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

0
votes
3answers
19 views

How can I express, “The set of integers greater than x and less than y”?

I know I could express it this way (x = 0, y = 10): $$ \{ 1, 2, 3, 4, 5 , 6, 7, 8, 9 \} $$ in simple cases. This is what I could come up with for the more general case: $$ \mathbb I = \{ i_n | i_n ...
0
votes
0answers
16 views

How to quickly reference to two subsets of the same set

Suppose $A\subset F$ and $B\subset F$. Would the following be a valid shorthand? $A,B\subset F$? What is the convention on this? Similar question for elements of a set: Suppose $a\in F$ and $b\in F$. ...
0
votes
0answers
21 views

correct use of notation in defining a function

So I have this function which takes a integer tuple and another tuple, and maps them to a value from some pre-defined set of values. I had the following signature: $\omega:(\mathbb{N} \times ...
0
votes
0answers
14 views

Standard notation for the indicator function of the odd integers

Is there a commonly used notation for the indicator function of the odd integers? One candidate I think is $$1_{2\mathbb{Z}+1}(x),$$ and I could always define one, $$\chi(x)=\left\{\begin{array}{ll} 1 ...
1
vote
1answer
27 views

How to formally write $f\left(k\right)={1\over p_1}+{1\over p_1p_2}+{1\over p_1^2p_2p_3}+{1\over p_1^4p_2^2p_3p_4}+\dots$

How do I write the following finite series as a sum of products: $$f\left( k \right) = {1 \over p_1} + {1 \over p_1p_2} + {1 \over p_1^2p_2p_3} + {1 \over p_1^4p_2^2p_3p_4} + \dots + {1 \over ...
0
votes
1answer
12 views

Sampling from a finite set of integers [on hold]

How do I construct the notation for random variable sampled from a finite set of integers uniformly? How about the one for discrete uniform distribution? Thanks.
0
votes
1answer
30 views

How to formally write $f\left(k\right)={1\over p_1}\left(1+{1\over p_2}\left(1+{1\over p_3}\left(1+\dots\right)\right)\right)$

How do I write the following finite series as a sum or product: $$f\left(k\right) = {1 \over p_1} \left(1 + {1 \over p_2} \left(1 + {1 \over p_3}\left(1+\dots \right) \right) \right)$$ …all the way ...
1
vote
1answer
41 views

Meaning symbol $\overline{\lim_{n\rightarrow \infty}}$ [duplicate]

I found this symbol on a math book that I'm studying. It had never happened before. What does this mean? $$\overline{\lim_{n\rightarrow \infty}}$$
6
votes
3answers
143 views

Challenge: Demonstrate a Contradiction in Leibniz' differential notation

I want to know if the Leibniz differential notation actually leads to contradictions - I am starting to think it does not. And just to eliminate the most commonly showcased 'difficulty': For the ...
0
votes
4answers
46 views

“$((A\times B) \to C)$” denotes what?

I'm having some trouble understanding notation. The question is For any three sets $A,B,C$ , $((A\times B) \to C) =_c (A \to (B\to C))$ Exactly what does "$((A\times B) \to C)$" denote? Is ...
4
votes
2answers
73 views

What does this $\asymp$ symbol mean? (subject: analytic number theory)

I'm reading a survey article by Andrew Granville on analytic number theory. On page 22 of the paper, there appears a strange looking symbol, undefined. I've circled it in red in the screenshot ...
0
votes
1answer
20 views

how to write it using sigma notation

I'd like to know how to create a pattern for these sum: 1) $a_{1}a_{2}a_3+a_1a_2a_4+...+a_1a_{n-1}a_n+a_2a_3a_4+a_2a_3a_5+...+ a_2a_{n-1}a_{n}+ ...+a_{n-2}a_{n-1}a_n = ?$ 2) ...
0
votes
0answers
34 views

if the role of a numeral system is to provide a mathematical notation for representing numbers. Then how do notation less numbers look like?

Our numeral system maps a unique(or at least standard) notation to every number in a set. for example : In decimal system we map natural number set by ${1,2,3,4,5,6,...}$. My question is What ...
0
votes
1answer
25 views

Why notations of numbers in standard positional numeral systems when evaluated, evaluates to decimal notation?

For a positional numeral system of radix b, evaluating a notation $a_3 a_2 a_1 a_0$ as shown below results in decimal notation of number, $a_3 a_2 a_1 a_0 = a_3 \times b^3 + a_2 \times b^2 + a_1 ...
0
votes
3answers
33 views

What does $f: 2^{\mathcal{S}}\rightarrow\,\mathbb{R}$ mean?

