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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5 views

Understanding a theorem of Saint-Donat

In his thesis on K3 surfaces Saint-Donat proves the following fact (thm 6.1) Let $L$ be a line bundle on a K3 surface $X$ such that the linear system $|L|$ has no fixed components and the morphism ...
4
votes
0answers
59 views

Why do some authors write dx after integral sign? [duplicate]

Much has been said of the $dx$ notation used for integration on this site, but some writers of mathematics papers (especially physicists), write integrals as $$ \int dxf(x) $$ For instance, one way ...
1
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1answer
16 views

Origin of min/max notation

Here I am referring to the notation $x \wedge y = \min \{ x,y \}$ and $x \vee y = \max \{ x,y \}$. These seem to reference the corresponding usages in logic, where $\wedge$ means "and" and $\vee$ ...
1
vote
1answer
45 views

Strange Sigma Notation

How do I interpret this form of sigma notation? Do e1 and e2 take on all combinations of 1 and -1? If they do, what's the point? They just get multiplied inside the sum! FYI, this comes from equation ...
4
votes
2answers
240 views

Meaning of the backslash operator on sets

I am self-studying analysis and ran across this: $\mathbb R \setminus \mathbb N$ is an open subset of $\mathbb R$ My best guess for interpretation was this: the set $\mathbb R \setminus \mathbb N$ ...
0
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0answers
27 views

Set of functions and sequences

By $A^G$ I mean $\left\{x\colon G\to A\right\}$. Is it then to same to write $$ A^G=\left\{x=(x_g)_{g\in G}, x_g\in A\right\}? $$
3
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3answers
78 views

Set notation and the difference between $\subseteq,\in,\subset$.

What does it mean to say $\mathcal F$ is a family of subsets? (an example would be much appreciated :)) What would be a layman's example? When $B=\{b,c\}$ is it appropriate to write ...
4
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3answers
70 views

what is meant by $ f ∈ C^{2}[a, b] ?$

What is the meaning of $ f ∈ C^{2}[a, b] ?$ I think it says that $f$ is twice differential on $[a,b]$, isn't it?
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0answers
19 views

What is $\Lambda^{i}$ in the “Show that the highest weight of $\Lambda^{i}V $ is $\omega_{i}”$?

Question: What is $\Lambda^{i}$ in the "Show that the highest weight of $\Lambda^{i}V $ is $\omega_{i}$"? In this question, $\omega_{i}$ are fundamental weights. Context: Highest weight modules of ...
0
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1answer
28 views

How should one interpret the term x:2a?

I was asked about the right interpretation of $x:2a$. There are two ways to interpret this term $$x:2a=x:(2a)=\frac{x}{2a}$$ and $$x:2a=(x:2)a=\frac{x}{2}\cdot a$$ I am not aware of a convention in ...
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0answers
36 views

Order of Riemann tensor indexes and the Ricci Identity

I have seen the Ricci identity written variously as $R_{ijk}{}^l x^k = (\nabla_i\nabla_j- \nabla_j\nabla_i) x^l$ $R_{ij}{}^l{}_k x^k = (\nabla_i\nabla_j- \nabla_j\nabla_i) x^l$ $R^l{}_{kij} x^k = ...
4
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2answers
59 views

Notations: use of parentheses with “mod” and the “|” symbol

I'm working through a practice test with no available solutions, and I came across this question. Let $a,b,c,d,e$ be integers with $c>0$. Suppose that $a\equiv b\pmod c$, and that $d\equiv ...
2
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1answer
44 views

What is the ideal of a point in algebraic geometry?

I found a problem as follows: Find the ideal of a point $z$, denoted by $\mathfrak j_z\subset\mathbb Q[X,Y]$, and its conjugates in $\mathbb C^2$ as $z=(\sqrt{2},\sqrt{3})$. I tried to Google but ...
1
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1answer
24 views

Writing in Cartesian tensor form

Write the following in Cartesian tensor form $$(1) \nabla (\operatorname{div} G) \times \nabla\Omega$$ $$(2) (\operatorname{curl}(F)\times G)\cdot \nabla(Φ)$$ I have answers for these two questions, ...
0
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1answer
28 views

Set builder form for representing strings

Is there a way to represent strings or palindromes using set notation? For representing palindrome using set notation, I arrived at this notation $$S=\{ab^{n}c:N\; |\; n \geq 1 \land n \leq 3\}$$ I ...
0
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1answer
18 views

What is meant by $AB$ in boolean algebra?

I am endeavoring to teach myself Boolean Algebra. Oh what fun! From the questions I've read on this site, one of the most common notations I've seen is $AB$ (examples: here, here, and here). Problem ...
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2answers
23 views

How to replace a complex term in an equation using a function?

