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.

learn more… | top users | synonyms

2
votes
1answer
61 views

Notation Question for summations

I came across this notation in a textbook of Algebra. With respect to the definition of linear independence in a Vector Space $V$. We define a subset $S = \{\alpha_i \ | \ i \in I\} \subset V$ as ...
0
votes
1answer
56 views

Is there a name for this theorem about the convergence of a function?

Let $f(x)$ be a continuous function over $\mathbb{R}$ such that for all $a < b$, we have $a < f(a) < b$. Then, for any $x < b$, the sequence $\{t_n\}$ defined by $t_0 = x, t_n = f(t_{n-1})$...
2
votes
2answers
467 views

Multiplying subscripts

I'm not too good with math, but once in a while I like to fiddle around with it. But one question has been bugging me lately. Let's say I have $x_{1} = 1$, $x_{2} = 2$, etc, $x_{352} = 352$. Is there ...
0
votes
1answer
56 views

Is there another notation for a characteristic of a domain of a measurable function?

Let $(X,\Sigma,\mu)$ be a measure space and $E\in\Sigma$. In measure theory language, one can prove that $\int_E f d\mu = \int \chi_E f d\mu$. Here, $\chi_E$ is not a function, but it merely means ...
7
votes
2answers
201 views

Why do we make a distinction between derivatives and partial derivatives?

The definition of a partial derivative is the "derivative of a multi-variable function relative to a single variable when all other variables are held constant". But isn't the regular derivative (for ...
0
votes
5answers
28k views

why the square root of x equals x to the one half power [duplicate]

Could someone explain how/why the square root of $x$ equals $x$ to the one half power? I know by definition it does, but is there any mathematical process we can go through to get from one to the ...
3
votes
3answers
68 views

whats the difference between $|v|$ and $||v||$?

$v$ being a vector. I never understood what they mean and haven't found online resources. Just a quick question. Thought it was absolute and magnitude respectively when regarding vectors. need ...
1
vote
2answers
62 views

What is this form of 'notation' called?

I was reading some of Max Tegmark's lecture materials and I found this little thing. Is there a name for it? Specifically, I am talking about $S_1$ R $S_2$ & $S_1$ R $S_2$ and the matrix. Is ...
2
votes
1answer
149 views

What's the difference between ]a,b[ and (a,b)?

Is there any difference between $]a,b[$ and $(a,b)$? If there is no difference, what would be the motivation of using $]a,b[$ over $(a,b)$?
0
votes
1answer
54 views

What is meant by this notation?

I found the following question: Let $\large f(x)=e^{x^2}$. Find and simplify $\large{f^{(3)}(x)}$. Is it asking to find the third derivative of the function? Which rule is used to find the ...
0
votes
1answer
334 views

Notation Question (Meaning of double inclusion symbols)

What does the notation $\subset \subset$ mean? In my class notes, our prof writes $\Omega \subset \subset \mathbb{R}^{n}$ to mean that "$\Omega$ is a convex subset of $\mathbb{R}^{n}$". Is that all ...
2
votes
5answers
106 views

What does $a$ mean in Taylor series formula?

I'm trying to code the Taylor summation in MATLAB, being Taylor's formula the following: I've also seen $a$ denoted as $x_0$ in distinct bibliography. Problem is that I'm not sure how should I ...
12
votes
4answers
2k views

Regarding the notation $f: a \mapsto b$

While I have come to understand that $f:a\mapsto b$ means that for input from the set $a$, the function will return a value from the set $b$, I am curious as to how far one may "drag" this notation. ...
1
vote
2answers
192 views

Ambiguity in Reverse Polish notation

Given the infix form: 1 * 2 * 3 What is the Reverse Polish notation? As I see things, two valid answers are: ...
1
vote
0answers
317 views

Tensor product symbol and convolution

The convolution of $f$ and $g$ is sometimes written as $f\ast g$ and sometimes as $f \otimes g$. Is convolution denoted by both of these symbols because the operations are related, or is it just ...
0
votes
2answers
57 views

Notational Question : (a) = (b)

What does the notation (a) = (b) mean? For context, a and b are elements of a ring. I have tried to find an answer by googling, but it's difficult to do this since I am not sure what to call it.
0
votes
1answer
27 views

A notation question on how to properly denote a function that takes inputs only of a certain form.

