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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4
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0answers
45 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 $R$, ...
2
votes
2answers
83 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
16 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
37 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
42 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
11 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
38 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
60 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
51 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
83 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
47 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
9 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
44 views

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

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
15 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
37 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
43 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
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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
55 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 ...
3
votes
3answers
77 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 ...
2
votes
1answer
97 views

When was contemporary logical notation established

When contemporary fundamental logical notation was established? I mean basic symbols as used nowadays $\iff\implies\land\lor\lnot\forall\exists\vdash\models$.
1
vote
1answer
31 views

Summation with two running indices

I don't understand the notation of the following summation. $$ \sum_{i,j=1}^m \gamma_i \cdot \beta_{ij} \cdot \alpha_j$$ I first thought $ i, j $ would be increased simultaneously, but that would ...
0
votes
0answers
11 views

Notation for Markov Model

I have a statement that says: "Show that conditional on $X_m = i$, $(X_{m+n})_{n \in \mathbb{N}}$ is Markov($\delta_i, p$) independent of $X_1, \ldots X_m$". What does the notation Markov($\delta_i, ...
1
vote
3answers
40 views

What does this summation notation denote?

I am having trouble figuring out how this notation works, specifically how the intersection relates to the rest of the summation. It's just stuck there after it. I would greatly appreciate any help ...
1
vote
1answer
20 views

Comma vs pipe/vertical line in notation for conditional probability

What is the difference between the following expressions: $$P(X_1 < X_2 \mid \min(X_1, X_2) = t) \qquad \text{and}\qquad P(X_1 < X_2, \min(X_1, X_2) = t)$$ For context, I am trying to ...
0
votes
0answers
30 views

Notation for intersection of functions

Suppose $f,g : [0,1] \mapsto [0,1]$ are continuous, $f$ is non-decreasing, $g$ is non-increasing, and $f(0)<g(0)$, $f(1)>g(1)$. Is there a standard notation for the intersection point $x_0$ of ...
-1
votes
1answer
36 views

What is the meaning of |⋯| notation for an index subset?

I am currently working on a research project. In the attached image what does the capital $|I|$ and $|J|$ mean ?
3
votes
1answer
52 views

Notation of logarithms

Here's the problem: Me and my teacher are having a discussion about the notation of a logarithm. My teacher says that the only way of notating a logarithm is like this: $$^2\log\bigg(\frac 15\bigg)$$ ...
0
votes
2answers
33 views

What does a mini circle between f and h(x) mean?

I am currently doing a math problem and have come across an unfamiliar notation. A mini circle between $f$ and $h(x)$ The question ask me to find for 'the functions $f(x)=2x-1$ and $h(x)=3x+2$' $$f ...
3
votes
1answer
32 views

How to learn ideals and quotient rings?

I have difficulties to learn ideals of ring and how to operate with them. Is there somewhere a good tutorial on those? Like I saw from an algebra book the Artin–Rees lemma and it looked a bit scary as ...
0
votes
2answers
19 views

Divide elements of a matrix by row

Suppose I have a matrix that looks like this: $$A=\begin{bmatrix} 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 \end{bmatrix}$$ I want to divide each term by the sum of terms in that row, ...
1
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0answers
28 views

Notation confusion about sum of $\Lambda (n)$

This is hopefully a small point of notation I am missing. I am used to the first two equalities below. $$\sum_{n \geq 1} \Lambda(n) n^{-s} = \sum_{p \mbox{ prime}} \sum_{m \geq 1} \Lambda(p^m) ...
1
vote
1answer
37 views

Set theory - Can someone explain sequence operator?

I'm reading up on set theory and relation and I need help understanding this: Two sequences of the same element type can be composed to form a single sequence in such a way that the order of each ...
0
votes
2answers
34 views

Notation for the vector space of functions with $k$ continuous derivatives

I saw the following definition given at the mathworld web site: A function with $k$ continuous derivatives is called a $C^k$ function. In order to specify a $C^k$ function on a domain $X$, the ...
2
votes
1answer
43 views

Naming a function in a paper

I'm writing a paper (in physics), and I want use the same name for two related functions that have different domains. Please allow me to elaborate. I have function $f: R\longmapsto R$. I want to ...
0
votes
1answer
50 views

What does it mean to write $|||x|||$ rather than $||x||$?

I am familiar with the notation $||x||$ meaning some norm of $x$. I have just come across the notation $|||x|||$ (in a text that also uses the former for norms). What is the difference?
0
votes
2answers
85 views

Why “thin groupoids” are not ubiquitous?

Google search for "thin groupoid" finds surprisingly few (namely 7) pages. But "thin groupoid" is a term to denote an important notation of a groupoid with every loop being the identity. I met it ...
0
votes
1answer
19 views

Average Distance of an element and a set of elements

Let $a$ be an element and $B$ be a set of elements $\{b_1,\dots,b_n\}$ which would be the best notation to represent the average distance between $a$ and all the elements of $B$? One way to describe ...
1
vote
0answers
63 views

Summation verification

I have a particular polynomial $$ 1-10x+35x^2-50x^3 $$ Which can be written nicely as $$1-(1+2+3+4)x+(1\cdot2+1\cdot3+1\cdot4+2\cdot3+2\cdot4+3\cdot4)x^2$$ ...
1
vote
1answer
21 views

Expressing the nth element of a set

Let's say I have a set $S$ of infinite length. How can I express a function that returns the nth element in the set?
1
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1answer
40 views

In graph theory, what does $o(G)$ usually mean?

I'm completing a graph theory assignment, and one of the problems states, Prove that a tree $T$ has a perfect matching if and only if $o(T-v) = 1$ for every $v \in V (T)$. I'm not asking for ...