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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15
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2answers
1k views

What does “∈” mean?

I have started seeing the "∈" symbol in math. What exactly does it mean? I have tried googling it but google takes the symbol out of the search.
1
vote
1answer
50 views

Definition of Kronecker Delta

Is $\delta _{mn}=1$ when $m\neq n$, and $\delta _{mm}=0$? I am not very good at Math. So would you give me the answer and explanation please?
-1
votes
1answer
38 views

Is there any notation for all elements of a sequence coming from another set?

Let $\{ A(\lambda, i) \}_{i=0}^{N-1}$ be a sequence denoted by $A(\lambda)$ and $B$ be a set. Is there any established notation to show that all elements of $A(\lambda)$ come from the set $B$ ? The ...
3
votes
1answer
105 views

Coincidence about nabla?

I was surprised to notice that gradient of function and Levi-Civita connection have the same notation, i.e. nabla sign $\nabla$. Moreover, extending any connection on tensors, one let it be ...
0
votes
1answer
45 views

What are the different ways of indicating that a random variable has a specific distribution?

Recently I have seen random variable distributions described in two ways: $$ X \sim Nb(r,p) \\ X \stackrel{d}{=} Nb(r,p) $$ Both indicating that $X$ is a negative binomial random variable with $r$ ...
2
votes
2answers
152 views

Is the decimal notation the “right” notation for arithmetic?

I am considering here the pre-decimal notations such as Roman numerals, Egyptian numerals etc. It seems reasonable that these must all be equivalent. And it seems that decimal notation (i.e. ...
0
votes
1answer
256 views

Notation for matrix and sum of matrix rows

I have a table that describes the influence of sources (columns) on sinks (rows) where rows=$(A,B,C)$ and columns=$(A,B,C,D,E)$. So my table looks like: ...
2
votes
1answer
66 views

What does this log notation mean?

Can someone please explain what $^2\log x$ means? Is it the same as saying $\log x^2$ or is it something completely different? Here is an image of it as an example:
1
vote
3answers
60 views

Is there standard notation for an arbitrary polynomial of degree $k$?

I was wondering whether there is standard notation for a polynomial of a certain degree, say, $k$. That is, I want to be able to write $<standard \text{ } notation> $ instead of "..., where ...
2
votes
1answer
194 views

“unity symbol” from Feller's “An Introduction to Probability”

I am wondering if anyone knows the name or source of the symbol shown below from page 22 of the Second Edition of Feller's "An Introduction to Probability" Volume I.
1
vote
1answer
39 views

Small notation question about union of chains (Set Theory)

The question is derived from this question I encountered: Let $A$ be a set, and let there be a function $f: A \rightarrow A$, so that for every $a \in A$, $f(a) \neq a$. Define $S=\{X \subseteq A: ...
2
votes
1answer
76 views

What is the notation for taking negative imaginary values for roots of negative numbers?

I have a formula which is analytic in its argument $x$. In it, there is a square root of a variable as in $\sqrt{x}$. Although meaningful results are obtained when positive roots are taken for for ...
0
votes
1answer
32 views

Reading set notation for the flow number

Could someone please help me to understand the following notation: Flow Number: In case of need, S refers to a set of flows, C(s) is called congestion and D(S) is dilation. How would you put in ...
0
votes
1answer
24 views

Notation for a collection of sets under a certain condition

I am looking for the notation to describe "A collection of sets that are the union of a finite number of intervals". Is this correct - $A = \{A_i\}_{i \in I}$ where each $A_i = \bigcup_{n \in N} ...
1
vote
1answer
105 views

What does ^ sign mean on a vector?

I have a maths homework question Given the vector b find bˆ The symbol is actually above the b, but I am not sure what it means. Guessing it means to find the unit vector of b?
4
votes
2answers
433 views

What is this notation, similar to the binomial coefficient?

I've come accross this notation: $$\left\{\begin{eqnarray}n\\m\end{eqnarray}\right\}$$ The only other info I have about this notation is that $\left\{\begin{eqnarray}4\\2\end{eqnarray}\right\}=7$ ...
0
votes
1answer
37 views

Is there a questionned ordering symbol like the questionned equality?

