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
votes
2answers
46 views

Why do right angles have boxes in the middle?

The picture you are about to see below is an example of a right angle (it's equal to 90 degrees (1/4 of a circle)). So, why do these angles have "boxes" right in the middle? Maybe it's to identify ...
1
vote
5answers
97 views

Is 1^2^3 = $1^{2^3}$ or $(1^2)^3$ [duplicate]

Caret ^ signs can be used to describe the power of numbers. Is $1$^$2$^$3 = 1^{(2^3)}$ or $(1^2)^3$ How do you calculate it? Do you start with $2^3$ and then do $1^8$ or do you start with $1^2$ ...
1
vote
2answers
30 views

Are there definition of percent?

In a school I was taught that percent is the same as 1/100. But I think that definition is not rigorous enough because that would imply for example that $5+4\%=5+4/100=5.04$ but this seems weird. So ...
1
vote
1answer
24 views

quadratic field extensions of $\mathbb{Q}_p$

Today during class we proved that there were exactly three quadratic field extensions of the $p$-adic number field $\mathbb{Q}_p$. To prove this it was stated that it was enough to look at the group ...
0
votes
2answers
25 views

Notational difference, functions and mappings, talking about sets and classes

A Function is a set of pairs such that no two pairs have the same first member. My question summarized: What if I want to consider proper classes of pairs? The closest question to mine I could ...
0
votes
1answer
24 views

What does $b^*$ mean?

What is this notation, my book explains nothing of it. I've colored it in yellow! I am guessing it stands for $b^{-1}$ or $b^1$?
0
votes
1answer
17 views

Partial composition

Here is a simplification of my problem. I have the two following functions: $$ f : \mathbb R^{(m+p)} \rightarrow \mathbb R $$ $$ g : \mathbb R^n \rightarrow \mathbb R^m $$ with $m, p,n \in \mathbb ...
1
vote
1answer
37 views

What are these tick marks after the x, y, and z called?

What are these marks called and what do they stand for? This is for a Affine Transformation.
2
votes
1answer
39 views

When to use implies

I often wonder about notation and what is acceptable. I have seen many different ways of linking equations together, sometimes with just $=$ and others with $\iff$ or $\implies$. Now, I know when ...
0
votes
2answers
31 views

If I say, $f|_{k}$, what does that mean?

If I say, $f|_{k}$, what does that mean? Sorry to be short on words but I can not find it anywhere on google so maybe someone could explain it and what we typically use it for. I ran into the notation ...
1
vote
1answer
27 views

Shorter expression of a special conditions

Let $A$ be a set and $B$ a condition (can be either true or false). Is there any shorter description of the expression $$ x = \begin{cases} A & B \\ \emptyset & \text{otherwise} \end{cases} ...
3
votes
3answers
36 views

Notation for non-empty subset [duplicate]

To denote non-empty subsets, I repeatedly find myself writing $A\subset S, A\neq \emptyset$. Is there any established shorthand for this, you know, like $A\subset S$ can be seen as a shorthand for ...
0
votes
0answers
3 views

Notation for discrete cross-correlation

Consider two real valued vectors $x$ and $y$. Suppose $x$ is $m$ dimensional and $y$ is $n$ dimensional with $n \ge m$. What is good notation for the function which returns an $n-m+1$-dimensional ...
14
votes
11answers
5k views
+50

Dividing by 2 numbers at once, what is the answer?

Let's say i have 4/1/5. or 4 divided by 1 divided by 5. Are there any rules that i am allowed to use to stop any mistakes?, for example this has 2 solutions, 4/5 , and 20. Edit: Thanks for your ...
1
vote
1answer
55 views

What is meant by $ab$ on words $a$ and $b$ in $\{ab\ |\ a,b \in Σ^*\}$?

Given language $L$ := $\{ab\ |\ a,b \in Σ^*\}$, $Σ := \{blue, green\}$. Is the notation "$ab$" above taken to be word concatenation, such that $\{bluegreen\} \subset L$? What occurs when $L$ := ...
2
votes
1answer
30 views

“Evaluated at” or “at” notation

Normally a variable that is a function another variable would be represented as in the following fashion: $ V(t) $ (voltage as a function of time). However, my engineering professor (who also wrote ...
2
votes
6answers
51 views

Notation for sum of products

Is there a summation notation for the sum of products made two by two? I have the following expression: $$x_1x_2+x_1x_3+\dots+x_1x_n+x_2x_3+x_2x_4+x_2x_5+\dots+x_2x_n+\dots+x_{n-1}x_n$$
0
votes
0answers
63 views

Help in simplifying this double summation

Can I express the following double summation $$\sum_{(i,j)\in\mathcal{R}} A_{v_i} G(v_j-v_i)$$ where $\mathcal{R}=\{ (i,j) \in \mathbb{Z}^2,i \in [1:n], j \in [1:m]\}$ while $G(.)$ is any function ...
2
votes
2answers
27 views

What is word reversal $w^R$?

