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

1
vote
0answers
74 views

difference between n - 1 and n-1

I hope things are going well. I am doing some recursion stuff with databases and the text book I am reading has made it clear there is a difference between n-1 for example and n - 1. The difference ...
0
votes
1answer
85 views

Why is the symbol ζ sometimes used in a complex function?

I just flipped through a book on complex analysis and found some functions being written as f(ζ) instead of f(z). It did not state why this is so. Can someone help enlighten me? Thank you.
17
votes
4answers
637 views

How to explain this quirk of the chain rule?

Assume I have a function $f = f(y, \phi(y,x))$ and I want to calculate $\frac{\partial f}{\partial y}$, I use the chain rule to get \begin{equation} \frac{\partial f}{\partial y} = \frac{\partial ...
1
vote
2answers
135 views

Rank these notations from most valid to least valid

$$\mathbb{Z}[\sqrt{-3}]$$ $$\mathbb{Z}\left[\frac{i \sqrt{3} - 1}{2}\right]$$ $${\bf{A}}(-3)$$ $$\mathbb{Z}[\omega]$$ $$\mathbb{Z}\left[-\frac{1}{2} + \frac{\sqrt{-3}}{2}\right]$$ ...
1
vote
2answers
45 views

Is $y'$ a valid notation for $f'(x)$?

In this context, let us say that: $$y=f(x)$$ I've seen both the notation $y'$ and $f'(x)$ being used. Are both correct?
1
vote
1answer
51 views

Notation: Difference between $C$ and $C^0$

Lately I have been running into the following notation fairly often: $f\in C^0(\Omega)$, $g\in C^0(B,\mathbb R^3)$ etc. I always thought this was just some peoples' way of saying that a function is ...
0
votes
2answers
35 views

Notation regarding Balls

What is meant by the notation : $y \in \partial B_\epsilon (x_o)$ Where B is a Ball centred at $x_0$ with radius $\epsilon$
0
votes
1answer
41 views

Is there a more rigorous method of notating arithmetic?

Is there a method of notating arithmetic that presents the transformations more explicitly than the standard method? For example. Someone using the standard method might present their solution ...
0
votes
2answers
58 views

In a metric space a compact set is closed

I want to show the following: Let $X$ be a metric space. Show that every compact subset $Y$ of $X$ is closed. The idea is to show that $X\setminus Y$ is open. So, for any $x \in X\setminus Y$, I ...
13
votes
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.
0
votes
1answer
35 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
29 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
92 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
0answers
30 views

Notation problem with a set of tuples and a metric

The first question: Assume we have tuples $T_i = (x_i, \vec{c}_i)$ ($x_i$ is the name of the object which is characterized by $\vec{c}_i$ in a d-dimensional space) and define a set of them $TS = ...
0
votes
1answer
34 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 $r$ ...
1
vote
1answer
97 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
29 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
57 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
51 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
114 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
23 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
72 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
30 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
20 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
54 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
414 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
34 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
29 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
0answers
37 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
41 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 ...
0
votes
0answers
56 views

Accepted symbol (or way of writing) “A is a subset of B or B is a subset of A”

I am looking for a concise way to write the statement "$A$ is a subset of $B$ or $B$ is a subset of $A$". The context is the Grassmannian and two elements $A,B\in G_k(\mathbb R^n)$ in it. The two ...
0
votes
1answer
75 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
60 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
50 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
55 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 ...
0
votes
0answers
29 views

Notations for elementary set theory

I wish to understand the following notations which defined for every cardinals, $a,b$: $P(a,b) = \left| In(A,B) \right|$ $C(a,b) = \left| P_b(A) \right|$ $E(ab) = \left| Eq(A,B) \right|$ ...
1
vote
2answers
82 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
27 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
47 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
21 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 ...
2
votes
3answers
94 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
24 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 ...
2
votes
3answers
67 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
22 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
54 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
21 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
23 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
12 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
2
votes
2answers
53 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
24 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 ...