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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Notation for proof with Tensors

I'm working on proving For a second order tensor $\mathbf{A}$,$\mathbf{u}\cdot\mathbf{A}\cdot\mathbf{u}=0$ for all vectors $\mathbf{u}$ if and only if $\mathbf{A}$ is skew symmetric. Now, I ...
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0answers
11 views

Notation question about scalar products and bilinear forms

Quick notation question. Is it necessary to distinguish between a scalar product and say a bilinear form $A: V \times V^* \rightarrow \mathbb{R}^n$. Would it be recommended that say you define ...
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1answer
108 views
+50

Problem with notation in a thesis

I am struggling with section 3.3 of the following thesis https://smartech.gatech.edu/xmlui/bitstream/handle/1853/29610/grigo_alexander_200908_phd.pdf. Page 21 is fine, then the problems occur in ...
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1answer
22 views

Is there a notation for incomplete quotient

If $n, m > 0$ are integers and $m \nmid n,$ how to denote the incomplete quotient this division?
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1answer
32 views

What does this function notation mean?

My text tells me that the general term of a sequence can be looked at like a function: $ f:\mathbb{N}\rightarrow \mathbb{R} $ What does that mean translated into common english?
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1answer
30 views

Question About Group Theory Notation

I am having trouble understanding what "Universal Cover of $\mathbb{Z} \times \mathbb{Z}$" mean exactly. Thanks
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1answer
54 views

How to find the domains of functions $f(x) = x-5$, $g(x) = \sqrt{x-5}$, and of their sim?

I've been studying on Study Plan Practice, on MyMathLab for my College Algebra class. We're going over the Algebra of Functions right now and several things don't make much sense. The question is: ...
4
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1answer
78 views

Origin and usage of $\therefore$ and $\because$

I've recently read a book which used the sign $\therefore$ (for "therefore"). It was more or less clear from the context what was meant, but I looked it up among the AMS LaTeX symbols just to be ...
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0answers
20 views

The space of alternating multilinear forms

I was just wondering if there is a standard (or even just usual) notation for the space of alternating $k$-linear forms on an $F$-vector space. I know that this space is naturally isomorphic to the ...
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2answers
61 views

In composition of two mappings, can the outer mapping access the arguments of the inner mapping?

In composition of two mappings, can the outer mapping access the arguments of the inner mapping? Here is an example to illustrate my question and my thought. E.g. $f: \cup_{n \in \mathbb N} \mathbb ...
3
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2answers
50 views

Complex number (square) root notation.

A mathematician told me that the notation $\sqrt{a+bi}$ isn't used, instead we use $w=z^2$ and substitute. Is this correct? If yes, is there any particular reason we don't want imaginary numbers under ...
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2answers
33 views

How does one interpret functions of topological spaces?

Let $f: X \to Y$ be a map of sets. We are given that $X$ is a topological space. We are to show that there is a topology on $Y$ making $f$ continuous, and moreover, determine if this topology is ...
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1answer
27 views

Type theoretic existential introduction and proof with subtypes

I'm working through a book[1], on type theory and categorial grammar (for linguistic applications). Sadly, I ran into problems pretty early on. I'd be very grateful if someone could Explain the ...
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0answers
34 views

Would the growth rate for base 2 and 10 logs be the same?

Since $\log_{2}(x) = \frac{\log_{10}(x)}{log_{10}(2)}$ and $\log_{10}(2)$ is just a constant, would their growth rate be the same?
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0answers
36 views

What does this operator $\odot$ mean

I read this about the second fundamental form in Wikipedia and I’ve no idea what does $\odot$ mean? Does anybody know? $$II=-dN\cdot dP=\omega^3_1\odot\omega^1+\omega^3_2\odot\omega^2$$
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1answer
23 views

Lower Bound Omega Notation

I have to prove that some number $S$ is bigger than $\Omega(|V|)$, where |V| is the number of vertices. I read the definition of asimptotic notations, but I am still confused with the examples. Fot ...
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3answers
60 views

What's the correct type of brackets to use in a matrix? [duplicate]

I had my first day of Linear Algebra today, and we got introduced to matrices, one thing that kept nagging me though, was that I kept seeing matrices written in a few different styles, namely $$ A = ...
3
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0answers
67 views

Can $\mathbb A=\{f(x)\mid x\in\mathbb R\}$ be shortened as $\mathbb A=f(\mathbb R)$?

