Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [notation]

Questions 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.

Before asking a question on the site, please check if you can find your answer in Earliest Uses of Various Mathematical Symbols or the book A History of Mathematical Notations.

Alternatively, a textbook or paper usually takes the time to explain the notation they're using; please remember to mention where you've seen the notation you are asking about.

12848 questions
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Is there notation for subset containing the n smallest (or largest)?

Suppose I have a discrete set $A=\{a_1,\ldots,a_k\}$ and I wish to write an expression for the minimum of this set. I would write: $$ \min \{a_1,\ldots,a_k\} $$ But what if rather than just an element, I want the subset of $A$ containing the $n$…
Alexander Soare
  • 271
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How to write the division function in arrow notation

Basically the title, I'm not sure which one is formal: $$ \begin{aligned} division:\mathbb{R} \times \mathbb{R} &\rightarrow \mathbb{R} \cup \text{\{"impossible"\}} \\ (x,y) &\mapsto \begin{cases} x/y, & \text{if $y \neq 0$}…
Raftel
  • 41
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What does the notation $x \in \mathbb{R}^V$ mean where V is a set?

In the context of submodular functions, I encountered the following statement : For a vector $x \in \mathbb{R}^V$ and a subset $Y \subseteq V$ we define the expression $x(Y)$ as $\sum_{u \in Y}x(u)$. $V$ is a set. What does this statement mean ?
AnkurVijay
  • 647
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How to combine these 2 notations to be as simple as possible?

Consider the following question: Find the antiderivative of $f(x) = 6x \, (x^2+1)^5$. I have been using 2 notations and I would like to combine them. Notice that $[x^2 + 1]' = 2x$, so $6x \, dx = 3 d(x^2+1)$ Take $(x^2 + 1) = u$, then $6x$ is…
ByeByeYa
  • 79
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Can you Use $x \in S$ with Interval Notation?

If I have some variable $x$ and I want to show that it takes values from the set of integers $\{1, 2, 3, \dots, n\}$, is it correct to write the following: $$x \in [1, n]$$
Connor
  • 647
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What does the notation $\mathbb{Z}[X]$ refer to?

Suppose that a mathematician wrote, Let $f_0, f_1, f_2, \cdots$ be functions in $\mathbb{Z}[X]$ What does $\mathbb{Z}[X]$ mean? I am aware that $\mathbb{Z}$ is used to denote the set of integers. In other words, $\mathbb{Z} = \{\cdots, -100000,…
Toothpick Anemone
  • 1,104
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Bracket notation convention and accepted use

I'm writing an assignment right now and getting into some quite lengthy derivations, which caused me to wonder about bracket notation in math and what is best practice. There are three primary types of brackets I'm familiar with: the curly brackets…
mathwiz97
  • 35
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Notation for Double differentiation

I am asking this question simply out of curiosity. Why the double differentiation is denoted by $\frac{d^{2}f(x)}{dx^2}$ and not by $\frac{d^{2}f(x)}{d^2x}$ or $\frac{d^{2}f(x)}{(dx)^2}$. Is there any mathematical reasoning behind it? It seems like…
IY3
  • 92
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How to write $(\pm x,+y)\;,\;(\pm x,-y)$ in a compact form?

I want to show these duplets in a compact form $$(\pm x,+y)\quad,(\pm x,-y)$$ Then, is it clear to use $$(\pm x,\pm y)$$ or this only considers upper and lower signs together?
charmin
  • 220
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Can little-o be composite with itself? $o(o(1))=o(1)$

(I know this example here uses the $o_p$ which is a bit different than $o$, but I'm guessing the same rule applies to both). In one proof my professor used the following: $$\hat \theta_n =\theta + o_p (\frac{1}{\sqrt n}) $$ $$o_p(\sqrt n(\hat…
Maverick Meerkat
  • 1,230
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Resources for learning formal math notation

Does anyone know of some resources that provide a good introduction to common notation used in formal math? For example, I honestly don't know how to interpret $f: \mathbb{Z} \rightarrow \mathbb{Z}$. I feel like the most difficult time I have with…
123456
  • 131
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What is the meaning of "$\gtrdot$" and "$\lessdot$"?

Good day, I've been searching the web for the meaning of these operators: $\gtrdot$ and $\lessdot$. The reason I ask is because they are used symbols that look like operators and in the Katex documentation for supported functions they are listed as…
Juli TR
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What does $(x, y) \in \mathbb{R}^2$ mean?

In my homework, we are given the following set $M = \{ (x, y) \in \mathbb{R}^2\, |\, x^2 + y^2 \leq 1 \}$. Obviously, this represents the set of all points $(x, y)$ that lie within a circle of radius $1$. However, I'm confused about the…
Hannesh
  • 725
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What is a Non-Expansion?

I was reading this article from arXiv and I got confused on the first page, when it says, "a non-expansion for all parameter settings ensuring convergence to a unique fixed point." What is a non-expansion? What does the excerpt mean?
Venkataram Sivaram
  • 125
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Correct Notation for Loop

What is the proper mathematical notation for a loop structure such as the following? FOR i=1 to 10 BEGIN {Perform loop task} END; I am a programmer, but prefer to work on paper and so I am slowly teaching myself notation as a shorthand way to do…
Stackguest
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