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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8
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2answers
577 views

Difference between $:=$ and $=$

I am sorry if this is quite elementary question. But I always think, that why we use $:=$ at some places, instead of $=$. Is there any fundamental difference between these two? Before reading Terry ...
2
votes
1answer
323 views

Sum and subtraction with sets and matrix with formal notation

Hello I have some problems with formal notations, I have to sum (do the union?) of two sets and the sum (union?) of a set and a row of a matrix, is this notation correct? 1) Imagine $T_1 = \{1,2\}$ ...
2
votes
1answer
107 views

Cycle notation question

With $\alpha = (12345)$ in the cycle notation, I should interpret it as: $1\mapsto 2 \mapsto 3\mapsto 4\mapsto 5\mapsto 1$ I need to find out $\alpha^2$ and write it in cyclic notation. As I am not ...
0
votes
2answers
66 views

Validity of the notation $S+\emptyset$

If $S$ is a subset, is $S+\emptyset$ defined and equals to $S$? Or is it just gibberish? Thanks again. 
1
vote
1answer
58 views

Question on the Range in Limit Notation of an Infinite Sum

I'm studying Knuth's The Art of Computer Programming, Volume 1 (3rd ed.) and came across the following on page 27: The precise meaning of $\sum_{R(j)} a_j$ is therefore $$\sum_{R(j)} a_j = ...
4
votes
3answers
188 views

Linear algebra notation

This is a notation clarification question: If $S$ and $T$ are subspaces of a vector space $V$, is $S+T$ equivalent to $S\cup T$? Thanks.
1
vote
1answer
147 views

What are the $\ker$, $\mathrm{kei}$ functions?

In a book titled 'Ordinary Differential Equations and Useful Polynomials', under the chapter 'Bessel's function', the author has introduced four new functions $\mathrm{ber}$, $\mathrm{bei}$, $\ker$, ...
5
votes
1answer
608 views

How do you pronounce $\mathbb{Q}[\sqrt{2}]$?

Is there a standard term for $\mathbb{Q}[\sqrt{2}]$? I say it as "Q adjoin root two".
2
votes
1answer
606 views

The Dual Pairing

My understanding from the reading the Wikipedia article on Dual Pairs is that a dual pair is comprised of two vector spaces $X$ and $Y$ over a field $\mathbb{K}$ together with a nondegenerate ...
5
votes
1answer
829 views

Symbol for twice differentiable functions

Is there a symbol for the set of twice differentiable functions (2nd derivative not necessarily continuous)? I believe the symbol for twice continuously differentiable functions is $C^2(\mathbb F)$? ...
1
vote
1answer
552 views

Little $o$ notation and series

I have this question: Consider the series $e^{\tan(x)} = 1 + x + \dfrac{x^{2}}{2!} + \dfrac{3x^{3}}{3!} + \dfrac{9x^{4}}{4!} + \ldots $ Retaining three terms in the series, estimate the ...
1
vote
2answers
101 views

Set Properties: Formal Semantics of Programming Languages

What is the difference between the two notations below? {x | x (is an element of) X & P(x)} vs. X = {x | P(x)} These ...
2
votes
1answer
666 views

Capital $\pi$ notation, i.e $\prod$

There is a step in a proof I don't understand. $$(\prod_{i\in K} p_{i}^{min(a_{i},b_{i})})\cdot (\prod_{i\in K, 1\leq i\leq k} p_{i}^{min(a_{i},b_{i})}) = \prod_{1\leq i\leq k} ...
5
votes
1answer
507 views

Is the Unicode designed assuming the Continuum Hypothesis?

The Unicode chart for "letterlike symbols" states that א 2135 ALEF SYMBOL = first transfinite cardinal (countable) ב 2136 BET SYMBOL = second transfinite cardinal (the continuum) I ...
2
votes
2answers
798 views

What does the long curly line mean?

Sorry to sound incredibly ignorant, but I am...at least in math anyway. What does this symbol: $\int$ mean?
11
votes
1answer
2k views

What is mathematical basis for the percent symbol (%)?

Percent means 1 part of 100 or 1/100 and is indicated with %. Per mille means 1 part of 1000 or 1/1000 and is indicated with ‰, so it seems that these symbols indicate the mathematical operations ...
1
vote
1answer
158 views

Cover & Thomas textbook notation

Exercise 2.27 in Elements of Information Theory (2nd ed.) reads: Let $\mathbf{p} = (p_{1}, p_{2}, \ldots, p_{m})$ be a probability distribution on $m$ elements (i.e., $p_{i} \geq 0$ and ...
6
votes
1answer
3k views

Is there a symbol to mean 'this is undefined'?

