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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2
votes
2answers
45 views

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

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
vote
1answer
22 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
votes
0answers
28 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
votes
1answer
57 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.
5
votes
1answer
401 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
votes
1answer
31 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]. ...
1
vote
2answers
38 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} ...
2
votes
1answer
101 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: ...
2
votes
3answers
29 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 ...
-4
votes
1answer
64 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
votes
2answers
37 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
votes
0answers
21 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
votes
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 ...
1
vote
0answers
9 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
vote
1answer
50 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
vote
2answers
39 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
votes
0answers
31 views

Powers in Latex not distinguishable [on hold]

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
votes
0answers
11 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
64 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?
1
vote
0answers
28 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
votes
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
76 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
181 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
votes
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
vote
1answer
54 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
votes
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
votes
0answers
40 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 ...
1
vote
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
votes
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
votes
1answer
52 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
votes
3answers
85 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 ...
1
vote
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?
4
votes
1answer
48 views

Is there any reason I can't use the $\cdot$ (dot product sign) instead of $\times$ (multiplication sign)?

Do note that I have read this question. However, I don't think it's quite the same question. When dealing with simple number multiplication, I actively try to use $\cdot$ instead of $\times$. Take ...
1
vote
2answers
10 views

Rationale behind tuple notation for structured sets

Defining structured sets typically involves the convention of using a tuple of some sort; for example, the real line can be thought of as the quadruple $(\mathbf{R},+,\cdot,<)$. But this convention ...
0
votes
1answer
23 views

Riemann integrable proof and notation

For Riemann integrable proof, I see $f \in \Re(\alpha)$. Also I see $U(p,f,\alpha)$. What does $\alpha$ stand for? Also to prove Riemann integrability, what do I do at very first step? I know my ...
1
vote
2answers
45 views

Clarification about notation for one-sided limits

Is $\lim_{x \to 3-0} f(x)$ the same as $\lim_{x \to 3^-} f(x)$, and is $\lim_{x \to 3+0} f(x)$ the same as $\lim_{x \to 3^+} f(x)$? Could anyone clarify this for me please? Thanks
1
vote
1answer
45 views

What does $\overline{f}(x)$ mean? [closed]

I need to solve this, but I don't know what the $\overline{f}(x)$ notation means. (I don't know anything about the context, I've just seen it on Facebook.) $$f(x) = 2e^{4x} +1$$ $$\overline{f}(x) = ...
0
votes
2answers
32 views

Clarification on quadratic ring notation

My Abstract Algebra text is using the notation $\mathbb{Z}[1 + \sqrt{-5}]$ and calling it a "quadratic integer ring." Just to clarify, $\mathbb{Z}[1 + \sqrt{-5}]$ is simply the set $$ \left\{ a + b(1 ...
1
vote
1answer
16 views

Notation in Srednicki's QFT

In the book Quantum Field Theory by Srednicki, equation 21 for the commutators of the generators of the Lorentz group is ...
1
vote
1answer
38 views

Why do the notation of the set of positive integers and the set of positive reals are different?

I read from my lecture notes that $\mathbb{R}_+^*=\{x|x>0\}$ and in http://mathworld.wolfram.com/PositiveInteger.html that $\mathbb Z^+$ is the positive integers. Why do we have to put plus to ...
3
votes
1answer
46 views

Good confusion-avoiding notation for iterated commutators?

I am doing some complicated and tedious calculation on iterated commutators. A typical term in my calculation looks like $$[x_a,[[[x_b,x_c]-x_d,x_e],[x_f,x_g]]]\text{.}$$ (I am considering ...
0
votes
0answers
25 views

Notation for selectors

I hope there is some agreed notation for this. The idea is very similar to DOM (or CSS) selectors, but on mathematical (or logical) formulas. I'll explain this with an example. Imagine I have some ...
0
votes
0answers
10 views

Verification and presentation of anisotropic sobolev space results

Hi I am interested anisotropic Sobolev spaces. Can someone with knowledge of this topic check if the following is correct in presentation. I am finding it hard to find a good book which deals with the ...
2
votes
1answer
44 views

Notation for the class of all cardinals

I have seen the notation for the class of all ordinals to be $\rm Ord$ or $\rm On$, is there an analogous notation for the class of all cardinals?
7
votes
1answer
1k views

What is the name of this letter? [closed]

I found the symbol below on an article, but I don't know its name. Thanks
2
votes
0answers
56 views

Notation $x^n=(x_1,\dotsc,x_n)$

In a book on statistics I saw the notation $x^n=(x_1,\dotsc,x_n)$ and wondering how common this is in measure theory/statistics. More precisely it is about a probability space ...
0
votes
1answer
15 views

Notation for all k-tuples that can be constructed from a set

Is there a generally accepted notation for a $k$-tuple that is constructed from a set? I have a set $\mathcal{A}$, and need to sum over all possible $k$-tuples (denoted $t_k$). Right now, I'm using ...
1
vote
0answers
11 views

Notation to express affine relationship

As you know, if we have a linear relationship between two variables $x$ and $y$ : $y=ax$, this is usually denoted by , $y\varpropto x $ y is proportional to x. The question is if they are affinely ...
4
votes
3answers
80 views

Why is $\mathbb{Z}^{+}$ sometimes used to denote the natural numbers?

This does not really make sense to me for several reasons: The integers are usually constructed using a given construction of the natural numbers Historically natural numbers were conceived of ...