A function $f: \mathcal{S}^n\rightarrow\,\mathbb{R}$ This is I understand. $x\in\mathrm{dom}\,f$ means that $x$ is a vector of size $n$ where its elements are taken from the set $\mathcal{S}$. ...
0
votes
1answer
12 views

Expression as argument in function definition

When a function definition has an expression (instead of just a single variable) as the argument to the function, what does this mean? For example, I have this question (part b): Given a certain ...
0
votes
0answers
63 views

The fundamental theorem of calculus: $\frac{\mathrm d}{\mathrm{d}x} \int_a^x f(t)\:\mathrm{d}t = f(x)$ and nothing more

My textbook writes, just as wikipedia, but I'd like to write it shorter. Can the fundamental theorem of calculus be written as $$\frac{\mathrm d}{\mathrm{d}x} \int_a^x f(t)\: \mathrm{d}t = f(x)$$
1
vote
3answers
26 views

The Notation for Derivatives

"The derivative of a sum is the sum of derivatives" Above theorem can be mathematically expressed as: $$h'(x)=f'(x)+g'(x)$$ where $f(x)$ and $g(x)$ are two differentiable functions. What is the ...
1
vote
2answers
28 views

How to represent the edges of a complete graph?

Let say I have a graph $\mathcal{G}$. Denote this graph by $\mathcal{G}=(\mathcal{V}, \mathcal{E})$ where $\mathcal{V}$ is the set of vertices and $\mathcal{E}$ is the set of edges. My question is ...
0
votes
1answer
15 views

Notation of a linear inequality system.

Sorry to bother with this rather trivial question, but nowhere in my lectures or books can I quite find out what the topmost line means. Maybe I'm forgetting something. Anyway: Line 2 and 3 are ...
7
votes
1answer
91 views

First usage of the symbol ∈

Concerning a book [1] I am reading the symbol $\in$ was first used by Giuseppe Peano and is the first letter $\epsilon$ (epsilon) of the word ἐστί (means "is"). Does anyone know in which work of Peano ...
0
votes
0answers
14 views

Representing trees in Set builder notation?

Is there a way to represent graphs and minimum spanning trees using set builder notation? e.g. I have a weighted graph of n nodes, all connected to each other in a mesh network manner. I am to ...
0
votes
1answer
33 views

Set notation of $S^1 \times S^1$

This is a simple question, but should this be written as: $\hspace{120pt}S^1 \times S^1 = \{(z_1,z_2)\in\mathbb{C}\times\mathbb{C}:|z_1|=|z_2|=1\}$
3
votes
1answer
77 views

What are the differences in mathematical notation around the world?

I just learned that $\text{sen}\,x$ is the Portuguese notation for $\sin x$, and I was inspired to ask: What differences are there in how mathematics is written around the world? Note 1: I am likely ...
1
vote
1answer
22 views

Notation question: Group generated by two elements?

Let there be $H$ subgroup of symmetric group $S_4$, so that $H= \langle (12)(34),(234) \rangle$. What does the notation $\langle (12)(34),(234) \rangle$ mean? I know that if there's one elements, then ...
1
vote
0answers
25 views

Abstract algebra notation

I am new to learning abstract algebra and using multiple books but the notation varies enough to throw me off. Could someone explain to me the differences between: $\mathbb{Z}\left\{ p\right\}$ ...
4
votes
1answer
41 views

Uncomfortable using Leibniz notation for the chain rule.

I am working through the following solved problem which uses separation of variables to get two ODEs. The problem is to show that $$\frac{1}{\sin\theta ...
1
vote
1answer
44 views

Notation question A $\subset \subset B$

I am a bit confused about the notation A $\subset \subset B$ used in functional analysis. The definition I have says: $A \subset \subset B$ iff $A \subseteq B$ and $\bar{A}$ compact in $B$. Wikipedia ...
4
votes
1answer
63 views

Is there a difference between writing $f: X\rightarrow Y$ and writing $f:X\mapsto Y$?

I think I've heard about a year ago that "$\mapsto$" is only used for a bijection, or do they mean the same thing?
2
votes
1answer
47 views

Lie derivatives and covariant derivatives (notation)

I am having troubling interpreting a particular expression in differential geometry. It arose in computing the Lie derivative along a unit normal, $n$, of the extrinsic curvature of a sub-manifold ...
1
vote
1answer
57 views
+50

$C^\omega$ notation for real analytic functions

I've seen the notation $C^\omega$ used for the set of real analytic functions (e.g. on an interval). Where does it come from? What exactly does it mean? What is the reason behind it? Who first used ...
1
vote
2answers
28 views

Looking for notation of set of all entries of some matrix?