I have recently been working on a few models that look at mosquito predation. Now one of the peers wants me to add the complete equation of my model in the manuscript. I previously had the equation ...
2
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2answers
59 views

What is the meaning of the notation $]a,b[$? [duplicate]

I've seen the notation $]a,b[$ in several questions on this site, but I am not familiar with it. Can someone clue me in?
1
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1answer
67 views

Proof regarding notations

I tried to solve the following question: Let $f,g$ be non-negative functions such that $f(n)=g(n)\left[1+o(1)\right]$. Prove that $f(n)=\Theta(g(n))$. I looked on two cases: ...
2
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0answers
38 views

Clarification on the definition of $X^{\omega}$

I have never seen this notation before (graduated with a math degree a few months ago; not in school currently). Here's what I gather from Munkres' Topology: Given a set $X$, an $\mathbf{\omega}$ ...
3
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1answer
62 views

formula for summation notation involving variable powers

I need help finding the formula for this summation notation: $$\sum_{k=1}^n{k^{2k} }$$ or $$1^2 + 2^4 +3^6 +.....+n^{2n} $$ And preferably not involving calculus.
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1answer
462 views

What is the Scientific Notation of Zero?

This question was asked here, where the answer uses this description. The last line reads: "The special case of $0$ does not have a unique representation in scientific notation, i.e., ...
3
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1answer
33 views

Question concerning the universe of sets.

I am reading Charles Pinter's Introduction to Set Theory Every proper class is in one-to-one correspondence with the universal class $\mathscr{U}$, that is, the class of all sets [emph. added]. ...
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2answers
43 views

Notation of inf

In this paper (equation 4.1) the following formula is listed: $\inf_{u \in R} \left \{ \frac{\partial V}{\partial \boldsymbol{x}}f(\boldsymbol{x},u) \right \} < 0, \quad \forall \boldsymbol{x} ...
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1answer
108 views

Where Does F' in Rubik's Cube Group Singmaster Notation Come From?

Basic 90° : F turns the front clockwise 180° : F^2 turns the front clockwise twice -90° : F' turns the front counter-clockwise Why are we calling the -90° rotation F' and not -F? (source: ...
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3answers
34 views

What ring-sum of vector spaces can possibly mean?

I'm given this test assignment, and I can't decipher what it says. Would you kindly help me? Here's the assignment itself: Let $U$ and $W$ be sub-spaces of the linear vector space $V$ s.t. $U ...
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1answer
67 views

How to describe the Cartesian product $\mathbb{R} × \mathbb{R}$?

I am taking a discrete mathematics course in the spring and in an attempt to fully understand the material I am reading ahead. I came across this statement Let $\mathbb{R}$ denote the set of all real ...
3
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2answers
38 views

What are the notations $k^{\prime n}$ and $\varphi^n$ in algebra?

I would like to understand what the following problem says: Let $k$ be a commutative ring and $f\in k[X_1,\ldots,X_n]$. Let $k^\prime,k^{\prime\prime}$ be commutative $k$-algebras and ...
2
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0answers
22 views

Difference between (partial) order, preference, transitive relation operators

This question is partly about the difference between orders, preference relations and binary relations in the context where they are similar, but mainly about the use of the associated operator. The ...
0
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0answers
26 views

Summation notation confusion in the Cauchy-Schwarz Master Class book

On page 5 of "The Cauch-Schwarz Master Class", Steele talks about the normalization of sequences. He says that if a sequence, $ \left\{ {a}_{k} \right\}$ isn't made up of all zeroes, we can introduce ...
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0answers
10 views

name, notation for “block inner product” $X^H Y$

Given a set of $k$ vectors of length $n$, $X = [x_1, \dots, x_k]$ and another set of $l$ vectors of length $n$, $Y = [y_1, \dots, y_l]$, I'd like to to compute the inner product of every combination ...
1
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1answer
52 views

How to denote the set of all students who take the same class as some given student $s'$?

