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

4
votes
2answers
2k views

In differential calculus, why is dy/dx written as d/dx ( y)?

In differential calculus, We know that dy/dx is the ratio of between the rate of change in y and the rate of change in x. In other words, the rate of change in y with respect to x. Then, why is dy/dx ...
13
votes
3answers
16k views

Element-wise (or pointwise) operations notation?

Is there a notation for element-wise (or pointwise) operations? For example, take the element-wise product of two vectors x and y (in Matlab, x .* y, in numpy x*y), producing a new vector of same ...
7
votes
3answers
3k views

Special arrows for notation of morphisms

I've stumbled upon the definition of exact sequence, particularly on Wikipedia, and noted the use of $\hookrightarrow$ to denote a monomorphism and $\twoheadrightarrow$ for epimorphisms. I was ...
1
vote
2answers
170 views

What does $y_i=f(\sum_j w_{ij}y_j)$ mean (in an artificial neuron model)?

While trying to understand artificial neural networks, I came upon an equation for finding the net input of an artificial neuron. Can someone explain this to me and what it means? Here is the original ...
1
vote
3answers
414 views

Probability proof, sequence of sets: help with understanding the notation?

I'm having some trouble with the formatting here, so here's a screenshot of the problem we were given: Let $\{ A_n \}_{n \geq 1}$ be a sequence of sets. Show that $$ \lim\sup\limits_{n\to ...
3
votes
3answers
2k views

Mathematical symbol for “and”

I have found some pretty complete lists (I think) of mathematical symbols here and here, but I don't see a symbol for the word "and" on either list. A person could easily just write the word "and" or ...
3
votes
2answers
1k views

Notation for a polynomial ring and formal polynomials

Given that we shouldn't say that "$f(z)$ is a function", shouldn't we also not write "$p \in k[X_1, \ldots, X_n]$ is a polynomial"? Along those lines, I usually write $p(X_1, \ldots, X_n) \in k[X_1, ...
2
votes
2answers
138 views

Is 2-multiset a valid term?

I am trying to describe the edges of an undirected graph that contains loops. On Wikipedia they are characterized as 2-multisets, meaning it has two elements which can be identical, and the order is ...
1
vote
2answers
165 views

Quick Question about Sequence Notation

If $b_n = \frac{1}{2n+1}$ does the notation $b_{n+1}$ make $b_n = \frac{1}{2(n+1)+1}$ or $b_n = \frac{1}{2n+2}$?
2
votes
3answers
1k views

Notation question on the colon symbol

I'm reading through the first chapter of Ahlfors's Complex Analysis book, and during the section on stereographic projections, he says that we can map any $z = x+iy \in \mathbb{C}$ onto the unit ...
14
votes
6answers
8k views

What software and/or language to use to take Math lecture notes?

I have a terrible hand-writing and I'm very good at typing, so I had an idea about taking my math lecture notes using a computer. I've tried using a simple syntax (using purely ASCII) but it's ...
2
votes
1answer
281 views

A question regarding the meaning of “lim”

I'm having an argument about what the notation of $\lim$ means. Assume you have $f_n: X \rightarrow \mathbb{R}$. Are the following two sets equal: $$\{ x \ |\  (f_n(x)) \ \text{converges} \} = ...
2
votes
1answer
108 views

Meaning of $C(I,\mathbb{R})$ and $C^{\infty}(I, \mathbb{R})$ related to continuous functions

What does this mean: ($f$ a function, $I$ an interval and $R$ the real numbers) $f \in C(I,R)$ Does it mean $f$ is an element of the collection of continuous functions with domain $I$ and range $R$ ...
2
votes
2answers
406 views

What does [n] mean here?

I am reading this document. What is the meaning of $[n]$ ? Is it power set of $\{1,2,3...n\}$?
14
votes
3answers
5k views

How did the square root get its shape?

