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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3answers
47 views

Is there any symbol for intersects?

Given two polygons $A$ and $B$ the intersection of them is represented by the notation $A \cap B$ that returns a geometry (more precisely the set of intersecting points) resulting from the ...
1
vote
0answers
10 views

Convolution notations and some miscellanous convolution questions

Convolution between distributions over the real number line, as it is mentioned in the optics course in my uni and also in wolfram is defined as: $$f(t) * ...
2
votes
2answers
47 views

Why does unary minus operator sometimes take precedence over exponentiation, and sometimes it doesn't?

How should I evaluate 2*-2^3? Which one of these two is the correct one? 2*((-2)^3) 2*(-(2^3)) I was wondering what was ...
2
votes
3answers
73 views

Is there official notation to represent “perform an operation n times”?

I would like to know if you can represent the idea of say, $$n^n$$ n amount of times without defining a function. For example: $$1$$ $$2^2$$ $$3^{3^3}$$ $$4^{4^{4^4}}$$ $$5^{5^{5^{5^5}}}$$ and so ...
2
votes
1answer
67 views

What is this semi-circular symbol in the middle of a formula?

I have tried every search term I can think of but I can find no way of knowing what this symbol between the (a) and the trP means: Some context here, Point 2 in the third paragraph. Original image ...
2
votes
1answer
23 views

Expressing a differentiable map and curve in a parametrization

This is a question mainly about notation that I just cannot seem to understand. I'm reading Do Carmo's book "Riemannian Geometry" on page 7. Here is some context: (Here, $\alpha : (-\varepsilon, ...
3
votes
0answers
25 views

Interpretation of composite of random variable

Let $~f:[0,1] \to[0,\infty]$ be a measurable function bounded by $c \in \mathbb R$. Let $X_1,X_2,..,X_n \sim i.i.d ~\text{uniform}(0,1)$. How do I interpret the following statement: $$ Var(f \circ ...
2
votes
1answer
72 views

What is the meaning of $:s$ after a mathematical symbol?

I started to read a book about regression analysis, and I faced this latex notation: $e_i$:s, where $e_i$ is a residual. What is the meaning of "$:s$"?
0
votes
1answer
78 views

Why does $\bigcap_{m = 1}^\infty ( \bigcup_{n = m}^\infty A_n)$ mean limsup of sequence of set?

Why does $\bigcap_{m = 1}^\infty ( \bigcup_{n = m}^\infty A_n)$ mean the limit superior of sequence of set? I'm not getting it. ${A_n}$ is a sequence of set in $S$. I do know what limsup means ...
2
votes
0answers
28 views

What's the advantage of using bra-ket notation over inner-product notation?

Both notations look pretty similar, and appear similar when undergo algebraic operations. Apart from personal taste (aesthetics) concerning commas ($\langle \phantom{\cdot},\phantom{\cdot} \rangle$) ...
0
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0answers
43 views

Math, logic symbol for “instance of”

I saw a discussion of a possible symbol for "example," but I need "example/instance of." There is of course $a \in S$ which is a is a member of/in S, but is there a specific way of stating $a ...
1
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0answers
21 views

asking about the meaning of a notation in a 1942 article

In this article http://projecteuclid.org/euclid.bams/1183505105 what is the meaning of the notation $YX\wedge$, that is what does it mean when you write the notations for two sets together side by ...
0
votes
1answer
44 views

How to insert Gothic letters in Word? [on hold]

I do not manage to find in any of the options provided by Word the real Gothic letters used my German mathematicians in their original works. Noe even under the two "gothic" rubrics. just some sparse ...
1
vote
1answer
24 views

How to express outer sum in a matrix form?

So I have the following equation for a matrix $\mathbf{B}$ given $\mathbf{A}$: $$ b_{ij} = \sum_k \sum_l a_{ki} a_{jl} $$ The question is if there is anyway that I can write that one compactly in ...
0
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0answers
27 views

How is the second part of a dual number called?

A complex number $a + bi$ has a real part $a$ and an imaginary part $b$. But, what about dual numbers $u + v\epsilon $? I have seen the non-real part $v$ been called the infinitesimal part. Is this a ...
-3
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0answers
24 views

Rewrite the following relationships using function notation. [on hold]

Rewrite the following relationships using function notation. Question 1 options: a) An airplane needs to travel 400 km. Determine a function for the speed of the airplane, with respect to time. b) ...
11
votes
6answers
317 views

What is the significance of using “$a$” vs “$x$” in this text?

