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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1answer
157 views

Category of topological pairs

Is there a standard abbreviation for the category of topological pairs? I have searched for it in vain.
1
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1answer
174 views

notation for a torus

I am trying to search for the meaning of this notation but unfortunately it seems that wikipedia even doesn't have it. The book I am following uses the following notation for a torus: $\mathbb{T}^d = \...
2
votes
1answer
89 views

How to read this mathematical expression?

I am very much interested in machine learning. I would like to do research in this subject. But presently the mathematical language used in this subject is hard for me. Here is an expression in wiki ...
1
vote
2answers
102 views

Meaning of the set $\mathbb N^\mathbb N$

I came across a question which requires one to check if there's a bijection from the set $ \mathbb N^\mathbb N$ to another set. I've never seen a set defined this way and was wondering if this was ...
2
votes
3answers
151 views

What does $|A|$ denote in set notation?

What does $|A|$ of a set $A$ denote? Also, what does $A\leftrightarrow B$ of sets $A, B$ mean? I encountered this in one of my textbooks which said: Of two sets $A, B$ we know $|B|$ but $|A|$ is ...
1
vote
1answer
370 views

Why are Set Cardinality and Absolute Value denoted the same way?

When we have a set $A$, it is conventional to denote the cardinality of $A$ as $|A|$. When we have some number $n$, it is conventional to denote the absolute value of said number as $|n|$. My ...
0
votes
4answers
267 views

Correct formal interval notation

I can't find any definitive answer on this topic, maybe that's because there isn't one, but I figured if there was a place to ask then SE was it! To describe a set in which $x$ and $y$ are in the ...
2
votes
1answer
77 views

What is the meaning of $1_{a>b}$?

What would this mean: $1_{a>b}$ .. Based on the context, it could mean "$1$ if $a>b$ else $0$", but it's the first time I see it so help would be appreciated.
2
votes
1answer
245 views

Notation in group theory?

I have three questions on notation. What does the squiggly line mean in the following: $Aut(G) \cong Aut(G) \wr \mathbb{Z}_2$ What does $\rtimes$ mean in the following: $ \varphi :(Aut(G)\times ...
1
vote
1answer
81 views

Can the elements of a direct sum be thought of like that?

I've asked here about the tensor algebra, and I think that my problem is being able to realise the elements of a direct sum as linear combinations. Indeed the rigorous definition I have of the direct ...
2
votes
0answers
232 views

About the raised negative sign in some basic textbooks

In a math document recently (a UK A level test paper from the EdExcel board), I noticed that the negative/minus sign was raised and aligned to the top of the number. I'm interested to know whether ...
0
votes
3answers
62 views

Where V is a Vector Space, $\forall \overrightarrow{v} \in V, 0\overrightarrow{v} = \overrightarrow{0}$

I'm denoting all vectors as such: $\overrightarrow{v}$. Any variable without an arrow above is a scalar. Suppose $V$ is a vector space over $F$, with additive identities $\overrightarrow{0}$ and $0$ ...
1
vote
1answer
298 views

Probability, mathematical symbol

Good day, Would like to ask about the meaning of ^ in P(S^B) as shown in the image below. Thanks for your help!! Regards, Math noob
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2answers
90 views

Notation for the Set of All Finite $n$-Tuples from a Set $A$

Let $A \ne \emptyset$. Let $S = \{(a_1, a_2, \ldots , a_n) : a_i \in A$ and $ n \in \mathbb{N}\}$. Now I'm curious if there is a more concise (and standard) way of writing this set down?
97
votes
28answers
8k views

What are some examples of notation that really improved mathematics? [closed]

I've always felt that the concise, suggestive nature of the written language of mathematics is one of the reasons it can be so powerful. Off the top of my head I can think of a few notational ...
2
votes
1answer
47 views

The order of equalities

First note that I am not a mathematician. I do use it for my studies, but I am not reading anything remotely complicated in regards to maths. That said, here is my question: Today I found myself ...
1
vote
2answers
1k views

Positive and negative integer that is congruent to 0 (mod 5) and incongruent to 0 (mod 6)

I'm kind of confused by this because I thought 0 mod 5 = 0, and 0 mod 6 = 0 as well. So what's an integer that is congruent to one but not the other?
0
votes
1answer
185 views

What does this notation mean? $f(x|\theta)=\frac{3x^2}{\theta^3}I_{(0,\theta)(x)}$

Particularly I want to know what the meaning of $I_{(0,\theta)(x)}$ is here.
0
votes
1answer
56 views

We refer to X for standard notations and definitions from Y

I'm having problems with my mathematical English, so I'd like to ask for your help! Is it correct to write something like "Unless stated otherwise, we refer to [1] and [2], respectively, for standard ...
2
votes
2answers
247 views

Is there a proper term and/or symbol for an “agnostic” conclusion?