I was wondering when in history did people start use the $\sqrt{}$ sign for square root, what did they use before, and why this curious nomenclature is adopted.
1
vote
1answer
122 views

Representing shortest distance of a matrix comparison

I have an input array of line segments (a,b)_1 ... (a,b)_n. Let's call it "S" so (a,b)_S_1 ... (a,b)_S_n. I have another array of the same construct, let's call it "I", so (a,b)_I_1 ... (a,b)_I_n. I ...
9
votes
4answers
8k views

Representing IF … THEN … ELSE … in math notation

How do I correctly represent the following pseudocode in math notation? EDIT1: Formula expanded. EDIT2: Clarification. (a,b) represents a line segment on a 1D line. a <= b for each segment. The ...
11
votes
5answers
6k views

Backwards epsilon

What does the $\ni$ (backwards element of) symbol mean? It doesn't appear in the Wikipedia list of mathematical symbols, and a Google search for "backwards element of" or "backwards epsilon" turns up ...
4
votes
2answers
382 views

Meaning of $\mathbb{R}[x]$

I ran into this expression in a paper I was reading, and I'm confused about part of the meaning. Here $u$ and $v$ are two polynomials. $$u, v \in \mathbb{R}[x]$$ I'm not really familiar with usage ...
2
votes
2answers
1k views

What is the mathematical symbol for the unique values in a vector?

I am looking for a symbol to represent the operation of taking unique values from a vector. So, say the symbol was $\theta$: $v = [0, 0, 0, 1, 1, 1, 3, 1, 2, 0]$ $\theta(v) = [0, 1, 3, 2]$ Or is ...
0
votes
2answers
1k views

Mathematical representation of the largest element in a set

I've looked but cannot find the mathematical way to represent the following: r = Max(x1, x2, x3) I want to mathematically show that r = max value of the set (x1, ...
2
votes
2answers
3k views

Prime notation for derivatives

This may seem like an overly trivial question, but I've just recently become confused about Langrange's 'prime' notation for derivatives (for example $f'(x)$). I know for sure that $f'(x) = ...
1
vote
0answers
304 views

Do the natural numbers include zero? And what should we call them, with or without zero? [duplicate]

Possible Duplicate: Is 0 a natural number? There seems to be no consensus, although perhaps one is gathering over the centuries to say yes to the first question and identify $\mathbb{N}$ ...
4
votes
3answers
380 views

What is the value of $1^x$?

I am trying to understand why $1^{x}=1$ for any $x\in\mathbb{R}$ Is it OK to write $1^{x}$? As the base 1 should not equal 1 for $1^{x}$ to be an exponential function? Is $1^{x}=1$ just because it ...
3
votes
3answers
4k views

What does max[] mean?

What does D = max[0; M(x)] mean? M(x) is a function.
6
votes
2answers
2k views

What does “$f\in C^2[a,b]$” mean?

What does this expression mean? $$f\in C^2[a,b]$$ More specifically, I don't know what $C$ means.
2
votes
2answers
426 views

Matrix transformation notation

I have a question about a transformation of a matrix. Lets say we have the following matrix $ M = \left[ {\begin{array}{cc} 4 & 3 \\ 4 & 3 \\ \end{array} } \right] $ Then I want ...
1
vote
2answers
177 views

Notation: $\mathrm{ord}_a(x)$ for $x\in \mathbb{Q}$

I'm familiar with the notation $\mathrm{ord}_a(x)$, when $x$ is an integer. However, I'm reading a book where this notation is used with $x$ rational. I'm not sure how to interpret this?
2
votes
2answers
83 views

Newbie question about the re-application of a function on its result

This is a newbie question, but I would be grateful for any reference that you could give. let $f(x) \in \mathbb{A}$, where $x \in \mathbb{A}$ Is there a symbol to indicate the repeated application ...
2
votes
1answer
171 views

What could the notation $l^\infty(\mathcal{F})$ mean, where $\mathcal{F}$ is a set of measurable functions?

In the book Weak convergence and Empirical Processes, by Aad W. van der Vaart and Jon A. Wellner, on page 81, the notation $l^\infty(\mathcal{F})$ appears, where $\mathcal{F}$ is a set of measurable ...
7
votes
3answers
3k views

Parenthesis vs brackets for matrices

When I first learned linear algebra, both the professor and the book used brackets like [ and ] to enclose matrices. However, in ...
3
votes
2answers
164 views

Notation help. What do $\mathcal{P}(A)$ and $\chi_{-}$ mean here?

Our math prof gave us this and we are not sure what to make of the notation, can someone give us a hand?
6
votes
2answers
2k views

Symbol for the cardinality of the continuum

The usual symbol for the cardinality of the continuum (i.e. the real numbers) is Fraktur $\mathfrak{c}$. However, I recall some sources also using $\aleph$ (with no subscript). This usage is not ...
3
votes
1answer
278 views

Inconsistent naming of elliptic integrals

This may be a question whose answer is lost in the mists of time, but why is the elliptical integral of the first kind denoted as $F(\pi/2,m)=K(m)$ when that of the second kind has $E(\pi/2,m)=E(m)$? ...
4
votes
4answers
399 views

A short way to say f(f(f(f(x)))) [duplicate]

Is there a short way to say $f(f(f(f(x))))$? I know you can use recursion: $g(x,y)=\begin{cases} f(g(x,y-1)) & \text{if } y > 0, \ \newline x & \text{if } y = 0. \end{cases}$
2
votes
1answer
628 views

What's the meaning of $x \choose y$ in the Catalan number formula?