Consider a partial function $f$ that is defined only for a few values of its domain (my exact use case is $\delta$ transition functions in automata). One can 'complete' it by saying $$g(x)=0\iff f(x) ...
2
votes
1answer
436 views

Concise notation for “Pairs of all items $\{ x, y, z \}^2$ without $\langle x,x \rangle$, $\langle y,y \rangle$, $\langle z,z \rangle$”

Is there a shorter notation for Pairs of all items $\{ x, y, z \}^2$ without $\langle x,x \rangle$, $\langle y,y \rangle$, $\langle z,z \rangle$ i.e. given an arbitrary set of items, construct ...
3
votes
3answers
7k views

How to represent XOR of two decimal Numbers with Arithmetic Operators

Is there any way to represent XOR of two decimal Numbers using Arithmetic Operators (+,-,*,/,%).
2
votes
1answer
178 views

Bound for multi-index sum

I have difficulties in evaluating the multi-index notation in the following context: Let $x \in R^n$ and let $i$ be a multi-index, $i=(i_1, \dots, i_n)$. Now I want to know the bound of the sum ...
2
votes
4answers
456 views

standard symbol for “to prove” or “need to show” in proofs?

Is there a standard symbol used as shorthand for "to prove" or "need to show" in a proof? I've seen "N.T.S." but was wondering if there is anything more abstract — not bound to English.
2
votes
0answers
109 views

What does it mean if a sequence is indexed beyond its bounds?

I'm looking at a paper (On Base and Turyn Sequences by C. Koukouvinos, S. Kounias and K. Sotirakoglou) that describes an algorithm for finding specific sequences. Part of the algorithm involves ...
0
votes
3answers
529 views

“Mathematical Induction”

I realize this question borders on not qualifying as answerable or mathematical enough, but I would suspect it relevant somehow. I'll remove it if it's not. If you look at some explanations of ...
0
votes
3answers
791 views

What does this range notation mean: 0:01 < x < 10:0

I've got a homework problem which states "use a range of 0:01 < x < 10:0" I'm thinking this would mean the range 0.00, 0.01, 0.02, ... 9.98, 9.99, 10.00 Has anyone seen this notation before ...
1
vote
1answer
319 views

Braket notation

$\def\pd#1#2{\frac{\partial#1}{\partial#2}}\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1}\def\ket#1{#1\rangle}$I am given that $$\bra{\theta,\phi}|L_+|\ket{l,m} = \hbar e^{i\phi} ...
2
votes
2answers
615 views

Tensors of order 3

I'm wondering what a tensor of order 3 looks like, and what it's purposes are. I've seen them written down before, but they look like matrices; I'm probably not understanding the concept well. How is ...
2
votes
2answers
263 views

What does $\mathrm{ms}^{-1}$ mean?

A baseball is hit with a velocity of $28.0 \ \mathrm{ms}^{-1}$. Should I just ignore this, or is it actually part of the question, what does it mean?
2
votes
1answer
1k views

Theta transposes to x

$$h(x) = \sum_{i = 0}^n \theta_i x_i = \theta^T x$$ I understand the above equation apart from the last bit on the right side. I think you have to read it Theta transposes to X. What does it mean? ...
27
votes
5answers
2k views

Who invented $\vee$ and $\wedge$, $\forall$ and $\exists$?

I can rather easily imagine that some mathematician/logician had the idea to symbolize "it E xists" by $\exists$ - a reversed E - and after that some other (imitative) mathematician/logician had the ...
4
votes
1answer
103 views

For a ring of char $p$ where $p>0$ is a prime, what does $R^{1/p}$ mean?

If $R$ is a ring of characteristic $p\gt 0$, what does $R^{1/p}$ mean? I am not sure how to search for it, since I don't know a name for it. From the notation, it seems to be a ring consisting of the ...
2
votes
1answer
90 views

Why is $\vec{x}$ in $A\vec{x}=\vec{b}$ in $\mathbb{R}^n$, when $A$ is an m x n matrix and $\vec{b}$ is in $\mathbb{R}^m$?

In my book on linear algebra (Lay), Lay writes A system of linear equations is said to be homogeneous if it can be written in the form $A\vec{x} = \vec{0}$, where $A$ is an m x n matrix and ...
0
votes
1answer
343 views

What does $\Rightarrow$ in the definition of a natural transformation mean?