My question stems from the material conditional: $p \rightarrow q\\p\\\therefore\space q$ However, if $\bar p$ then the conditional is silent. I would like a way to represent this fact using, if ...
0
votes
1answer
236 views

Need help with Graph notation for a subgraph

I have an undirected, unweighted, simple graph $G=(V,E)$, with $V=\left\lbrace v_1, v_2, ..., v_n \right\rbrace$ and $E= \left\lbrace e_{vu} \mid v,u \in V,\mathrm{some-condition}\right\rbrace$, where ...
1
vote
1answer
65 views

Is $g(x,y) = f(\frac{x}{2},\frac{y}{2})$ correct notation?

I was a bit confused when I saw this statement $g(x,y) = 2f(\frac{x}{2},\frac{y}{2})$, and seeing it used in a double integral $\int \int g(x,y) = 2 \int \int f(\frac{x}{2},\frac{x}{2}) \, dx dy$. I ...
3
votes
3answers
1k views

Notation: subscript vs. superscript for coordinate vector fields

Some books write the coordinate vector fields with a subscript as $$\frac{\partial}{\partial x_i}$$ while some write it with a superscript as $$\frac{\partial}{\partial x^i}.$$ Is there a conceptual ...
0
votes
1answer
29 views

What is the name for this operator, and how can it be applied to multiple variables within the same equation?

My question is in two parts; the first is, what is the $|$ operator called? Here's an example of it in use: $$(x + 5)|_{x=3} = 8$$ My second question is, how do I use this operator for more than one ...
3
votes
2answers
101 views

Additive analogy of proportionality symbol

The relation of proportionality is quite abundant, and so for convenience there exist symbols, such as "$\propto$", to denote it. I would like to know if there is likewise a symbol to denote the ...
3
votes
1answer
155 views

What does this huge X mean that is written like the sigma notation?

I hope that you will not mind if I do not explain the background of this formula. The problem which I encounter is probably a simple one: What does the huge $\large \times$ mean and why is it written ...
2
votes
1answer
142 views

Why is $m$ used as the variable for slope in slope-intercept form?

I was wondering if you could answer a question I have on slope intercept form of a linear equation. I know its $y=mx+b$, but why is it $mx+b$? Don't get me wrong. I know that $m$ is the slope and $b$ ...
0
votes
1answer
62 views

Aggregating a vector of $1\times K$ into a vector $1\times J$, such as $J<K$

I am stuck with a matrix algebra operation: how do I do (and mainly which notation to use) to aggregate the numbers of a vector $1\times K$ into a vector of $1\times J$, such as $J$ is of course lower ...
2
votes
1answer
393 views

How can a single integral equal a triple integral?

Here is part of a discussion about the gravitational potential of a sphere: Let $dx$ $dy$ $dz$ represent an infinitesimal volume containing matter of density $\rho$ and mass $dm$. Then the ...
2
votes
2answers
1k views

Addition of Sets which isn't union

today a student asked me to prove $${A} \cup B \cup C = A+ B+ C- A\cap B - A\cap C$$ I really had no idea what precisely the "+" sign meant, they insisted, "You know you just add the sets together"; ...
2
votes
1answer
97 views

Repeated Summation function

I am writing a solution to a question, and the solution requires a lot of $\sum$ functions, is there a way to notate many $\sum$ functions in a row? for example is there one function that can simplify:...
3
votes
1answer
885 views

Notation for the set of symmetric matrices and symmetric positive definite matrices

I would like to know if there exists a notation for the set of symmetric matrices and symmetric positive definite matrices. For instance, the set of $N \times N$ matrices with real entries is denoted ...
1
vote
1answer
98 views

A definition check.

In Daniele Turi's "Category Theory Lecture Notes" from the University of Edinburgh, shouldn't "cone" be "cocone" in the definition of a colimit? A generic arrow $\tau : J\Rightarrow \Delta Y$ from ...
0
votes
3answers
8k views

Geometry notation: what does $m\angle ABC$ mean?

