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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9 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 ...
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1answer
40 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
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1answer
16 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
22 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
19 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
7answers
271 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 ...
7
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2answers
211 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 ...
3
votes
1answer
26 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 ...
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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
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0answers
42 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 $n\times n$ ...
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2answers
46 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 ...
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2answers
25 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
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2answers
43 views

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

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: ...
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0answers
58 views

Please help? Because I need help? [on hold]

Why does math have numbers????
3
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1answer
49 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
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1answer
20 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
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2answers
76 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
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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
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2answers
44 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
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2answers
55 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 ...
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4answers
87 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
410 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 ...
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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 ...
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1answer
20 views

Parallel operator in formula [on hold]

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 ...
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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
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0answers
22 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
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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 ...
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1answer
31 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
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1answer
53 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
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1answer
23 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
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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
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0answers
25 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
23 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?
1
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0answers
24 views

Congruence relations and congruence modulo m

What are some congruence relations appart from congruence modulo $m$? Also, is the congruence modulo m called that way because the sets of all the integers $0,1, ..., m-1$ form an isomorphic group ...
0
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0answers
24 views

Random Variables: Expected Values and Values computed from a data

Given a random variable $X : \Omega \rightarrow \mathbb{R}$, we have $E[X]$, which is called expected value of the random variable. I have one random variable $X$, ...
0
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0answers
12 views

Generalized superfactorial notation.

I would like to know if there's a general shorthand notation for denoting the following product: $$\mathcal{P}=a!\times (a-k)!\times (a-2k)!\times\cdots\times (a-nk)!$$ where $a$ and $k$ both ...
3
votes
1answer
78 views

$\leq$ V.S. $\leqslant$ [duplicate]

Is there a substantial difference between $\leq$ and $\leqslant$? My textbook uses both, but I could not tell why the authors selected one or the other. I asked my teacher, and she said that there was ...
2
votes
1answer
43 views

Do I write $f\in C^{-n}$ for an integrable function?

I have seen in a variety of texts that an $n$-differentiable function $f$ is written \begin{align} f\in C^{n}\Longleftrightarrow f^{\left(n\right)}\in C,\tag{1} \end{align} such as in Widder's ...
0
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0answers
13 views

Name for maximal number of pre-images under a function

Let $E$ and $F$ be sets and $f:E\to F$ be any function. I want a name for the quantity $$\displaystyle\sup_{y\in F}\operatorname{Card}(f^{-1}(y)).$$ I am currently calling it the "maximal ...
1
vote
2answers
30 views

Equality symbols in modular arithmetic

E.g., can I write $(a^{p})^{2p} \equiv a^{2p}=a^pa^p\equiv aa\equiv a^2\pmod{\! p}$? I often see equality symbols inbetween mod equivalences. The equality signs point out the equality is not ...
1
vote
1answer
45 views

Ambiguous? Notation for Cross-Correlation

Is it true that $f(t)\star g(-t)$ is not the same as $f(t)\star h(t)$ if $h(t)=g(-t)$? ($\star$ means cross-correlation). The example I was thinking of was if $g(t)=t$. Then $(f(t)\star ...
0
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2answers
24 views

How is the cartesian product $E^F$ defined?

For arbitrary sets $E, F$, how is $E^F$ defined? It seems to be the set of all maps from $F$ to $E$, i.e. $E^F := \{\phi : \phi\colon F \rightarrow E\}$? Is that right?
1
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1answer
24 views

How to simplify this expression using tensor notaion?

$\nabla^2 (\phi A)-A \nabla^2 \phi -2(\nabla \phi \cdot\nabla)A$ Where $A,\phi$ are any sufficiently smooth vector and scalar fields respectively.
1
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1answer
43 views

What does this symbol mean here in this context?

The colon ("$:$" sign) - I am seeing this a lot in Chapter 8 of PDE Evans, like this (page 497 of the 2nd edition): THEOREM 6 (Pressure as Lagrange multiplier). There exists a scalar function $p ...