In the definition of a natural transformation from http://ncatlab.org/nlab/show/natural+transformation it is said that a natural transformation is $\alpha : F \Rightarrow G$ (and the definition ...
5
votes
2answers
167 views

How should one interpret an interval like $[2,1]$?

Normally, when we're dealing with intervals $[a,b]$, it is at least implied that $a\leq b$. In this case, there are multiple equivalent ways to define what the interval actually is: ...
5
votes
1answer
2k views

What is $B'_L$ and why is it equal to 1?

I understand all the other ones, but the $B'_L$ has me stumped. What does it mean and why is it equal to 1?
3
votes
0answers
623 views

Notation for sampling random variate

Is there standard notation for sampling a value from a probability distribution? Like, if I had a random variable $X$, setting $x$ to whatever value I happened to sample from $X$ on this occasion? I ...
1
vote
1answer
283 views

The meaning of a notation from complex analysis

I have read the book Function Theory of Several Complex Variables of Krantz.But there is a notation I don't know what's it meaning. Can somebody give me a definition.Thank you. The notation is ...
1
vote
1answer
126 views

Conventional letters to use

I have already defined a group of errors of different types: $\omega_a, \omega_b, \ldots, \omega_z$ As well as another group of errors of various types: $\Omega_A, \Omega_B, \ldots, \Omega_Z$. Now I ...
18
votes
4answers
5k views

Why does drawing $\square$ mean the end of a proof?

To end a proof, I often write "as was to be shown" or "q.e.d". Both of these terms make sense to me as a reader. On the other hand, I feel a little strange to put down $\square$ although I saw it ...
0
votes
1answer
265 views

Notation of overloaded functions

I define an overloaded function, for instance as follows: $$f: \mathbb{Set}_1 \rightarrow \mathbb{Set}_3$$ $$f: \mathbb{Set}_2 \times \mathbb{Set}_2 \rightarrow \mathbb{Set}_3$$ My first question ...
4
votes
4answers
567 views

How to read permutation symbols like $(123)$?

I'd be grateful for some help reading permutation symbols such as $(123)$. Does it mean, when applied to a target sequence such as $(x y z w)$, "replace the element in the first slot of the target ...
1
vote
1answer
902 views

How to describe an algorithm with mathematical notation?

I often have to create new computer science algorithm. The problem come when I have to describe them in a scientific way. I don't know where I should look for to learn how to describe my algorithms ...
5
votes
2answers
797 views

Notation for the set of all finite subsets of $\mathbb{N}$

Is there a "standard" notation to denote the set of all finite subsets of $\mathbb{N}$? (or any set, not just $\mathbb{N}$) Thanks
0
votes
1answer
569 views

Multiset Notation

There is a multiset $A$, of length $n$ that can contain only $1s$ or $0s$. How would I notate that? How about for a multiset that could contain any number from $1-1000$, or that could contain any real ...
2
votes
0answers
149 views

The most appropriate way to cite a mathematical notation

I am writing a report with some mathematical formulae. I have a well-known book along side, very often, I just use the same notation as the paper. For instance, at the moment I write: $((x_n, ...
3
votes
2answers
251 views

Order of precedence of “()”, “implies”, “forall” and “and”

I would like to know the order of precedence of $()$, $\implies$, $\forall$ and $\wedge$. For instance, how many "$()$" possibly could we remove for the following formula: $(\forall a, ((b_0 \wedge ...
0
votes
1answer
73 views

Confusion on a differential notation

This is a notation I see in page 8 of Guy Barles and Espen R. Jakobsen, namely $$ \partial_t^{\beta_0}D^{\beta'}\phi(x,t) $$ where $\phi: \mathbb{R}^n\times[0,T]\longrightarrow \mathbb{R}$ is ...
4
votes
2answers
1k views

Math notation for location of the maximum

My question is about notation. I have maximum of the function $f(x)$. This can be expressed as $\max(f)$ How can I express in compact form that $x_0$ is the location of that maximum.
0
votes
1answer
119 views

Need Help in Tabular Notation to represent a Relation

I am stuck with a question. It is stated below. Let $R$ be a relation defined on the set of integers $\mathbb Z$ by the rule $aRb \iff |a-b|\leq 2$. Write the relation $R$ as a set. Now there ...
1
vote
1answer
298 views

Notation for Curve/Path Concatenation in Calculus Integrals

I can't find this online from a simple search, and I cannot remember. Given two curves/path $C$ and $D$, what is the notation for path concatenation when describing a path integral? Here are some ...