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

-2
votes
1answer
72 views

What's the meaning of $o(x^2)$? [closed]

What is the meaning of $o(x^2)\;$? Thank you.
3
votes
1answer
53 views

Is there a standard notation for building sets up form a given one?

In ZFC each set $S$ has a well-founded membership tree building $S$ up from the empty set $\emptyset$. You could attach the membership tree for any given set $A$ on each of the bottom nodes for the ...
6
votes
2answers
102 views

The meaning of notation like $f\colon \mathbb R^2 \to \mathbb R$, $x \in \mathbb R^n$, and $x \in \mathbb R$.

I am in second year university and am taking linear algebra this semester. Never having been a strong maths student, I am certainly struggling with some basic concepts and especially notation. I ...
0
votes
1answer
33 views

Meaning of function mapping notation $d: X \times X \to \mathscr{R}$

I am trying to do some self-studying and am consistently getting bogged down by sophisticated mathematical notation. For example, something simple like this in a book: Let $X$ be a non empty set and ...
3
votes
3answers
140 views

What is the difference between $\delta$ and $\Delta$? [closed]

Is there any difference between $\delta$ and $\Delta$? If there is one, is it a mistake to use one instead of the other? Update: I was not aware that symbols may have different meaning/usage in ...
0
votes
0answers
39 views

notation - minimum number and at least

How can I represent this formally: The Graph of Interest (GOI) of a graph G is a subgraph of G which contains the minimum number of nodes that is sufficient to get the top-k nodes. In other words, ...
3
votes
4answers
166 views

Partial derivative notation

I still have a little problem with notation for partial derivatives. Let $$ f(x,y) = x^2y $$ What do you this that this should equal to? $$ \frac{\partial f}{\partial x}(y,x) =\, ? $$ There are two ...
2
votes
1answer
31 views

Integrals in Index Notation and Orientation

I am wondering what is the correct way to write integrals in index notation. At first I thought $$\int_M f \varepsilon_{ij}$$ would be the index equivalent of $$ \int_M f dx \wedge dy $$ but I started ...
3
votes
1answer
105 views

How can I convert $A =$ {$c > 1$ : there exists a natural number $m$ … to mathematical notation?

In this post A = {c > 1 : there exists a natural number m, such that for every n > m, there is a prime between n and cn}. Now I don't want to discuss on the problem itself, but only on how to write ...
1
vote
0answers
36 views

Precedence table for mathematical symbols (like in programming languages, e.g. C/C++)

I want to write long expressions which include the common "standard" math symbols like $\in$, $<$, $\forall$, $+$, $\cdot$, $\land$, $\lor$, $\Rightarrow$, $\sum$, ... Only for $+$ and $\cdot$, I ...
0
votes
1answer
38 views

A basic notational doubt

I have seen the following notation in a book for the continuous function $f$: $f(.,.):\Bbb R^d \times \Bbb R^d \to \Bbb R$ is uniformly continuous in the first argument on compacts w.r.t the second ...
1
vote
1answer
31 views

Row-wise non zero product in matrix notation

If I have a matrix $\mathbf{A}\in R^{m\times n}$, I'd like to express in matrix notation (or at least in a good mathematical notation) the vector $\mathbf{z}\in R^{m}$ whose $i$-th component is the ...
2
votes
1answer
50 views

Notation for the number of times one element divides another.

Let $R$ denote a commutative ring with unity. Consider elements $a,b \in R$. Is there an accepted notation (like $a \| b$ or some such) for the number of times that $a$ divides $b$? Explicitly, we can ...
3
votes
1answer
65 views

Where f is a function, does $f ab = f(a)b~ \text{or}~ f(ab)$?

I know $\sin ab = \sin(ab)$, but does this apply to other functions?
0
votes
3answers
53 views

Sum with three notations around it.

Have seen the below notation (How to calculate number of triangles and points after dividing a triangle n times?) and need to break it down into plain english so to speak. This just so I can catch up. ...
0
votes
1answer
70 views

What is the meaning of the $\phi$ symbol in calculus?

My textbook shows the following step.. $$\large{F_{T}(t) = \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi}}e^{\frac{-y^{2}}{2}} \left(\int_{-\infty}^{t|y|} \frac{1}{\sqrt{2 \pi}}e^{\frac{-x^{2}}{2}} dx ...
0
votes
2answers
46 views

Events $A_n\uparrow A$ meaning. $A_n\downarrow A$ meaning.

i simply do not understand the arrows in this context! :\
4
votes
1answer
43 views

How to denote sum over partitions?