I see in some math formulation that a certain angle is called, let say $$\angle ABC$$ and sometimes there is a letter put in front of the angle $$m\angle ABC$$ What does the $m$ represent here? A ...
0
votes
1answer
102 views

Need help solving A×((B×C)×D) in index notation

How do I solve A×((B×C)×D) in index notation? I ended up with three Levi-Civita symbols and have no idea how to contract them. Thanks for the help!
0
votes
1answer
103 views

ENS is an abbreviation of?… [duplicate]

In CWM Mac Lane uses the term $\mathbf {ENS}$ for a category having as objects the subsets of a given set and as morphisms the functions from these sets to these sets. What is abbreviated by the ...
3
votes
2answers
479 views

Should I use parentheses when writing $\log$?

Should I be using parentheses when using things like $\log$ in LaTeX, and when handwriting? Should I use $\log x$ or $\log(x)$? If it's just one value or variable, I can see getting away with not ...
0
votes
0answers
52 views

Alternate convention in matrix multiplication?

I'm going through Halmos's Finite-Dimensional Vectorspaces. I noticed an oddity in a proof where the indexes seemed to be swapped when multiplying a matrix by a vector. I went back about 30 pages to ...
0
votes
1answer
64 views

Easy question concerning notation(Abstract Algebra)

I have a very easy question concerning some notation I have been coming across in Abstract Algebra (Dummit & Foote) Context: The relation between actions and homomorphisms may be reversed. ...
0
votes
2answers
970 views

Notation for integer between two values

This may be a silly question, but it has been a long time since I have used set notation to any real extent. How would I write that $i$ is an integer ranging from $1$ to $N$? My (possibly faulty) ...
2
votes
2answers
129 views

$\underset{x}{\bigvee} \mathfrak{P}x \wedge \underset{x}{\bigwedge} \underset{y}{\bigwedge}(\mathfrak{P}x \wedge \mathfrak{P}y\rightarrow x=y)?$

I'm reading Behnke's fundamentals of mathematics, he written that the following proposition: $$\underset{x}{\bigvee} \mathfrak{P}x \wedge \underset{x}{\bigwedge} \underset{y}{\bigwedge}(\mathfrak{P}x ...
1
vote
1answer
209 views

Summation notation with multiple subscripts

I am not sure how exactly to interpret this kind of notation. I understand the second one to read sum of over $k$ of $\gamma_{k,j}$ is equal to zero. Is that the same as: $\gamma_{1,1}+\gamma_{2,1}+\...
4
votes
4answers
334 views

Velleman - How to prove it - Do these two statements really mean the same thing?

Hello and thanks in advance for reading! In How to Prove it P29 Velleman writes: " In general, the statement y ∈ { x | P(x)} means the same thing as P(y), ... " In my understanding the first ...
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vote
0answers
549 views

What is the modern use of $\bigodot$ sign?

I've seen $\bigodot$ used in various contexts. It's used for a special set theory operation by some authors (say, Saks) and as sign for Hadamard product by a couple other authors (say, Wiener) in the ...
5
votes
0answers
421 views

Paul Erdős Joke.

I was watching the great documentary "$N$ is a Number" and in it Erdős tells a joke where he writes: PGOM LD AD LD CD Which means poor great old man, living dead, archeological discovery, legally ...
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votes
1answer
70 views

Sum of a set normalize by total items in set

This might be a be simple but I just want to make sure I didn't use the wrong notation. If I have a set of weighted terms, ${w_1, w_2, \dots, w_n}$ and the score is the sum of $w_1$ to $w_n$ ...
1
vote
2answers
113 views

Meaning of $\{ a,b \}$, and comparison with $(a,b)$

What does $\{a,b\}$ mean in real analysis? I'm also little bit confused about set definition Can you tell me the main difference between $(a,b)$ and $\{a,b\}$? Thank you.
1
vote
1answer
117 views

What is the standard notation for $\arcsin$

I found a lecture notes that claims the following. Is this standard? The notation $\overline{\text{arc}}\text{ sin }x$ is the inverse function of $\sin x$ restricted to $\left [ -\frac{\pi}{2},\frac{\...
2
votes
1answer
104 views

The origin of notation Z(f) and U(f) in algebraic geometry

It is common in algebraic geometry to denote a hypersurface $f=0$ in the affine space $\mathbb A^n$ as $Z(f)$ and the complement to the hypersuface by $U(f)$. What is the origin of these notations? I ...
2
votes
0answers
400 views

Set Notation with Intercepts

I really love set notation, and I'm finding myself using it more and more. My question is whether this would be a valid symbolic representation of intercepts. For example, take $$y=x^2-10x+16$$ ...