Suppose I have a set $B = \{n^2 + n + 1 : n \in \mathbf{N}\}$ and I want to define a function $g: B \rightarrow \mathbf{N}$ that only accepts as it's arguments numbers of the form $n^2 + n + 1$ for $n ...
1
vote
1answer
103 views

Name and notation convention for “unnormalized probability”

Given a finite set of non-negative numbers $S={s_1,...,s_n}$, we can divide them by a normalization constant $Z$ (i.e. their sum) to get a probability distribution. Then we typically say (and write) ...
1
vote
2answers
54 views

Confusion regarding notation on a matrix which have $I$ as an element

I'm given this transformation matrix for a linear map between two general vector spaces. I've never seen this notation before: $\begin{bmatrix} I &0 \\ 0& 0 \end{bmatrix}$, where I is the ...
0
votes
3answers
44 views

What is the correct notation for simplifying O notation?

For instance I want to say something like: "Here is the resulting runtime: $$\sum_{x}^{n}\sum_{y}^{x} (1) = \frac{n(n+1)}{2} \implies n^2 \implies O(n^2)$$" But what is the proper way to state this ...
1
vote
2answers
90 views

Basic Cartesian prodcuts

I am having some issues grasping basic ideas of Cartesian products. I am reading a PDF my professor gave us explain sets/Cartesian products. If $\mathbb{R}\times \mathbb{R}$ can be written as $\...
1
vote
2answers
81 views

Basic set notation - has this textbook made a mistake?

An answer to one question claims that if it is true that $B=\{a,b\}, G=\{\{a,b\}, \{c,2\}\}$, then it is also true that $\{B\}\subseteq G $ But wouldn't $\{B\}=\{\{a,b\}\}$ and there is no $\{\{a,b\}\...
1
vote
0answers
73 views

What is the correct notation for defining norms in measure spaces?

For a function $f \in L_2(R)$, we can define its norm as $$ \|f\|_2^2 = \int f^2(x) dx $$ If I use a different measure $\mu$, I can in turn define the norm as $$ \|f\|_2^2 = \int f^2(x) \mu (x) dx $...
1
vote
1answer
135 views

Explain the symbol $\bigvee$ in “Adventures in Stochastic Processes”

What does the symbol $\bigvee$ mean in statement 1.5.1.2? Thank you.
3
votes
2answers
132 views

Notation for quotient ring

I'm wondering where the notation for the quotient of a ring by an ideal comes from. I.e., why do we write $R/I$ to denote a ring structure on the set $\{r+I: r\in I\}$, wouldn't $R+I$ be more natural?...
0
votes
3answers
71 views

In set notation, why does the meaning of A differ from the meaning of {A}?

If the identity of a set depends on what the set contains, then wouldn't a set represented as A contain the same entities a set represented as {A} contains?
4
votes
1answer
124 views

What is the proper notation for integer polynomials: $\Bbb Y=\{p\in\Bbb Q[x]\mid p:\Bbb Z\to \Bbb Z\}$?

I would like to write down some of my thoughts on "the set of polynomials $p\in\Bbb Q[x]$ which map the integers to the integers" and I would like to know what the proper notation is for discussing ...
1
vote
5answers
743 views

What does this symbol “$\gg$” mean

I was reading a paper and came to a symbol as follows: "$\gg$" (e.g. $x\gg 5$). What does that mean? Is it larger than or has more information to mention? Thanks.
0
votes
2answers
43 views

Help with notation: $\triangle_{\gamma}\arg f$?

What is denoted by the term $\triangle _{\gamma} \arg f$ , where $f$ is analytic in region of complex plane and $\gamma$ is any curve in the region. Can anyone explain me this notation with example? ...
1
vote
2answers
142 views

Is there a factorial for factorials?

Is there a more succinct way to notate this? $$(n!)((n-1)!)((n-2)!)\cdots(2!)(1!)$$ for clarification, if I had asked a similar question, how to succinctly notate: $$(n)(n-1)(n-2)\cdots(2)(1)$$ I ...
1
vote
1answer
207 views

Use set notation to define vector or matrix?

I'm looking for a concise way to define the following (horizontal) vector: $$\mathbf{x} = [x_{-k}, \dots ,x_{k}]$$ where $x_k = \mathrm{i}$ if $k$ is odd and zero otherwise, and $|k| \le K $. So ...
2
votes
1answer
60 views

Comparison of notation for sets

Different authors use different notation, no question here...but doesn't this make the study of maths a little more difficult, always chasing different definitions of how a set is represented? I ask ...
3
votes
0answers
156 views

What is a common symbol for angles and what are semantic differences?