To question the equality between $a$ and $b$ we can use $a \overset{?}{=} b$ From what I understand, the $\overset{?}{=}$ sign is to be replaced either by $=$ or $\not=$ and the writer will guide me ...
0
votes
2answers
30 views

How do you write the set where $2$ numbers are chosen

A = the event that the sum of outcomes of $2$ dice being thrown So do I say $A = \{14;41;23;32\}$ That looks like I'm saying $41$ (the number) not $4$ from one die and $1$ from the other which ...
0
votes
1answer
176 views

What is the amalg symbol?

I saw this formula: $A \amalg B$, where $A$ and $B$ are sets. I searched for the name of the symbol, "amalg", but haven't found a definition. What is the meaning of this symbol?
0
votes
1answer
239 views

subscript notation in conditional probability

$X$ and $Y$ are two discrete random variables with joint p.m.f $p_{XY}$ such that $p_{XY}(x_i,y_j) = P(X=x_i, Y=y_i)$. I came across a notation that refers to $p_{X}(x|y)$. How do I express it in the ...
1
vote
1answer
114 views

Mathematical notation for expressing the top n elements

I would like to know what is the mathematical notation to express the top n elements. Look at the equation below. Here $x_w$ is a feature vector representing the contribution of a particular word $w$. ...
0
votes
0answers
99 views

Tuple and vector. What do I have here?

For a cluster analysis I have elements with two features/attributes. The first feature is in $\mathbb R$ and bounded to the interval $[0,1]$ and the second feature is in $\mathbb N$. Is it ok to ...
2
votes
3answers
63 views

What does this combination notation mean?

I feel stupid even asking this but when they have a combination like $15\choose5,7,3$ does that just mean $15\choose5$ $10\choose7$ $3\choose3$
2
votes
2answers
128 views

Both Linearly Independent and Dependent?

Is it possible for two vector functions of, for the moment's simplicity, one variable be both independent and dependent? The reason I'm asking this is because on a problem from a book of mine (not ...
1
vote
2answers
172 views

What does $\vee$ mean in set theory?

The following proof is from Probability by Davar Khoshnevisan. There is a symbol $\vee$ in the third sentence of the proof. What does this symbol mean, please? There seems no definition about it in ...
0
votes
1answer
35 views

Prove equilvalence of generating series with compositions.

weight function: w(c1, ..., ck) = c1 + ... + ck and w(ci) = ci, 1<=i<=k Could someone explain to me what the N notation stand for? My take would be that the left N notation represents a set ...
1
vote
1answer
48 views

Integral notation from cartesian from polar coordinates

Given an integral $$I=\int\limits_{\mathbb{R}^n} \cdot \; dx,$$ we can introduce polar coordinates, such that $$I=\int\limits_{\Bbb S^{n-1}} \cdot \; d\theta.$$ Another way to express the latter one ...
0
votes
1answer
23 views

Function with similar properties

Suppose I have a function $f$ and derive another function from it with similar properties. For example I have that my new function is zero when the other function is zero. I would still like to use ...
3
votes
3answers
177 views

Notation for a space of finite sequences

For a given set $X$, what is the notation for the space of all finite $X$-valued sequences? I realise that the space of $n$-tuples is written as $X^n$, and the space of infinite sequences is ...
1
vote
1answer
33 views

Is there notation or a name for the complement of the unbounded face of a planar graph?

Let $G$ be a finite graph embedded in $\mathbb{C}$. Let $F$ denote denote its unbounded face. Is there notation or a name for $F^c$ without referring directly to $F$. Of course this is equivalent ...
3
votes
3answers
113 views

Symbol for rational/irrational part of a number

Just as $\Im(z)$ and $\Re(z)$ denote the imaginary and real parts of $z$, respectively, do there exist symbols for the rational and irrational parts of a real number?
2
votes
1answer
49 views

Domain of a composite function

I was given the question: Find the domain of the function $f(x)=\ln(\ln(\ln x))$ I found the answer by inspection: $\qquad D(\ln x)=(0,\infty)$ $\therefore\quad D(\ln(\ln x))=(1,\infty)$ ...
0
votes
3answers
57 views

Name of quantity that is not invariant, but only changes in one direction

How do you call a quantity that is not an invariant, but only changes in one direction during the process? Example: The degree of the polynomials go down when Euclidean division is applied, so the ...
1
vote
0answers
36 views

element subset for adjacency matrix

I am trying to create an element of a matrix that is a subset of a larger matrix. However, I am told that my subscripts do not match. I wanted other people's opinion as to what I am doing wrong and ...
0
votes
1answer
25 views