Can $\mathbb A=\{f(x)\mid x\in\mathbb R\}$ be shortened as $\mathbb A=f(\mathbb R)$? I saw this notation in the IMO olympiad training materials (the solution to the Problem 16 (IMO 1999 Problem ...
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1answer
35 views

Simple notation question about brackets

Is this notation correct? I am not sure about the brackets. $x^2=4$ $x=\{-2,2\}$ Thanks in advance.
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1answer
48 views

Number after binomial coefficient

What does the number 2 mean in this picture? link Thanks. Sorry I'm not a math expert. I need this to make a program in C to generate a trinomial triangle for a guy who asked it on StackOverflow ...
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3answers
54 views

Find the value of $m$ given that $\displaystyle\int_0^m \dfrac{dx}{3x+1}=1$

I have to find the value of $m$ such that: $\displaystyle\int_0^m \dfrac{dx}{3x+1}=1.$ I'm not sure how to integrate when dx is in the numerator. What do I do? edit: I believe there was a typo in ...
3
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1answer
73 views

What does $\mathbb{P}(d\omega)=dw$ actually mean?

I am currently reading S. Shreve's book Stochastic Calculus II, and I have a question regarding Example 1.6.4 (p.35-36) which describes a change of measure, but I am puzzled by the notation. ...
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2answers
264 views

Why two symbols for the same purpose? Summation and integral symbol.

I was reading this question. Im not mathematician but I like a lot and in spare time I try to learn something. My question is: reading the previous question of the link I understand (if Im not wrong) ...
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0answers
25 views

Notation for multiple chained indefinite integrals

The reduction formula for $\int\frac{x^ndx}{Ax + B}$ is given by $$ \int\frac{x^ndx}{Ax+B} = x\int\frac{x^{n-1}dx}{Ax+B} - \int\left(\int\frac{x^{n-1}dx}{Ax+B}\right)dx. $$ Is there any special ...
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Math symbol in German thesis from 1963

I have the following math symbol in a German thesis written in 1963. Is it anything more than just a function name? It is used in the following context and then goes on to state that "If the ...
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1answer
50 views

Unfamiliar notation. (actuarial science)

I am a math instructor self studying for the actuarial exam and I am trying to understand the following notation that I have encountered today. $$E[X \land d]$$ The explanation in the book told me ...
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0answers
20 views

Standard notation for Differential Equation Solutions

Quick question: I was solving a differential equation, and wanted to know which of these expressions is in the standard notation for an answer to a differential equation: (a) $y^{3/2} - x^{3/2}=7$ ...
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2answers
138 views

What is “ terminating reciprocals”

I meet a problem "What kinds of numbers have terminating reciprocals in base 60?", but I don't know what is "terminating reciprocals". Please help me, thanks.
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59 views

Why does the author define these “logical notations” for set logic with “if then” and &?

In Section 1.1 of "Set Theory for Computer Science", the author defines $ \forall x \in X. P(x) $ and $ \exists x \in X.P(x) $ as shorthand for $ \forall x.(x \in X \Rightarrow P(x)) $ and $ \exists ...
3
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3answers
311 views

Math 'equal to?' symbol

My teacher used the following symbol: $\boxed{\overset{\wedge}{=}}$ We had to write down a vector equation, and he said my direction vector $\begin{pmatrix}6\\2\\2\end{pmatrix}$ could be simplified ...
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3answers
67 views

What is the correct notation for flipping $a$ and $b$ values in a complex?

I'm currently doing some experiments on fractals and in one of my equation I need to flip the real and imaginary components of a complex number, such as : $$ z = a + bi $$ Becomes : $$ z = b + ai ...
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1answer
76 views

What are sets and classes in maths, and how are they related to $O()$ and $o()$ notation?

Are there many definitions of sets and classes in mathematics, as given in Formal definion of the notations used in measuring time complexity? And in particular, why the notation given in Fedja's ...
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1answer
153 views

Modular forms are arithmetic objects

What does arithmetic object exactly means? In an article, I found the following statement: modular forms are arithmetic objects. What this should means? Bests.
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1answer
52 views

What is difference between ≈ and ~?