I have a set of Students: $S = \{s_1, \ldots, s_2 \}$. Now each student takes some class (doesn't matter what class). Now I need to have a set $X$ that contains all students that take the same class, ...
1
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2answers
40 views

Meaning of a symbol

I've seen the symbol "$B_\epsilon(a)$", but I don't know what it means. The context is limits of a subsequence. Here, $\epsilon>0$ is a real number, and the limit of subsequence $a_{n_k}$ is $a$, ...
0
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0answers
31 views

Powers in Latex not distinguishable [closed]

I am writing a document in latex. If I want to show x^2 it prints it exactly how I want it. How ever if I want to do x^(2-\beta) it will only have the first bracket in the power position and ...
0
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0answers
16 views

Wording: l2/SSE/Sum-of-Squares Objective Function

The least-square problem is a very common optimization problem, where the objective function describes the sum over squared residua $r_n$ with respect to a parameter vector $p$: $$p \mapsto ...
3
votes
1answer
66 views

What does “versin” mean?

$$\newcommand{\versin}{\operatorname{versin}}2\versin A+\cos ^2 A= 1+\versin ^2 A$$ I don't understand the word 'ver' in this equation. What does it mean?
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0answers
42 views

Math notation for expressions using logical (binary) masks on images (matrix)

I need to write up what I have written in matlab: I have an image (that is, a matrix) $K$ and some other matrix of the same size $M$ which acts as a mask which represents the values I would like to ...
0
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1answer
12 views

Question on notation: Using Conditional Sums to express the total distance traveled by a moving body with position $x=x(t)$

This is a question on notation Can I express the total distance $s=s(t_1,t_2)$ that a moving body has traveled using the following (conditional) sum? $$s(t_1,t_2) = \sum_{\forall [t_a,t_b] ...
6
votes
2answers
77 views

Blackboard bold, Bold, Fraktur, and Reserved Variable.

There seems to be an arbitrary choice of how one would want to represent the set of all real numbers. Most commonly, I've seen $\Bbb{R}$, followed by $\textbf{R}$, then by a reserved variable $R$, ...
4
votes
2answers
201 views

Why do we write $a^n$ instead of $^n\!a$ for exponentiation?

For subtraction I can understand why $2-3 = 2+(-3)$ since we read from left to right, but I don't see why this need apply to exponentiation. What benefit is there to writing the base before the ...
3
votes
1answer
20 views

Chain rule notation for composite functions

Suppose I have a function $ f(x, y, g(x, y)) $ How would I express $ \frac{\partial f}{\partial x} $? Using the chain rule, you'd naturally come up with $ \frac{\partial f}{\partial x} + ...
0
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1answer
45 views

Proper notation question?

Are these two ways to define a set both correct? $$\{Z_t|Z_t \in A_5 \& Z_t=Z_i \cap Z_k, Z_i \in A_2, Z_k\in A_3\}$$ and the same written in this way: $$\{Z_t|Z_t \in A_5 \& (\exists Z_i ...
1
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1answer
55 views

Why schemes are $(X,\mathcal O_X)$ rather than $(\mathcal O_X,X)$ or $\{X,\mathcal O_X\}$

Is there a reason why schemes are ordered pairs $(X,\mathcal O_X)$ rather than for example $(\mathcal O_X,X)$ or $\{X,\mathcal O_X\}$?
2
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0answers
12 views

Column and row vectors (spinors) in Landau-Lifshitz vol.IV Theoretical Physics

I am getting confused by the notation the authors of this book since they define: $$ \bar{\psi}\equiv \psi^\ast \gamma^0 $$ where (I suppose) $^\ast$ means complex conjugate and $\gamma^0$ is one of ...
3
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0answers
42 views

Why is the slope-intercept form of the equation of a line often written $y=mx+b$? Why $m$ instead of $a$?

After a quick google search, I read something about Conway suggesting the $m$ having to do with "modulus" ... This seems odd to me, but perhaps there is some mathematical reason? I've heard of the ...
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2answers
51 views

Notation question: $\ll$

I was perusing http://mathworld.wolfram.com/HighlyCompositeNumber.html and saw the following at the end: Nicholas proved that there exists a constant $c_2>0$ such that $Q(x) \ll (\ln x)^{c_2}$. ...
4
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1answer
61 views

notation (ab)use for random variables, distributions, pdfs/pmfs

This question is about notation for random variables (RVs), distributions and pdfs/pmfs and their common (ab)use as I recently got confused. Let $X,Y$ denote random variables. First, notations I ...
0
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1answer
55 views

Who introduced the term indefinite integral and the notation $\int f(x)dx$?

I find the notation $\int f(x)dx$ for the indefinite integral of $f(x)$ on some interval $I$ is both suggestive and confusing. On the one hand, this notation is very suggestive when we calculate ...
3
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3answers
86 views

Is there a concise way to notate 'There are exactly 482 x, such that Px…' in logical notation?

My prof has taught us that we can express the proposition $⟦$there are exactly two entities characterized by $P$$⟧$ thus: That proposition looks verbose, despite the fact that it references just ...
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2answers
34 views

An explicative definition of what is meant by $\{A_i\}_{i\in I}$?

What does $\{A_i\}_{i\in I}$ mean exactly? I know it's an index, but what exactly is that?