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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.

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notation - sigma algebra

i am trying to study borel sets and sigma algebra- and came across the following on wikipedia (https://en.wikipedia.org/wiki/Sigma-algebra): (However, after n flips of the coin, you may want to determine or revise your betting strategy in advance of…
Wouter
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Inserting parentheses to produce different values

Without grouping symbols, the expression $$\verb/2 ⋅ 3 ^ 3 + 4/$$ has a value of $58$. Insert grouping symbols in the expression $\verb/2 ⋅ 3 ^ 3 + 4/$ to produce the indicated values. A. $62$ B. $220$ C. $4{,}374$ D. $279{,}936$ I…
Marisol
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Set numbering representation

I want to represent proper element of sets. For example, $$ A=\{1,2,3,4\} $$ $$A(2)=2$$ But I wonder that this expression is right. Because I know that the set has not order. How can I do this??
KimJuntae
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Notation in Munkres' Elements of Algebraic Topology

What is $ R^{N} $ in section 1 of chapter 1 of the book Elements of Algebraic Topology by J.R. Munkres? Is $ N $ some natural number?
Chern
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Query description into mathematical notation

I need to formalize two query descriptions into mathematical notation. The source of this description, if anyone is interested in broader context. Query 1: Frequent routes The goal of the query is to find the top 10 most frequent routes during the…
Jernej Jerin
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In the expression $p^2=4q_1$, what does the small $1$ mean?

In the image below there is $p^2 = 4q$ and then a small $1$. What is the name/meaning of this notation? I have never seen it before and can't find what the meaning of it is. Help is appreciated! See this image:
Kottakji
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Question concerning big-Oh and small-Oh notation

What would the notation $a_n = (1+ o(1))b_n$ stand for? (And similarly for $a_n = (1 + O(1))b_n$).
user127022
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About the exact form of a gaussian kernel

Traditionally we define a gaussian function at a point x (assuming mean to be 0) as follows $$g_{\sigma}(x) = \frac{1}{\sqrt{2\pi \sigma^{2}}} \exp\left(\frac{x^{2}}{2\sigma^{2}}\right)$$ In some sources however, the exact form is given as…
Ujjwal Aryan
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Notation for binary permutation

Given a number $x \in \mathbb{N}$ , I want to write down following algorithm in a notation which can be written without the need for providing an example. Step (1): Find all unique prime factors $p_1, p_2, ..., p_n$ of $x$ ( $p_1 \neq p_2 \neq ...…
Daniel Marschall
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Notation of the average of a subset with a constraint

I'm quite new to mathematical notations, so please forgive me for my lack of skills in creating technically correct formulas. I came across a problem, when I have a variable set of numbers. Let the set $S$ be $\{53, 12, 4, 56.3, 30\}$. I need a…
Gabor Farkas
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Proper Writing of Functions of Vectors

Let $x \in \mathbb{R}^n$ and $y \in \mathbb{R}^m$. Consider a real-valued function $f = f(x,y)$. Which of the following is the more correct writing of this map, or are they equivalent? $$ f: \mathbb{R}^n \times \mathbb{R}^m \to \mathbb{R} \\ f:…
bcf
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Is there any symbol for intersects?

Given two polygons $A$ and $B$ the intersection of them is represented by the notation $A \cap B$ that returns a geometry (more precisely the set of intersecting points) resulting from the intersection operation. Is there any symbol for intersects…
user206695
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What does the $2$ in $\|Xw-y\|_2$ mean?

I was going through this link and I found the minimization expression. It says $\|Xw-y\|_2^2$. What is the significance of $2$ in the subscript? What does it mean? I understand that the double vertical lines mean the length of the vector.
Srikanth Guhan
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Ambiguous? Notation for Cross-Correlation

Is it true that $f(t)\star g(-t)$ is not the same as $f(t)\star h(t)$ if $h(t)=g(-t)$? ($\star$ means cross-correlation). The example I was thinking of was if $g(t)=t$. Then $(f(t)\star g(-t))(t)=\int_{-\infty}^\infty…
John
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Notation: express the minimum absolute value of a scalar function.

I have a pretty simple function that I want to express, but I'm having trouble coming up with a pleasing notation to express it. The function is: $h(y) = \arg \min_x |f(x, y)|$ $g(y) = f(h(y), y)$ In English, "$g$ is the value of $f$ at which its…
user52676
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