In the following context, what is the formal meaning of "reversal of word $w$"? The free monoid on $A$ is the syntactic monoid of the language $\{ ww^R\ |\ w \in A^*\}$, where $w^R$ denotes the ...
10
votes
0answers
119 views

Why is $J$ sometimes used to denote $\mathbb{Z}_{>0}$?

In older books, such as Rudin's Principles of Mathematical Analysis and Herstein's Topics in Algebra, I've noticed that authors tended to use $J$ to denote $\mathbb{Z}_{>0}$. Does anyone have any ...
1
vote
2answers
21 views

Reason for defining a quantity with “inf”

In some applications (in my case statistics) I find quantities defined using "inf", e.g. $ ABC = \inf\{x|F_X(x)\ge\alpha\}$ Why not define simply: $F_X(x=ABC) = \alpha$ I imagine it has something ...
0
votes
1answer
20 views

Mapping of elements notation - Cohn - Classic Algebra Page 13

So Cohn uses the notation that many have wanted to change to, being $xfg$ rather than $g(f(x))$, and I have had the example: Let $f,g: \mathbb{N} \to \mathbb{N}$, be given by $xf = x + 1,xg=x^2$, ...
1
vote
2answers
24 views

is there a notation to designate the induced homomorphism including base point?

Let $X,Y$ be a topological spaces. Let $f:X\rightarrow Y$ be a continuous function. Fix $x_0\in X$. Define $f_*([r])=[f\circ r]$ for every loop $r$ at $x_0$. Then, $f_*:\pi_1(X,x_0) \rightarrow ...
0
votes
0answers
27 views

Probability and calculus notation

I just need help to make sense of some notation that I have seen on a document related to monte carlo integration. There is a portion talking about expected values of a continuous random variable ...
1
vote
1answer
28 views

What does the notation $\equiv 1\ (\text{mod}\ p)$ mean?

I'm trying to understand the Fermat theory : $a^{p-1} \equiv 1\ (\text{mod}\ p)$ I know that $a\ (\text{mod}\ p)$ gives the remainder of division of $a$ by $p$. So what is $\equiv 1\ (\text{mod}\ ...
1
vote
0answers
24 views

Operator for scaling a function?

Let $\mathbb{F}$ denote the set of functions of the form $f: \mathbb{R} \to \mathbb{R}$. I am interested to know whether there exists a well-known linear map $T_\alpha: \mathbb{F} \to \mathbb{F}$ ...
1
vote
0answers
21 views

Product notation $\prod$ when product does not commute

This is kind of a dubious question, but is the product notation $\prod$ often used in noncommutative rings? For example, if $M_i$ are matrices, I guess the common definition of $\prod$ is $$\prod_i ...
2
votes
0answers
28 views

Better notation for a product

Let $A,B$ are two positive integers. Assuming that we have a product of the form $$ \prod_{\substack{a\mid A \\ \gcd(a,B)=1}}f(a). $$ Is there a better notation to be used instead of $a\mid A$ and ...
2
votes
1answer
25 views

What does the following set symbol notation mean

[6] x [6] -> Z I know it's the cartesian product of [6], but I don't quite understand what [6] means? Does it mean all numbers until 6, or is another way to write {6}?
2
votes
1answer
17 views

Incongruencies with derivatives and differencials

I read in Piskunov that the increment $\Delta y$ of a function can be written as: $\Delta y = f'(x) \Delta x + \alpha \Delta x$ And, when ${\Delta x\to 0}$ , $dy=f'(x)dx$ The problem is, doesn't ...
1
vote
1answer
46 views

When is Leibniz' notation for derivatives useful?

So Lagrange's $y'$ and Leibniz' $\frac{d}{dx}y$ seems to be the two most common notations for differentiation, but it seems puzzling to me that there are two notations for this. I've been taught ...
0
votes
0answers
17 views

Does the diagonal of a gradient exist?