I've just seen that LaTeX offers at least three symbols for denoting angles: $\text{\sphericalangle}:\sphericalangle ABC \\\text{\measuredangle}:\measuredangle ABC\\\text{\angle}: \angle ABC$ I ...
0
votes
1answer
127 views

Comma after equation

ps: I have asked this question on http://tex.stackexchange.com/ (here) but is regarded as off-topic. So I moved it here. I have seen different ways in papers to put comma after equation. right ...
0
votes
2answers
289 views

Difference between two inequality symbols

I have come across the symbol $ \leqq$ in a paper I am reading. Is there any difference between this symbol and the symbol $ \leq $?
1
vote
1answer
1k views

Notation: using dot instead of argument

Is there any difference between: $f\left(\cdot , \theta \right)$ is continuous in x for each $\theta$ $f\left(x , \theta \right)$ is continuous in x for each $\theta$
0
votes
1answer
53 views

Notation for permutation corresponding to the action of a group element

Let $G \times X \to X,\ \ (g,x) \mapsto g.x$ be an action of $G$ on $X$, i.e., $e.x = x$ for all $x \in X$; $gh.x = g.(h.x)$ for all $g \in G$, $x \in X$. For a fixed $g \in G$, how should I refer ...
1
vote
2answers
2k views

What does the 'triple line equals' sign with a strikethrough mean?

I understand that the triple equal sign can mean "identical to" or "defined to be equal to", so intuitively, I assume that the triple equal sign with a strikethrough means "is not identical to" or "...
1
vote
1answer
63 views

Notation for quadratic form

My book states the following for a generalisation on $\mathbb{R}^k$: $\displaystyle\sum_{i,j=1}^{k} a_{ij}x_ix_j$ Is this the same notation as $\displaystyle\sum_{i\leq j=1}^{k} a_{ij}x_ix_j$ or is ...
2
votes
0answers
121 views

Lucas Number Equivalent of the Pisano Period?

I'm doing some work with the Pisano Period, and it's leading to also talk about the Lucas numbers $mod \ m$, and their period. Is there a specific notation already designated? Sticking with using a ...
1
vote
1answer
43 views

notation for equations solving

I have some notation questions on the following equation solving: 2+x=5$\iff$x=5-2$\iff$x=3 Would you read the above as "two plus x equals five if and only if x equals five minus two if and only if ...
2
votes
1answer
44 views

Is there a name for this structure?

I don't know what branch of math best characterizes what I'm thinking of, so I'll use a concrete example. Suppose you have four boxes, A, B, C, D Box A is an empty box Box B contains Box A ...
0
votes
1answer
84 views

What does the notation $Dx(a-bi-x)$ mean?

Sorry for completely newbie question, but could not the answer anywhere else. On the Wikipedia page about "Steiner inellipse" there is the following notation equating roots of cubic polynomial and ...
2
votes
1answer
958 views

Double left-right arrow meaning

While reading Hilbert's Tenth Problem (English version of a talk by Y. Matiyasevich) at page 3 I found: ...On the other hand let $$D(x_1,...,x_m) = 0 \quad (3)$$ be an arbitrary Diophantine ...
1
vote
2answers
461 views

Notation for summing all elements under the diagonal of a square matrix

I have a simple question: What is the notation for summing all elements under the diagonal of a square matrix? I appreciate your help.
12
votes
4answers
988 views

The origin of the function $f(x)$ notation

What are the historical origins of the $f(x)$ notation used for functions? That is when did people start to use this notation instead of just thinking in terms of two different variables one being ...
1
vote
1answer
57 views

Other than $\models$, is there standardized notation for semantic consequence?

It is common practice to use $\models$ both for the satisfaction relation between models and sentences, and for the corresponding semantic consequence relation. Question. Suppose I don't want to use $...
3
votes
1answer
85 views

Semidirect product notation convention

I was taught that if $G \simeq H \ltimes K$, then (by convention) $H$ is the subgroup that is normal, but I see on Wikipedia and elsewhere that other people use the convention that the above indicates ...
0
votes
3answers
84 views

Sequence Notation in Analysis

If real sequence is a function from the set $\mathbb N$ to the set $\mathbb R$ and function is represented by $(a,b)$, where $a$ is domain and $b$ is range, then why do we represent sequence only by $\...
1
vote
1answer
235 views

Notation for intersection of two sets each containing a set of intervals

I have a dataset about wireless devices describing when they were connected to a network access point $p$. Any given device can connect to $p$ for some duration, disconnect, and then later reconnect ...