcal{S}}(h^\infty)$$ mean in Zworski's semiclassical analysis? (To be clear, I know what $O(h^\infty)$ means in the context of normed and ...
2
votes
3answers
2k views

Why is the Jacobian matrix the transpose of what I would think it'd be/usefully be (total derivative is a synonym) (EDIT: I was a total wally)

I'm sorry this isn't a yes/no/am-I-right question but I seriously cannot see why the Jacobian/total derivative matrix is what it is? I am also using it as LaTeX practice (for maths) hence the barely ...
2
votes
2answers
75 views

Acceptable to write $\sup\,\{f(x) \mid x \in \mathbb R\}$ as $\sup\,\{f(x)\}_{x \in \mathbb R}$?

Is it acceptable to write $\sup\,\{f(x) \mid x \in \mathbb R\}$ (where $f\colon \mathbb R \to \mathbb R$) as $\sup\,\{f(x)\}_{x \in \mathbb R}$? I have seen it written as $\sup\limits_{x \in \mathbb R}...
4
votes
2answers
267 views

Symbols: If but not only if

I was searching for a Latex symbol that indicates $A \Rightarrow B$ and $A \not\Leftarrow B$ ($B$ if not only if $A$, $B$ ifnf $A$). I thought of using $A \Leftrightarrow B$ with the left arrow tick <...
5
votes
5answers
5k views

What is the standard notation to represent the set of primes?

I have seen $\mathbb Z_p$. Are there others, perhaps $\mathbb N_p$? or the set of natural numbers where the totient of $ n $ equal $ n - 1 $ ? $$ \{n \in \mathbb N \mid n\ge2,\phi (n) = n-1\}$$
1
vote
0answers
140 views

Question On Modulo Notation

I understand what the Modulo/Modulus is and how it operates and everything, but a textbook is using some notation that I just can't quite grasp. Basically, we have the solution $(x,y) = (\pi($mod$(2\...
-1
votes
2answers
255 views

Notation for the set of real numbers

I've seen R used for the set of reals, and also a hollow R, but I seem to remember an elegant copperplate cursive R. Is this correct? Can I use this R? Handwritten, going cursive seems to be clearer. ...
8
votes
1answer
120 views

Notation: “$+$” exponent sign

I'm following this paper and came across some notation that I don't know; I've tried a number of queries such as "power to the plus", "plus exponent" etc but can't seem to find anything: From page 4: ...
2
votes
3answers
360 views

Set notation confusion (Empty Sets)

Could anyone explain the difference between the following: $\varnothing$ $\begin{Bmatrix} \varnothing \end{Bmatrix}$ $\begin{Bmatrix} \varnothing & \begin{Bmatrix} \varnothing \end{Bmatrix} \...
3
votes
1answer
78 views

What is this expression?

I saw this nice relief on the University of Warsaw's library building, but I'm left wondering what the line beneath $\pi$ and above Collatz is saying. I'm not familiar with the arrow notation. Can ...
2
votes
0answers
79 views

Why write $\mathrm dx, \mathrm dt$ etc. at the beginning of an integral? [duplicate]

I've noticed that many people here (on Math.SE) as well as elsewhere write integrals out like this: $$\int^a_b \mathrm dt \; f(t)$$ instead of the more common (at least from what I've seen): $$\int^...
6
votes
5answers
2k views

What character can replace word “let” in proofs?

For example, suppose I have a line of a proof introducing new “variable” $x$: $$\textrm{Let}\:\:x\in f(y)$$ I am looking for ways to express the word “let” in this context and ...
0
votes
2answers
304 views

What is this problema asking for? I don't understand the question. (set notation, composite relations)

In the following problem, what does the "circle" between set names represent? What exactly is this problem asking me to do? Consider the following relations on Z: $R1 = \{(x, y) | y = x + 1\}$ $...
10
votes
0answers
199 views

Origin of $\mapsto$ notation

Who invented the brilliant $\mapsto$ notation for describing a function's action on a point, as in $x \mapsto x^2$? This is in some sense a counterpart to Who came up with the arrow notation $x \...
2
votes
1answer
308 views

Name for collection of sets whose intersection is empty but where sets are not necessarily pairwise disjoint

According to Wolfram MathWorld, a collection of sets $A_1, A_2, \ldots, A_n$ is said to be disjoint if $A_i \cap A_j = \emptyset$ for all $i \ne j$. In other words, 'disjoint' refers only to 'pairwise ...
3
votes
4answers
158 views

What is the meaning of $(2n)!$

I came across something that confused me $$(2n)!=?$$ What does this mean: $$2!n!, \quad 2(n!)$$ or $$(2n)!=(2n)(2n-1)(2n-2)...n...(n-1)(n-2)...1$$ Which one is right? The exercise is to show that $...
7
votes
2answers
159 views

Unsure about a maths symbol

Help, help, help! I've come across this maths symbol, $[n(i,j)]^{0.5}$ where $n$ is a square matrix. Does this mean that it is the $(i,j)$ element of $n^{0.5}$? or $n(i,j)^{0.5}$? source: http://...
0
votes
1answer
73 views

Are functions which say $X$ onto $Y$ mean the function is surjective?

