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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6
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4answers
2k views

Sequence Notation — Which brackets to use?

I'm teaching sequences at the moment. I've always put sequences in round brackets, for example $(1,2,3,4,5)$ is a sequence whose first member is $1$, whose second member is $2$, and so on. I've also ...
6
votes
1answer
699 views

Ideas for denoting parameters of a function, as opposed to variables, in the list of arguments?

In general, the list of arguments of a function includes only variables, not parameters. In some specific cases, a parameter could be incorporated into the function name, like $y$ in $$\log_y (x)$$ ...
2
votes
2answers
474 views

Lipschitz and Holder continuous

Let a function $f(t,x)$, which is Lipshitz continuous in $x$ and $1/2$-Holder continuous in $t$. Is there any "official" and widely accepted way to denote the class of such functions ? I am ...
0
votes
1answer
365 views

Math notation for histogram selection process

Suppose you have values and classify them in a histogram. In pseudo code this may look like this: ...
2
votes
2answers
53 views

Is there a notation for a given order-preserving bijection?

Let $A,B$ be sets and $G,H$ be order-relation for $A,B$ respectively. Say, i proved existence of an isomorphism $\psi$ such that [$(x,y)\in G$ iff $(\psi(x),\psi(y))\in H$]. However, "$A\cong B$" ...
1
vote
3answers
138 views

What is the term for a graph on $n$ vertices with no edges?

What is the term for a graph comprised of $n$ pairwise disconnected vertices? I could call these $1$-colorable graphs or something like that, but I would rather use standard terminology if it ...
1
vote
3answers
1k views

What does the “n choose multiple numbers” symbol stands for?

The question is: How many ways can you align 3 red balls, 2 blue balls and 2 yellow balls ...
3
votes
1answer
127 views

Set theory: notation

I have a question w.r.t. notation that appears dealing with product sets. Let $T$ be any index set and $X$ and $Y$ be any two sets. Then $X^T = \{f:T\to X\} $ and $Y^T = \{g:T\to Y\}$. Let $A\subset ...
6
votes
2answers
2k views

The notation for partial derivatives

Today, in my lesson, I was introduced to partial derivatives. One of the things that confuses me is the notation. I hope that I am wrong and hope the community can contribute to my learning. In ...
1
vote
1answer
98 views

Notation Confusion

This is an extremely soft question. This is a definition from Ramsey Theory: $n\to (l_1,\ldots, l_r)^k$ if for every $r$-coloring of $[n]^k$, there exists $i$, $1\le i\le r$, and a set $T$, ...
3
votes
1answer
206 views

A question concerning multi-indices

I am having difficulties understanding the following formula : $$(x_1+\cdots+x_n)^k=\sum_{\alpha,|\alpha|=k}\frac{|\alpha|!}{\alpha!}x^\alpha $$ where $\alpha$ is a multi-index. I find this notation ...
13
votes
4answers
1k views

Why doesn't Spivak ever write $dx$ in an integral?

I've noticed that Spivak, and many other analysis books I read like Munkres, do not use $dx$ when they integrate. Why is that? This is a serious question.
1
vote
1answer
354 views

Meaning of the bar over $\bf{c}'$ in $\bf{\bar{c}}'=\bf c' -\bf c'_B \bf B^{-1} \bf A\geq \bf 0$?

I am trying to understand the page 87 Bertimas about Linear Programming. The author uses bolding and bars -- now I am starting to think that the bar means something else to vector, bolding apparently ...
7
votes
3answers
9k views

“Such that” symbol “$\mid$”

I know the "such that" symbol $\mid$ from the definition of sets: $$\{x \mid x \in \Bbb N \land x < 3\}$$ Is it OK to use this symbol outside of sets. For instance, if I want to define a function ...
2
votes
2answers
198 views

Functions, domains and codomains

I am refreshing a bit my basic knowledge of mathematics, and I have some doubts, I am sure you can help me with. Let's take this function in python: ...
1
vote
1answer
153 views

Graph decomposition and union by mathematical notation

(I guess, readers might misguided by my original post, So I modify it) If I have an undirected graph, Could you please help me to describe Decomposing a undirected graph into cycles Cycle breaking ...
2
votes
2answers
315 views

Correct notation or operator to remove elements from sequence

I'm currently using the following notation to denote a sequence (i.e. ordered list of elements): $\langle x_n | x \in \mathbb{N} \rangle$ E.g. $S = \langle 1,3,5,7 \rangle$ and $S_2 = 3$ I know ...
6
votes
4answers
11k views

Differentiation, using d or delta

Are the symbols $d$ and $\delta$ equivalent in expressions like $dy/dx$? Or do they mean something different? Thanks
3
votes
1answer
216 views

What does $R_P$ mean, for a ring $R$ and an ideal $P$?