I'm a web development guy currently learning Calculus and am having some trouble understanding the seemingly unwritten rules of variable naming conventions in mathematics. I've read several other ...
8
votes
2answers
228 views

Does this math formula with $1/PI\begin{cases}^\infty_{-\infty}\end{cases}$ mean anything?

I happened upon an image on the Internet and I wondered whether the math on the chalkboard means anything. Using Google's image search, I found three other related images. Piecing together ...
4
votes
1answer
31 views

Notation for the set of holomorphic differential forms

I used to write $\Omega^p(M)$ for the set of $p$-forms on $M$ and $\Omega^{p,q}(M)$ for the set of $(p,q)$-forms on a complex manifold $M$. Now some authors use $\Omega^p(M)$ to denote the set ...
1
vote
2answers
33 views

Notation for a unit vector

If I have a vector $\vec{v}$, is there a standard concise notation for the unit vector in the same direction of $\vec{v}$ that is $\frac{\vec{v}}{|\vec{v}|}$?
2
votes
0answers
47 views

Is there a name or symbol for the matrix division resulting in a scalar?

I am not talking about the inverse matrix, $A^{-1}$ which gives $A\times A^{-1}=I$, but rather the operation $\frac{1}{n}tr(\space\cdot \times A^{-1})$, which gives 1 when applied to a $n\times n$ ...
0
votes
2answers
48 views

Matrix notation in handwriting

I understand that typically matrices are printed in bold to distinguish them from other mathematical entities with the same symbols. However I find it difficult to actually handwrite in bold. With ...
1
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1answer
28 views

What does the $2$ in $\|Xw-y\|_2$ mean?

I was going through this link and I found the minimization expression. It says $\|Xw-y\|_2^2$. What is the significance of $2$ in the subscript? What does it mean? I understand that the double ...
1
vote
2answers
31 views

Game Theory: Can someone explain the notation used in the definition of “best response”

I am reading a paper which states that that the best response correspondence of a player is mapping: $B_i(s_{-i}): S_{-i} \Rightarrow S_i$ such that $B_i(s_{-i}) \in arg\ max_{s_i \in S_i} ...
2
votes
2answers
46 views

What do the symbols $\mathbb{Z}$ and $\mathbb{Z}_n$ mean on this discrete math problem? [closed]

Currently I have come across a problem set which I cannot decipher or begin to ask or search because I do not know what kind of notation or problems these are. Please circle the best description: ...
-16
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0answers
64 views

Please help? Because I need help? [closed]

Why does math have numbers????
3
votes
1answer
57 views

Correspondence between Ext group and extensions (from Weibel's book)

I am trying to understand the proof of Theorem 3.4.3 from Weibel's book Introduction to homological algebra. The statement is the following. Let $R$ be a ring. Given $R$-modules $A$ and $B$, an ...
1
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1answer
27 views

Can somebody explain the notation $f \in C^4$

To give some context the full question is: Suppose $f \in C^4$ in a interval containing the root $\alpha$ and that Newton’s method gives a sequence of iterates $\{x_k\}$, $k = 0, 1, 2, \dots$ which ...
1
vote
1answer
22 views

Set builder notation for matching element pairs

I have a set of pairs, $S = \{ \langle a,b \rangle_1, \langle a,b \rangle_2, ..., \langle a,b \rangle_n \} $ where $a$ is not unique amongst the pairs. If I want to express the extraction of all the ...
4
votes
2answers
77 views

How I can express in a pure symbolic way common reasoning? Examples inside.

I have a broad question here, I know, but I will go define it clearly through examples. I want to know how express reasoning in a pure symbolic way, with no words, this is possible? Example: I was ...
0
votes
1answer
14 views

fourier series notation question

Find the fourier series for the given function $$f(x)=-x \quad \text{for } -L\le x < L, f(x+2L)=f(x)$$ this is a question from my book, and im just wondering about one thing and that is what does ...
3
votes
2answers
46 views

What does the multiply sign mean in set

A question about set notation. What does the multiply sign here mean? $$\omega = \times_{i\in N}T_{i}$$
2
votes
2answers
57 views

What does $\mathbb{R} \setminus S$ mean?