How does one denote a sum of partitions of an integer when writing an article? For example, I have a formula regarding an integer-valued variable (say q=5), and I need to write an expression of the ...
0
votes
0answers
54 views

Well-formed formulas: Difference between $\forall x(x \in A \implies x \in B)$ and $(\forall x \in A) x \in B$? [duplicate]

Let $A$ and $B$ be sets. There seem to be two ways of writing $A \subseteq B$: \begin{equation} \forall x(x \in A \implies x \in B) \end{equation} or \begin{equation} (\forall x \in A) x \in B ...
3
votes
1answer
185 views

Confusing notation $D(p)(x)$ in a vector space of polynomials

If we have a vector space that consists of all polynomials of degree less than or equal to 4, and we consider the following function: $$D(p)(x) = 2.5\cdot p(x-1)$$ where $p$ is a function from the ...
2
votes
2answers
83 views

What is $\rightarrowtail$ used for?

I have come across this symbol many times, but I am unsure as to how to correctly use it. So I can read up on it, what is the name of this mapping function? When would it be correct to use and when ...
29
votes
11answers
2k views

What is a function?

I have been quite confused by the definition of functions and their uses.. First of all can one define functions in a clear understandable way, with a clear explanation of their uses, how they work ...
1
vote
0answers
36 views

Consistent notation in multivariate statistics

I'm reading The Elements of Statistical Learning. In the process I found myself lost in the notation, so I'm trying to get one that's as explicit and pedantic as possible: $X$, $Y$: continous random ...
1
vote
2answers
34 views

Define what it means for $\langle A,R\rangle$ to be a wellordering

The definition of a wellordering is as follows: If $\prec$ is a partial ordering of a set $X$. $(X,\prec)$ is a wellordering if (i) it is a strict total ordering and (ii) for any subset ...
1
vote
2answers
102 views

Symbol for zero element

Is there a symbol used for an element which a function sends to zero? Like this: $f(?) = 0$, where "$?$" would be the symbol for which I am wondering if exists. I think this could be useful for ...
0
votes
0answers
32 views

Writing $a\leq x,y\leq b$ instead of $a\leq x\leq b\land a\leq y\leq b$

If you have some function that has a restricted domain, e.g. $c(x,y)=x+y,\ \ \ \ x \in \mathbb{Z}, y \in \mathbb{Z} \text{ for}\ 1 \leq x \leq 3 \text{ and}\ \ 1 \leq y \leq 3$ then $c(x,y)$ can ...
-1
votes
1answer
98 views

what does this symbol mean (like a perpendicular symbol, in set theory) [closed]

Sent from my phone so have pity on me (long train journey) Azriel Levy basic set theory, Dover, p13 What does the symbol after the P* mean in 4.5? Will edit in picture. Mobile mode doesn't have it. ...
1
vote
0answers
17 views

Compact notation for block diagonal matrices?

Is there a more compact notation for representing a block-diagonal matrix than $\left[\begin{array}{cccc} \mathbf{W}_1 & 0 & ... & 0\\ 0 & \mathbf{W}_2 & ... & 0\\ 0 & 0 ...
1
vote
2answers
62 views

What may be meant by the $\wedge$ here?

I am dealing with article Two Moments suffice for Poisson Approximations: The Chen-Stein Method by Arratia, Goldstein and Gordon. On page 11 there is an expression with a $\wedge$ appearing in it: ...
1
vote
0answers
47 views

Confusion in a Mathematics Symbol

I fail to understand what a certain symbol means, please explain. It is in my permutation and combination chapter and it is for arrangements of 7 digits where something repeats thrice and something ...
0
votes
2answers
92 views

The usage of notation $\lim a_n = 1^+$ for “$a_n$ approaches $1$ from above”

I have a seemingly trivial problem that I cannot seem to figure out. Imagine I want to prove that the series of $n$ does not converge, and for that I use the d'Alembert rule (yes it's ridiculous ...
3
votes
1answer
29 views

Single Preceding Vertical Bar

I'm trying to implement the NIST test suite for (p)RNGs (http://csrc.nist.gov/groups/ST/toolkit/rng/documents/SP800-22rev1a.pdf), however I've very quickly run into some notation I'm not familiar ...
0
votes
1answer
30 views

Notation from predicate transformer semantics textbook

I'm reading my professor's text book on predicate transformer semantics (an extension of Floyd-Hoare logic) and I stumbled upon the following notation, in this case describing a solution to the ...
4
votes
5answers
174 views

Is there a symbol for integrating and setting $C=0$?

Too often it's useful to just set $C$ to $0$ after integrating, so I was wondering if there is a symbol for that? Formally this would mean a shorter way of writing: $\int_{t_0}^x f(t)\,\mathrm{d}t = ...
1
vote
2answers
89 views

More rigorous notation than “ellipsis” for “and so forth?”

