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.

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What does $L^2$ on an arrow mean?

This post says If the $n$ observations in the sample $$\xi_n = [x_1, \dots, x_n]$$ are the realizations of n mutually independent random variables $X_1 \dots X_n$ having the distribution function $F_X(x)$, then $$F_n(x)\stackrel{L^2}\to…
whnlp
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Linked plusminus notation $\pm$

Given an expression with multiple $\pm$ where some of the $\pm$ have to behave the same. What is the correct notation? Colours? $$1 \color{red}\pm (x \color{red} \pm 3) \pm 4$$ Here the two red $\pm$ must either both be $+$ or both be $-$ and the…
Ben Crossley
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What does the math symbol $\propto$ mean?

I came across this symbol in my engineering class and I have never seen it before. Anyone know this?
C. K.
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what is the infinity subscript mean in a real number?

I have come across an inequation in an optimization paper. $$\left\lVert x\right\rVert _{2} \leq G$$ $$\left\lVert x\right\rVert _{\infty} \leq G_{\infty}$$ I know that the euclidean norm of a vector is bound by some real number $G$, but what does…
dawen
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Notation question: $E(x)$

I'm reading a 1975 paper by a Polish mathematician (Michal Misiurewicz) written in English and published in Astérisque. It uses some notation that I'm not familiar with, although I can understand it from the context. It seems he's using the notation…
anthonyquas
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Italic or upright letters for corners/points in geometry

What is the recommended typeface for "corner points" (e.g. "the triangle ABC"), distances (e.g. "the side AB"), etc. in geometry? Should it be upright or italic? Some say all constants should be upright (even $e$ and $\pi$) and since "corner points"…
mf67
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Making sense of a map, given a new domain and codomain

I'm having trouble making sense of a definition from Seven Sketches in Compositionality. Exercise 1.66. Let (P, ≤) be a preorder, and recall the notion of opposite preorder from Example 1.58. Show that the set $\uparrow p := \{p' \in P | p ≤…
A_P
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Problem converting matlab formula for relative frequency vector to mathematical formula

I have the following matlab code: range = 7; vector = [1 2 3 3 5 6 7 5 4]; freq = zeros(1,range); for i=1:range freq(i) = length(vector(vector==i))/length(vector); end I'd like to transform it into a mathematical formula but need help with the…
dsimmie
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Notation to describe vector

I want to describe a vector of n length, where each element is described by it's index. What is the correct notation? As it is now, to describe the vector [ 1 4 9 16 ] i write: $\{a^{2}\}_{a=1}^{4}$ But I can't remember if this is something i made…
user8111
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Define a set ordered by index?

I have the following, which uses set-builder notation, and where double square brackets means take the fractional part: $$a_k = \min\left\{ a_n\:\bigg|\:a_n =\left[\!\!\left[ \frac{nf_2}{f_1} \right]\!\!\right] \right\}_{n=1}^s$$ This reads: $a_k$…
Ewan Donovan
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What does it mean to add a number to a set?

I have the following problem: Show that the interval $[0,1]$ cannot be partitioned into two disjoint sets $A$ and $B$ such that $B=A+a$ for some real number $a$. My question is what does $B=A+a$ mean in this context? Does it mean $B=A\cup\{a\}$?…
Andrew Paul
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Having trouble reading this notation

I'm having trouble reading and understanding this mathematical notation about conformal meshes: $$\bar{\Omega} = \cup_{K\in T_{h}}K.$$ $\Omega$ is a domain, and $K$ is an element of $T_h$. $T_h$ is a conformal mesh of domain $\Omega$. One, is this…
EarthIsHome
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What is the difference between equal ($=$) and colons equal($:=$)?

From the context I guess colons equals add the implication of setting. As in $t:=0$ means lets set $t=0$.
ms2r
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A question about notation of transformations.

Let’s say we translate a triangle ABC to the triangle A’B’C’, my question is, how do we say A’B’C’? I believe it is said A prime, B prime, C prime, but why are we using the word prime here? Any connection with prime numbers or just a coincidence of…
Jamminermit
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A question about Riemann sums

Take: $$ (u*v)(k) = \sum_{i=-\infty}^\infty u(i)v(k-i). $$ $k$ is there, it's because you want to define $$ \ldots\ldots, (u*v)(-3), (u*v)(-2), (u*v)(-1), (u*v)(0), (u*v)(1), (u*v)(2), (u*v)(3), \ldots\ldots $$ etc. The number in the parentheses…
user1095340
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