I'm reading a quantum mechanics book, and it has the following equation: $$ \Delta x \approx \frac{\lambda}{\sin\alpha} \sim \frac{h}{mc\sin\alpha} $$ What is the difference between $\approx$ and ...
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1answer
41 views

What is the correct notation for showing something is a union of many sets?

If I wanted to show this would it look something like Whatchamacallets = (Things + Stuff + Pandas)
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2answers
28 views

Rationale for expressing as a direct sum and a direct product

In "Ireland and Rosen" page 35, it says if $R_1, R_2, ..., R_n$ are rings, then $R_1 \oplus R_2 \oplus \dots \oplus R_n = S$ is the direct sum of the $R_i$. Later in a proposition it says if $S = ...
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2answers
25 views

Notation for an integer being square-free

An integer $n \neq 0$ is square-free if $n$ is divisible by no prime square. Can you figure out any notation for simplifying this long description? It may be guessed that $p^{2} \nmid n$ for any ...
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0answers
27 views

What is the notation for pull-back and push-forward of an exponential map?

So there is a nice notation for a one-parameter group of transformations $\Phi_t$ corresponding to its infinitesimal generator $\boldsymbol X$: $$\Phi_t = \exp \left(t \boldsymbol X \right)$$ But ...
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3answers
105 views

Confused about the $\pm$ sign?

I have multiple questions about the $\pm$ sign, since it seems to confuse me in general... Question 1: Say I have $15=\pm(a+x)$, Can I use the distributive property so it becomes $15=\pm a \pm x$? ...
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35 views

Tilde Notation in Additive Combinatorics

A, B are some finite subsets of a abelian group. |A + B| ~ |A| The problem is I couldn't precisely understand what does ~ mean in that case. For example, it could be found in notes of Tao's ...
1
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1answer
47 views

$f\in C(\mathbb{R})$. What does it mean?

$f\in C(\mathbb{R})$. What does it mean? My guess is "Differentiable on $\mathbb{R}$" but I'm not sure.. Thanks.
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14 views

Compounding unary operators

I am working with the symmetric group $S_5$. I have 3 unary operators defined: $R$, $T$, and $O$, and I'm writing about their composition. Suppose I want to denote the compound operation of "$T$, ...
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30 views

Question on notation - real analysis

"There exists an open interval J containing a such that f(x) > 0 and g(x) > 0 for x in J \ {a}." What does the notation J \ {a} mean? Thanks
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1answer
33 views

Expressing a solution in interval notation

I am faced with this problem. I am told to express the answer in interval notation. |3x| > 12 I solve like usual, by doing this: ...
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1answer
17 views

The meaning of notation $\|x - x^*\|$

I was just wondering what $\|x - x^*\|$ in the following equation means: $$B(\epsilon) = \{x : \|x - x^*\|<\epsilon\} $$ Thanks.
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1answer
17 views

Understanding this characterization of Schwartz's space

While reading up on tempered distributions I came across this definition of Schwartz's space: $S(\mathbb{R}^n) = \{ f \in \mathbb{C}^\infty : \underset{x \in \mathbb{R}^n}{sup} \: \underset{\lvert ...
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37 views

formal notations

I have a problem of expressions with proper notations. If you can help me to give a formal and exact expression, it will be helpful. The specific description is Given a set of non-negative ...
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1answer
22 views

Notation of list expansion to a tuple

I have a set $S$ that I want to expand to a $|S|$-tuple. How is the notation for that? Currently I have something like that: $$ T = (f(x) : x \in S) $$ An example: $$ S = \{A,B,C\}\\ T = (f(A), f(B), ...
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1answer
79 views

Is $C(C(\mathbb R))$ notation for the set of continuous functions mapping $C(\mathbb R)$ to itself?

Given that in general functional analysis we have $C(\mathbb{R})$ being the set of all continuous functions, $f: \mathbb{R} \to \mathbb{R}$. However, could I use $C(C(\mathbb{R}))$ notationally to be ...
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1answer
66 views

What is $1 / \mathbf{Set}$ if $1$ is a one-element set and $\mathbf{Set}$ a category?

What does $1 / \mathbf{Set}$ denote? A pointed set is a set $X$ equipped with an element (a basepoint) $x \in X$. Let $\mathbf{Set_*}$ be the category of pointed sets and basepoint-preserving ...