What does $R_P$ mean, for a ring $R$ and an ideal $P$? This appeared in some notes by a teacher of mine, but he didn't define this notation. He used it as follows: suppose $R$ is a commutative ring, ...
4
votes
1answer
251 views

Mathematical formal notation of a dictionary

I was wondering how to express a dictionary or associative array (as known in programming) formally in mathematical notation. A dictionary is basically a set of ordered pairs of keys and values, but ...
5
votes
2answers
562 views

What is the correct notation for a multivariable function?

Many mathematical texts define a multivariable function $f$ in the following way $$f := f(x,y)$$ However, if we focus on the fact that a function is really a binary relation on two sets, (say the ...
1
vote
2answers
1k views

What are the $\succ$ and $\prec$ operators for when used with matrices?

I understand that $A\succ0$ means that "A is a positive definite matrix" (i.e.; all of the eigenvalues of A are positive). But what does it mean when the right hand side is a different value than ...
3
votes
1answer
1k views

Square brackets instead of parens for functions?

Why are sometimes square brackets used to apply parameters to functions instead of the usual round parentheses? For instance, in my probability course, they use $\text{P}[X]$ to denote the ...
1
vote
3answers
1k views

Graph theory notation of path concatenation

I was wondering what the proper notation would be when concatenating paths, written as a sequence of nodes, rather than a set of edges. That is: Given: $$ P = ( x, y, z ) $$ Is it valid to ...
1
vote
6answers
300 views

Super or subscript notation on the left hand side of a symbol?

Are there any commonly used notations with super or subscripts on the left hand side of the symbol? or on both sides of a symbol? If so, then what is the latex for having sup/sub script on left or ...
4
votes
1answer
236 views

Diagrammatic (Postfix) Composition of Functions

Consider the functions $f : X \to Y$ and $g : Y \to Z$. According to the Wikipedia articles on Function Composition, the application of $f$ to an input $x$ can be written as $xf$ (as opposed to the ...
3
votes
2answers
138 views

Expressing Subset in terms of Other Subsets of the Same Set

I am very much a newbie, and couldn't find a straight-forward example to answer my question. What is the correct way to express the below: I have set $S$, and subset of $S$, $T = \{T_1, T_2, T_3\}$ ...
0
votes
1answer
95 views

Basic question about matrix algebra- notation

The representation $X=(I_p,0_{n-p\times p})$is confusing me. I get that $I_p$ is an identity matrix with $p$ rows and columns and the rest of the representation is confusing me. Can someone clarify ...
0
votes
1answer
305 views

Notation and meaning of coordinate system in geometry

I am trying to understand projective geometry to build a 3d scanner, using this text. http://mesh.brown.edu/byo3d/notes/byo3D.pdf When describing an idea pinhole camera it says In the ideal ...
2
votes
2answers
429 views

How do I write $\{3,6,11,18,27,38,…\}$ in set-builder notation?

For the set $\{3,6,11,18,27,38,...\}$, the $(n+1)^\text{th}$ term, which I'll call $a_{n+1}$, is: $$a_{n+1} = a_n + 2n+1$$ How can I write this set in set-builder notation? My best guess doesn't seem ...
1
vote
1answer
1k views

What does colon mean between function inputs

I would like to calculate a function, but I am a bit confused with F(x,y:U,s) notation, $$g\left( {x,y:\theta ,f} \right) = \exp \left\{ { - \frac{1}{2}\left[ {\frac{{x_\theta ^2}}{{\sigma _x^2}} + ...
0
votes
1answer
237 views

Extend the domain of a function

I get back to a question I post long time ago, because that is quite important to me... Let $\mathbb{X} = \{a, b, c...\}$ be a finite set, $\mathbb{N}$ refers to the set of all natural numbers. I ...
2
votes
1answer
61 views

Seminaire Chevalley, 1958, exp no. 2

I was trying to read Seminaire Chevalley, 1958, exp no. 2 and I encountered some notation I don't understand. T and U are varieties. He defines Z as a closed subvariety of $U \times V$ such that for ...
1
vote
1answer
152 views

Which definitions of builder notation exist for multiset theory?