What's the meaning of $\choose$ in this formula: $$C_n=\frac1{n+1}\binom{2n}{n}=\frac{(2n)!}{n!(n+1)!}\qquad\mathrm{for}\;n\geq 0$$ Is it a division?
1
vote
3answers
255 views

If $V$ is a vector space, that what is $V^\mathbb{N}$?

Notation question (I believe the notes that I'm reading uses pretty common notation): Let $V $ be a vector space over a field $K$. What is $V^\mathbb{N}$? Is it a vector space of infinite dimensions? ...
5
votes
4answers
660 views

Long division notation (census of nations)

The Wikipedia article on long division explains the different notations. I still use the European notation I learned in elementary school in Colombia. I had difficulty adapting to the US/UK notation ...
12
votes
6answers
1k views

In written mathematics, is $f(x)$a function or a number?

I often see notation/wording like "let $f(x)$ be a continuous function" or "let $f(x) \in C^0(\mathbb{R})$". I would say that $\sin$ and $x \mapsto \sin(x)$ are functions, while $\sin(x)$ is a real ...
0
votes
2answers
156 views

Conjecture about the set of Sphenic numbers

Sum of a set of sphenic numbers can't be equal to the sum of any other set of sphenic numbers. By that I meant, Say S is the set of sphenic numbers. Let S$_1$ $\subset$ S. Then there is no such ...
3
votes
2answers
1k views

Definition of $C_0$

This is probably a silly question, but a couple of people that I have talked to have had different responses. Does $C_0$ denote the set of continuous functions with compact support or the set of ...
3
votes
2answers
2k views

Proper notation for distinct sets

Consider I have two sets that neither one is a subset of the other (for example, the set of prime numbers and the set of odd integers). Is there a specific notation that combines the meanings of both ...
7
votes
2answers
2k views

Precedence of set union, intersect, and difference?

Online, I have read contradicting opinions on whether intersect should take precedence over union (by analogy to logical ...
18
votes
3answers
88k views

What does E mean in 9.0122222900391E-5?

I am not a mathematician(IANAM), however I wish I could be. My question: I often find this at the bottom of pages. Page generated in 0.00013899803161621 Sometimes, I come across Page ...
13
votes
4answers
2k views

Notation question: Integrating against a measure

Suppose $\mu$ is a measure. Is there any difference in meaning between the notation $\int f(x)d\mu(x)$ and the notation $\int f(x) \mu(dx)$? Many thanks.
9
votes
2answers
72k views

what does ∇ (upside down triangle) symbol mean in this problem

Given $f(x) = \frac{1}{2}x^TAx + b^Tx + \alpha $ where A is an nxn symmetric matrix, b is an n-dimensional vector, and alpha a scalar. Show that $\bigtriangledown _{x}f(x) = Ax + b$ and $H = ...
7
votes
4answers
691 views

Can Leibniz Notation Be Treated As a Quotient?

Why is saying $\frac{dy}{dx}\frac{dy}{dx}=y\frac{d^2y}{(dx)^2 }$ not valid? Does Leibniz notation (and thinking of it as an infinitesimal quotient) not work for higher-order derivatives?
7
votes
1answer
321 views

Why do lambda and pi go together?

In measure theory, we have "lambda systems" and "pi systems". Pearl's message passing algorithm has "lambda messages" and "pi messages". Is there a reason that lambda and pi go together?
14
votes
4answers
628 views

Solving (quadratic) equations of iterated functions, such as $f(f(x))=f(x)+x$

In this thread, the question was to find a $f: \mathbb{R} \to \mathbb{R}$ such that $$f(f(x)) = f(x) + x$$ (which was revealed in the comments to be solved by $f(x) = \varphi x$ where $\varphi$ is ...
1
vote
1answer
465 views

Einstein notation - difference between vectors and scalars

From Wikipedia: First, we can use Einstein notation in linear algebra to distinguish easily between vectors and covectors: upper indices are used to label components (coordinates) of ...