What does $\mathbb{R}\setminus S$ mean? I am not getting it what it actually means. I have found it manywhere in real-analysis like in the definition of boundary points of a set. Can anyone tell me ...
1
vote
4answers
92 views

How to write the set of all permutations on a set $n=\{1, 2, \ldots, n\}$

Let $n ∈ N$. Let $S_n$ denote the set of permutations on $\{1, . . . , n\}$. For any $σ ∈ S_n$, define $sign(σ) := (−1)^N$ , where $σ$ can be written as the product of $N$ transpositions. Now, let ...
4
votes
2answers
418 views

What is meant by the delta equivalent sign?

What is the meaning of the delta equivalent ($\overset{\Delta}{=}$) sign? I met this in a communication theory text. It said, signaling rate: $r\overset{\Delta}{=} 1/D$ symbols/s or also called ...
0
votes
0answers
19 views

Meaning of complement of vertex and edge sets

I am reading about maximum bipartite matching and everywhere I look there is thing: $$ U':=U\setminus M $$ Sometimes it's written like this: $$ U':=U\setminus\cup M $$ where $U$ is a set of vertices ...
0
votes
1answer
20 views

Parallel operator in formula [closed]

I need to use some formulas, but i don't understand, what i am supposed to do with a parallel operator (used on electrical resistance, if it makes more sense that way). What does this expression mean? ...
3
votes
1answer
40 views

What does “$\mathbb{1}$” mean in this document?

I understand everything in this document on the first page except the following: \begin{align} \overline{\int_a^b}f&=\inf\left\{\int_a^b\psi:\psi\geqslant ...
1
vote
1answer
18 views

What is the correct way of writing a vector element?

When using the convention making a label bold to indicate a vector, should you still use the bold if you are only referring to a single element of the vector? for example, which of these methods of ...
0
votes
1answer
30 views

Notation about factors

What is the name (if there is one) of the "full factorization representation" of a number, in which also the powers of the factors are (recursively) decomposed until all the numbers used in the ...
0
votes
1answer
55 views

Reverse Polish Notation Quadratic formula

The quadratic formula is $$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ I tried converting this to RPN; I am new to doing this, and I have thus: b-ac*4*-b2^+±a2*/. Am I ...
0
votes
0answers
23 views

What do the ellipses mean in $x^TW_{\dots ij}$

I cam across this notation: $x^TW_{\dots ij}$. I don't understand the notation. Why are there 3 dots? Source: http://jmlr.csail.mit.edu/proceedings/papers/v28/goodfellow13.pdf, top of second page, ...
0
votes
1answer
16 views

Notation for piecewise equations with vertical lines

I feel silly for asking such a simple conceptual question, but it's something that's been bugging me for a while. Is there any notation that makes it possible to define a piecewise equation that ...
1
vote
1answer
32 views

What is the meaning of expressions of the type $f(\cdot)$ (function (dot))?

Simple question, fully expressed in the Title line. Is the dot within the parenthesis intended to mean, "any possible function"?
3
votes
1answer
54 views

Why are power sets called power sets?

Why are power sets called power sets? What is so powerful about them?
0
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3answers
39 views

Some questions about notation in “$[T]_\alpha^\beta$”

I just have a few questions about the general meaning of the notation "$[T]_\alpha^\beta$". I would really appreciate if someone would dumb it WAY down to the most basic level (no assumptions, no ...
0
votes
1answer
24 views

S-indexed Family of A's vs. a Family of A's indexed by S

I looked at here, and here, and here, to understand the terminology used regarding indexed family of sets (but I still left with some questions): Take S as the set $S=\{1,2,3\}$ we define: 1) K ...
0
votes
2answers
34 views

Proof $\sum_{i=1}^{n}x ^i=O(n)$

I just started working with Big-O notation. Proof: for which $x$ is $\sum_{i=1}^{n}x ^i=O(n)$ true. First case: $x>1$ $\sum_{i=1}^{n}x ^i=s_n=x\frac{x^{n+1}-1}{x-1}$ and $\lim_{n->\infty} ...
3
votes
0answers
28 views

Notation for Christoffel symbols used by Gödel in “An example of a new type of cosmological solution of Einstein field equations of gravitation”

I have difficult to understand the meaning of the notation used by Gödel in the article cited in the title of this post. You can find it here: http://www.lygeros.org/10552b.pdf In the second page ...
0
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0answers
25 views

What does $]-\pi, \pi[$ mean [duplicate]

I sometimes see a notation like $]-\pi, \pi[$, but I don't know how it is different from $[-\pi, \pi]$. Could you tell me what it means?