Throughout my reading I've encountered theorems which use certain wording, which is unclear at times. For example, consider the following corollary taken out of Intro to Topology by Mendelson, Let $X$...
1
vote
0answers
55 views

Function Definitions that Appear Circular

There are many instances where definitions of functions appear self-referential, but are in fact consistent and well-defined. Here are a couple cases: The proof of the existence of a maximal ...
2
votes
1answer
113 views

A few basic questions about the arithmetical hierarchy, mostly about terminology.

I was reading about the arithmetical hierarchy, and I have a few questions, mostly notational. For completeness, here's the definition given over at Wikipedia. The classifications $\Sigma_n$ and $\...
2
votes
1answer
66 views

Help with ambiguous notation

I am reading Probabilistic and Graphical Models, and uncertain about the meaning of the following use of the notation $\mathbf{I}$. The textbook defines the use of $\mathbf{I}$ to mean flow of ...
17
votes
3answers
25k views

Is there an accepted symbol for irrational numbers?

$\mathbb Q$ is used to represent rational numbers. $\mathbb R$ is used to represent reals. Is there a symbol or convention that represents irrationals. Possibly $\mathbb R - \mathbb Q$?
2
votes
3answers
75 views

Notation for definition and equivalence

I would like some clarification about the usage/meaning of $:=$ and $\equiv$. I have been using $A := B$ to denote "Let $A$ be defined as $B$." This is akin to assignment ...
1
vote
2answers
279 views

Notation for function $ + \rightarrow \times $

Is there a standard notation to represent the function building the multiplication from the addition (I'm talking of the usual $+$ on $\Bbb N$)? I'm tempted by: $$ x \times y = + ^ y (x) $$ With ...
0
votes
1answer
363 views

Is there a standard notation for the set of negative integers and zero?

There is $\mathbb Z^-$, $\mathbb Z^*$, $\mathbb Z^+$. There does not seem to be a notation for negative integers and zero.
1
vote
1answer
115 views

Notation in propositional logic

If in propositional logic one is trying to simplify a formula by evaluating its subformula, would it be considered an abuse of notation to actually substitute the bits $\{0,1\}$ in for the formula, to ...
1
vote
2answers
132 views

What does $R_{0}^{+}$ mean?

I'm reading this paper: http://www.aaai.org/Papers/KDD/1996/KDD96-027.pdf, and the authors used the symbol $R_{0}^{+}$ in the definition of Exact Exception Problem, such as $D: P(I) \rightarrow R_{0}^{...
2
votes
2answers
438 views

Is this notation for the set of limit points a standard notation?

Well, this doubt is probably silly. We have a standard notation for closure of a set $E$, we denote it $\bar{E}$ or $\operatorname{cl}{E}$ and we have a notation for the interior of a set $E$ we ...
1
vote
1answer
215 views

A name for set of disjoint intervals

What's in a name? That which we call a rose by any other name would smell as sweet. William Shakespeare I'm looking for a short name for the phenomenon collection of disjoint intervals. I ...
7
votes
1answer
484 views

On the pronunciation of the second derivative

I have been looking at Lancelot Hogben's Mathematics for the Million (first published in 1936). In the chapter on calculus he says that the second derivative $\displaystyle \frac{d^2y}{dx^2}$ is ...
0
votes
1answer
53 views

Notation question arising from physical problem

I'm a physicist and am a bit confused about the notation in one of the computations here: Let $S = S(U,V,N)$ be a real valued scalar function, and $z = (U,V,N)$. Let $\lambda \in \mathbb{R}$. Given ...
1
vote
1answer
31 views

How would you explicitly define the number type of a function's parameters?

Say I make a function $f$ that takes a parameter $a$, but I want to make sure that $a$ can only be $\mathbb{N}$, no $\mathbb{Z}$ or $\mathbb{R}$ allowed (as an example), how would I write that in a ...
3
votes
1answer
833 views

What does the following symbol mean? (direct sum? o-plus? — subject: matrix theory)

In this paper equation 11, the author uses a symbol that is a cross in a circle. I believe I have seen that referred to as a direct sum, but I am not completely sure what that is. $$\bigoplus$$ ...
3
votes
2answers
2k views

Proper Notation for Lines in Geometry

If a line is simply named with a single letter, say for example $k$, is it incorrect to refer to this line as $\overleftrightarrow k$?
3
votes
6answers
303 views

What is $a$ in $F(x)=\int_a^xf(t)\,dt$?

I often see things like $$ F(x)=\int_a^xf(t)\,dt. $$ What is $a$? Is its value important? I ask this because I often get the feeling that $a$ could be any constant. I also see $a$ sometimes be ...
2
votes
2answers
103 views

What is the notation of 'a single term in the DFT'

I have a notation/terminology question: I am writing a paper in not-quite-my-area and can't figure out the right way to phrase/notate the following: I have a discrete function $p[x]$, of which I can ...
2
votes
2answers
93 views

When to use $\{a_i\}_{i\in I}$ and when $(a_i)_{i\in I}$?

I was wondering: are $\{a_i\}_{i\in I}$ and $(a_i)_{i\in I}$ simply different notations for the different (?) sets/lists $\{a_1, a_2, \ldots, a_I\}$ and $(a_1, a_2, \ldots, a_I)$, ...
2
votes
1answer
69 views

What does $f \in L^p(I,V) + L^q(I,H)$ mean?

What does $f \in L^p(I,V) + L^q(I,H)$ mean? What does the addition mean?? I see this in PDE theory.