If $\nabla \cdot \vec x$ is okay, why not $\text{diag}(\nabla)\vec x$? Should we write $\nabla \vec x$ or $\nabla \vec x^\intercal$ since the result is an outer product? E.g., if I want to write ...
0
votes
2answers
16 views

Notation for the “scalarization” of a vector with a single non-zero entry

Suppose I have a vector $v$ in the complex space $\mathbb{C}^N$ with only a single non-zero element. Is there a standard notation to replace the vector with a scalar equal to the non-zero value of ...
0
votes
1answer
43 views

Understanding a weird notation when proving a theorem

I'm reading a paper that's trying to prove a theorem. However there is a weird notation that I couldn't understand. First they present the theorem and then they present two claims. In the first claim ...
1
vote
0answers
47 views

What does $V^*$ represent in linear algebra?

If $V$ is a vector space, then what does the notation $V^*$ normally stand for? Thank-you
0
votes
0answers
14 views

Explaniation of symbols in Moment of Inertia

Im looking for an explaination of what the TWO axix symbols (x,y and z) in the down right next to the capital I (Moment of Inertia) mean. I have looked on google and youtube, all my math and physics ...
1
vote
3answers
41 views

What does “wedge” mean?

In Allen Hatcher's Algebraic Topology, $X\vee Y$ means the "wedge sum" of two (topological) spaces $X$ and $Y$. However, in $\LaTeX$, \wedge is the notation for ...
1
vote
0answers
23 views

Notation for gradients analogous to partial derivatives

Is there an equivalent of partial differentiation for functions taking multiple vectors as input? I mean the following. If we have a function $f(x,y)$, then a partial derivative is denoted as ...
7
votes
1answer
109 views

The meaning of a definition involving multiple sums with Bernoulli numbers

Reading a paper regarding Bernoulli numbers, and I stumbled onto a definition. First let $$\frac{x}{e^x-1}=\sum_{k=0}^{\infty}B_k\frac{x^k}{k!}$$ The author then goes on to define new terms. Let ...
0
votes
0answers
38 views

Exist some kind of irreversible transfomations on maths?

I know that this kind of transformation by itself without control can lead to contradiction because it value change depending the state of the function where you do the transformation. Anyway I want ...
4
votes
1answer
139 views

Unfamiliar notation in an AoPS paper

Here it is, from this paper: Proposition 5.1.1. The number of skyline polyominoes of area $A$ and width $w$ is $\left(\!\binom{w}{A-W}\!\right) = \binom{A-1}{w-1}$. I'm referring to the first ...
0
votes
4answers
43 views

Can someone explain the meaning of \ in operations with sets? [duplicate]

I have never faced with such operator... what does '\' mean? Does this expression make any sense? (A ∪ B) \ C = A ∪ (B \ C)
0
votes
1answer
28 views

Question about sums with a negative limit for the index

To me, it looks like we have $\;\sum_{i = 1}^{0} x_i = 0\;$ and $\;\sum_{i = 1}^{1} x_i = x_1\;$. What happens if I write the following? $$\;\sum_{i = 1}^{-123} x_i\;$$ Would this be defined?
0
votes
0answers
44 views

Is there a notation for the set of zero divisors?

While the multiplicative subgroup $R^*$ denotes the set of units, I wonder whether there is a notation for the set of zero divisors. It's quite painful to me everytime I write down zero divisors..
0
votes
0answers
18 views

Notation for bounds on derivative

I am working on a problem where the assumptions are that some derivatives are bounded. I want to refer to the individual bounds in the proof but there are about 7 of them in total. I am wondering if ...
0
votes
2answers
42 views

Correct notation for union of all elements in a set?

Say I have a set $H$ and I want to describe the union of all elements in $H$. How would I write that? I believe I've seen a big U with a subscript used before.
2
votes
1answer
26 views

Confusion about Notation for Bayesian Statistics

I'm currently trying to learn Bayesian Statistics but I keep losing time trying to figure out what exactly is meant by notation. Could someone answer the following for me? Let's say $X \sim ...
2
votes
2answers
184 views

Shorthand notation for partial?

If I am taking a regular derivative, and I want to show the process in detail, I'll do something of the sort $f'(x) = g'(x) + h'(x) - l'(x) ..... $, etc, using that "prime" notation. However, what ...
1
vote
2answers
37 views

Meaning of : Set is closed under finite intersections and arbitrary unions

I have been working through "Set theory for working mathematician" and near the end of chapter about real numbers there is a small bit of topology. Namely the natural topology $\tau$ on euclidean ...
2
votes
1answer
62 views

Is this notation nonsensical?

I know personally made notations are generally a bad thing, but I've not seen any reason to stop using the notation I've made, and it feels more natural to use. Now, this my seem like a biased ...