I'm busy writing my thesis, and I'm looking for some concise notation to denote the supremum of the matrix entries of, say $A \in M_n(\mathbb{R})$. How should I do this? Looking for something like ...
0
votes
1answer
24 views

Notation Question about Rings

If $S = \langle2\rangle$ is the ideal generated by $2$ in $\mathbb{Z}$, what does $S[x]$ represent?
0
votes
1answer
46 views

How does the presenter in this video derive this formula?

I am watching this coursera video on entropy (in the information theory sense of the word). Right around the two minute mark the presenter shows two forms for H(p). The first (after the equals sign) ...
1
vote
2answers
35 views

How would I express the statement “Let H be a subspace of V” in mathematical notation?

How would I express the statement "Let H be a subspace of V" in mathematical notation? Does something like this work? $$ ( \ \ H(\mathbb{R})\subset V(\mathbb{R}) \ ) $$
1
vote
0answers
21 views

Groups - Compositions

If the f is written to the right of its argument does that mean the composition of $f g$ is actually $g(f(x))$ instead of being $f(g(x))$ which is the notation I'm used to. I ask this because I read ...
0
votes
1answer
30 views

Groups/Sets Notation Question

Simple question: But what does the sigma small Y mean, does it just represent a group? Also have seen this with numbers, and not quite sure what it means. Thanks
2
votes
1answer
70 views

What does $\in$ mean?

I'm reading a textbook on complex analysis and I've come across notation using this ($\in$) symbol. In the context of "an argument of $z = x + iy$ is a number $\phi \in \mathbb R$ such that $x = ...
2
votes
2answers
40 views

Notation - Transpose of Block Matrices [Lay P121 Q2.4.12]

Definition of Transpose is $(A^T)_{ij} = A_{ji}$ $1.$ Why $\begin{bmatrix} M & N \end{bmatrix}^T = \begin{bmatrix} M^T \\ N^T \end{bmatrix}$, and NOT $\begin{bmatrix} M \\ N\end{bmatrix}$? ...
1
vote
1answer
25 views

Understanding $Po(np)\{A\}$ probability notation

I am trying to read a textbook on probability and am already stuck on what must be basic notation. It says Thus, for example, if $A$ is any subset of $\mathbb{Z}^+$, it follows that for some ...
0
votes
1answer
29 views

what does this triangle-like notation mean?

$$\triangleright\quad \text{and}\quad \triangleleft$$ I saw these notations in some abstract algebra texts and i don't know what does this mean. What do they mean?
0
votes
0answers
36 views

Is there a traditional name for the “eigenspace” function?

Let $A$ denote a field, $X$ denote an $A$-vector spaces, and suppose $\varphi : X \rightarrow X$ is a linear transformation. Is there a traditional name for the corresponding "eigenspace" function? By ...
0
votes
3answers
31 views

Question about variable and constant notation in some properties

I am just starting to think about mathematical notation a lot more and some parts of it do not make as much sense to me as I would like. I am operating under the convention that beginning alphabet ...
0
votes
2answers
23 views

Limit notation question

lim(d^2 --> infty) d - 1 = infty Is this valid notation, or must it be written using lim(d --> infty) instead? I would like to express that as d^2 tends to infinity, d - 1 tends to infinity as well. ...
0
votes
0answers
26 views

Convert nested for loop to mathematical expression

Does anyone know how I can convert this nested for loop into a mathematical expression? ...
0
votes
0answers
35 views

Precise notation of a sum of a sequence

I need help in rewriting the support of a function $f$ in a more compact or precise way given its upper bound $b$ and lower bound $a$ as \begin{eqnarray} b&=&\max\left( \sum_{n}\alpha_n ...
2
votes
3answers
61 views

Why the name “umbilic”?

Umbilic points are points on a surface at which the principle curvatures of the surface are equal. "Umbilic(al)" refers to the navel/belly button. But why do we call these points so? What about the ...
0
votes
2answers
33 views

What does P(A U B) mean, in terms of real values?

I can't find a proper summary or reference of how to translate formulas in probability notation to arithmetic notation (i.e. when using real values). For example, if $P(A) = .7$ and $P(B)=.35$, what ...
1
vote
0answers
13 views

Is there any shorthand notation for linear interpolation?

It is quite common for me to encounter or manipulate expressions of the form $$ x + \alpha(y-x) $$ or equivalently $$ (1 - \alpha) x + \alpha y $$ where any of the expressions ($\alpha, x, y$) ...
0
votes
1answer
8 views

An indexed family of filters and their elements

Let $X$ is an indexed (by some set $n$) family of filters (on some poset $\mathfrak{A}$). Is there any standard notation/terminology for the set $\{ y\in \mathfrak{A}^n \,|\, \forall i\in n:y_i\in ...