Interesting cases would be $A=[1,1], B=[2]$ $[(a,b) \mid a \in A \wedge b \in B] = [(1,2),(1,2)]$ ? or $C=[1,2,3]$ $[x \mid c \in C \wedge x = c \mod 2] = [1,0,1]$ ? The only kind of informal ...
1
vote
1answer
168 views

Difference of 2 notations with powerset

Let $\mathbb{N}, \mathbb{V}$ two sets, $\mathcal{P}(\ldots)$ means the power set of a set. $\mathcal{P}({\mathbb{N}})\rightarrow \mathbb{V}$ can be the type of a function mapping a part of ...
2
votes
1answer
71 views

Define a domain filter of a function

Let $\mathbb{B}, \mathbb{V}$ two sets. I have defined a function $f: \mathbb{B} \rightarrow \mathbb{V}$. $\mathcal{P}(\mathbb{B})$ means the power set of $\mathbb{B}$, I am looking for a function ...
3
votes
2answers
81 views

Why is $S/R$ a ring extension?

If $S$ is a ring and $R \subset S$ is a subring it's common to write that $S/R$ is an extension of rings. I frequently find myself writing this and read it quite often in textbooks and lecture notes. ...
2
votes
3answers
68 views

Convenient way to write $x \bmod{n}$

I'm trying to figure out an easy way to write $x \bmod{n}$. For example, in this exercise, where I need to show that this is an homomorphism: ...
3
votes
1answer
57 views

Appending a point at infinity to $\mathbb{F}_q$

Is there any standard notation for the set $\{\infty\}\cup \mathbb{F}_q$? Thanks, and feel free to move if there is a better forum for this question.
2
votes
1answer
108 views

Notation of differential equations

I have just started a course on differential equations, and unfortunetely enough for me, we immediately used notation foreign for me, for example: $$ x^2 \left(\dfrac{d^2y}{dx^2}\right)^2 = \sin( ...
1
vote
1answer
50 views

Name a stable output of a function taking 2 arguments

$\mathbb{C}$ is a fixed finite set, a fair chaotic sequence $(c_n \in \mathbb{C})$ is defined such that $\forall c \in \mathbb{C}, \exists n_0 \in \mathbb{N}, n > n_0 \wedge c_n = c$. That means ...
1
vote
3answers
45 views

Correct notation of function with given property

I require a function with the following property: $$ f(x) = \begin{cases} x & x \ge 0 \\ 0 & x \lt 0 \end{cases} $$ This function will be used within an integral, e.g. $$ \int_0^T ...
0
votes
2answers
323 views

How to formally denote that something is a variable

For example, let's say I want to say that in notation $\frac{\partial f}{\partial x}$, $x$ is a variable in real domain. Is there some way to denote it mathematically? For example if I was to say that ...
0
votes
1answer
87 views

Expression Writing: Random variable inside bayesian (Notation)

What is the best, most clear way to denote this example. Event $A$: outcomes $(0,1)$. $P(C)=P(B)$, if $A=1$ $P(C) = 0$, if $A=0$ Which one is best $P(C) = P(B|A=1)$, $A$: indicator random ...
2
votes
1answer
79 views

“[T]ransversely isotropic and mirror-symmetric (space group:$D_{\infty h}$)”, its orbifold notation?

I am trying to understand this frieze pattern $D_{\infty h}$ aka its orbifold notation. This describes spider's silk. The authors call it a space group, some sort of generalization from orbifolds. ...
6
votes
3answers
20k views

Symbol for “such that” (not in set)

If $A$ is a set, we can use the set notation $$A= \{ b \mid\text{property $p_1$ of $b$}\}$$ But say $A$ is an element like $b$, $$A = b \mid \text{property $p_1$ of $b$}$$ is this a usual ...
2
votes
0answers
683 views

Writing a probability expression (Notation)

What is the best way to denote, Probability of $n_i$ changing its value from $0$ to $1$ at time $t$. I come up with these, any suggestions _ $$ P_{n_i,0\rightarrow1}(t) \\ P(n_i:0\rightarrow1, t) $$ ...
3
votes
1answer
225 views

What is the notation for set of prime factors of a number?

Is there a notation for the set of prime factors of a number, or set of factors of a number?
2
votes
1answer
262 views

Notation of $\max$

What is the meaning of: \begin{equation} \max_{x_0\le x\le x_2}f^{\prime \prime}(x) \end{equation} Is it the max of the second derivative at any $x$ between $x_0$ and $x_2$
0
votes
1answer
93 views

Odd matrix notation: $||\mathbf{A}||$

My friend was reading the text for her engineering class, and came across the symbol $||\mathbf{A}||$, where $\mathbf{A}$ is a matrix. My guess is that it is a determinant, but it is essentially ...