So I understand that in general, ellipsis are used in math where the pattern is easy enough to discern that it is up to the reader to understand what is meant by it. However, for such cases, I was ...
1
vote
1answer
57 views

Understanding a theorem of Saint-Donat

In his thesis on K3 surfaces Saint-Donat proves the following fact (thm 6.1) Let $L$ be a line bundle on a K3 surface $X$ such that the linear system $|L|$ has no fixed components and the morphism ...
4
votes
0answers
78 views

Why do some authors write dx after integral sign? [duplicate]

Much has been said of the $dx$ notation used for integration on this site, but some writers of mathematics papers (especially physicists), write integrals as $$ \int dxf(x) $$ For instance, one way ...
1
vote
1answer
20 views

Origin of min/max notation

Here I am referring to the notation $x \wedge y = \min \{ x,y \}$ and $x \vee y = \max \{ x,y \}$. These seem to reference the corresponding usages in logic, where $\wedge$ means "and" and $\vee$ ...
1
vote
1answer
52 views

Strange Sigma Notation

How do I interpret this form of sigma notation? Do e1 and e2 take on all combinations of 1 and -1? If they do, what's the point? They just get multiplied inside the sum! FYI, this comes from equation ...
4
votes
2answers
272 views

Meaning of the backslash operator on sets

I am self-studying analysis and ran across this: $\mathbb R \setminus \mathbb N$ is an open subset of $\mathbb R$ My best guess for interpretation was this: the set $\mathbb R \setminus \mathbb N$ ...
0
votes
0answers
28 views

Set of functions and sequences

By $A^G$ I mean $\left\{x\colon G\to A\right\}$. Is it then to same to write $$ A^G=\left\{x=(x_g)_{g\in G}, x_g\in A\right\}? $$
3
votes
3answers
105 views

Set notation and the difference between $\subseteq,\in,\subset$.

What does it mean to say $\mathcal F$ is a family of subsets? (an example would be much appreciated :)) What would be a layman's example? When $B=\{b,c\}$ is it appropriate to write ...
4
votes
3answers
74 views

what is meant by $ f ∈ C^{2}[a, b] ?$

What is the meaning of $ f ∈ C^{2}[a, b] ?$ I think it says that $f$ is twice differential on $[a,b]$, isn't it?
0
votes
0answers
25 views

What is $\Lambda^{i}$ in the “Show that the highest weight of $\Lambda^{i}V $ is $\omega_{i}”$?

Question: What is $\Lambda^{i}$ in the "Show that the highest weight of $\Lambda^{i}V $ is $\omega_{i}$"? In this question, $\omega_{i}$ are fundamental weights. Context: Highest weight modules of ...
0
votes
1answer
36 views

How should one interpret the term x:2a?

I was asked about the right interpretation of $x:2a$. There are two ways to interpret this term $$x:2a=x:(2a)=\frac{x}{2a}$$ and $$x:2a=(x:2)a=\frac{x}{2}\cdot a$$ I am not aware of a convention in ...
1
vote
0answers
46 views

Order of Riemann tensor indexes and the Ricci Identity

I have seen the Ricci identity written variously as $R_{ijk}{}^l x^k = (\nabla_i\nabla_j- \nabla_j\nabla_i) x^l$ $R_{ij}{}^l{}_k x^k = (\nabla_i\nabla_j- \nabla_j\nabla_i) x^l$ $R^l{}_{kij} x^k = ...
4
votes
2answers
74 views

Notations: use of parentheses with “mod” and the “|” symbol

I'm working through a practice test with no available solutions, and I came across this question. Let $a,b,c,d,e$ be integers with $c>0$. Suppose that $a\equiv b\pmod c$, and that $d\equiv ...
2
votes
1answer
49 views

What is the ideal of a point in algebraic geometry?

I found a problem as follows: Find the ideal of a point $z$, denoted by $\mathfrak j_z\subset\mathbb Q[X,Y]$, and its conjugates in $\mathbb C^2$ as $z=(\sqrt{2},\sqrt{3})$. I tried to Google but ...
1
vote
1answer
28 views

Writing in Cartesian tensor form

Write the following in Cartesian tensor form $$(1) \nabla (\operatorname{div} G) \times \nabla\Omega$$ $$(2) (\operatorname{curl}(F)\times G)\cdot \nabla(Φ)$$ I have answers for these two questions, ...
0
votes
1answer
46 views

Set builder form for representing strings

Is there a way to represent strings or palindromes using set notation? For representing palindrome using set notation, I arrived at this notation $$S=\{ab^{n}c:N\; |\; n \geq 1 \land n \leq 3\}$$ I ...