Basic matrice notation

I want to compute the L2 distance between a set of points X and M using matrices, for that I proceed as follows: 1) I substract both matrices, X-M 2) I square each matrice member (X-M)^2 3) I ...
1
vote
0answers
82 views

Notation to count tuples

I have the following set: V={(0,0),(1,2),(1,3),(2,2),(3,2)} I need to count tuples containing x = 1. Can I use |V_{(1,y)}| ? Or I should use |{(x,y) \in V | x = 1}| ? Thanks, Luiz
3
votes
2answers
270 views

How to denote domain and range

Is there a common way to denote the domain or range of a function? I've seen things like $ \cal{D}\left(f\right) $ and $ \cal{R}\left(f\right) $ for the domain and range, respectively, but I wasn't ...
0
votes
1answer
34 views

Understanding the definition of the d-dimensional Hyperube

Please see the picture bellow about the definition of the nodes of the d-dimensional Hypercube. Could anyone please tell me what does that notation means. I get confused with the superscript after the ...
2
votes
1answer
82 views

Is there a recommended symbol for “equal by abuse of notation”?

Can anyone suggest a good candidate for a symbol to be used for "equal by abuse of notation"? I can only think of "$\stackrel{\text{def}}{=}$", but it does not seem to be quite appropriate. For ...
0
votes
3answers
38 views

need help explaing the complex roots of a cubic

I am trying to understand a Galois theory example and we are looking at the solutions of $x^3-2=0$. It says they are $2^\frac{1}{3},2^\frac{1}{3}\omega, \text{ and } 2^\frac{1}{3}\omega^2$. I know ...
1
vote
1answer
48 views

Quantifiers bind tightly?

Is this true that it is a commonly agreed rule that $\forall x\in A:P(x) \wedge Q$ and $\forall x\in A:P(x) \Rightarrow Q$ should be interpreted correspondingly as $(\forall x\in A:P(x)) \wedge Q$ and ...
16
votes
1answer
278 views

How and why did Weierstrass $\wp$ get its special symbol?

I kind of always hated drawing the Weierstrass $\wp$ symbol by hand, and it struck me as odd how and why it achieved its special status in the first place. After all, there are tons of other important ...
2
votes
0answers
42 views

Understanding notation with regards to tangent derivatives.

I am currently reading a paper on monge-ampere equations, and in one part the author does as follows. Let $\Omega,\Omega^*$ be two uniformly convex subsets of $\Bbb R^n$, and let $h\in C^{2,1}(\Bbb ...
0
votes
1answer
63 views

What does F(a)(b) mean in the context of extension fields?

I understand that F(a) is the smallest subfield that contains both F and a. What is the definition of F(a)(b)? I'm supposed to prove that it's equal to F(a,b), but without knowing how F(a)(b) is ...
1
vote
1answer
293 views

What is box tensor product?

I have seen the symbol $\boxtimes$ (LaTeX: \boxtimes) in a few places, but I couldn't find a good reference for that. What does it mean and how is it different from ...
2
votes
2answers
256 views

Linear algebra notation involving $\preceq$

I am trying to read a paper which involves some linear algebra. I would appreciate if anyone could clarify what the below statements exactly mean. 1-) $0 \preceq B^TB \preceq A^TA$ where $A \in ...
2
votes
1answer
52 views

What does $Z_2(S)$ mean where $S$ is a group.

In an article by Bob Oliver "Simple fusion systems over p-groups with abelian subgroup of index p" in Notation 2.2., he defines a set $Z_2 = Z_2(S)$ where $S$ is a nonabelian $p$-group. The problem is ...
3
votes
2answers
122 views

Examples of misleading notation that gives correct results

A lot of the time, in maths, especially when I'm trying to remember a formula, I'm taught to remember it in a way that is not notationally correct, but produces the right result. e.g. when learning ...
2
votes
1answer
111 views

What does an $\oplus$-sign in the superscript mean?

I've come across an expression $ M^{\oplus n_i}$ in an article and I have not seen this before? What does is mean? The whole expression looks like this: $$\large M=M_1^{\oplus n_1}\oplus M_2^{\oplus ...
3
votes
3answers
182 views

Do all mathematical symbols in LaTeX have a meaning?

I debated whether I should post this on the TeX forum or here. Mathematics seemed more appropriate. LaTeX has a ridiculous amount of symbols, including countless variations of the integral sign and ...