# Questions tagged [notation]

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.

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### Ravi Vakil's notation $\operatorname{Proj}_A S$

I saw the notation $\operatorname{Proj}_A S$ for a ring $A$ and a graded $\mathbb{Z}^{\geq 0}$-graded ring $S$ being used in Ravi Vakil's notes on Algebraic Geometry. I first came across the notation ...
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### How is $A_3^3$ evaluated?

I stumbled upon the expression below, but I don't know how it is evaluated. Any help will be appreciated. $A_3^3 = 6$ Edited 1: It is a random expression that happen to be on a clock face which I hope ...
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### Notation to represent constants as variables and solve for them in a function

I have a classic probability density function in the literature of the form $$f(x) = \frac{4x}{\left(a^2b^2\right)} \Sigma(x, a, b)$$ where $\Sigma(x, a, b)$ is a complicated function full of ...
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### What does $\sum_i\sum_j$ mean? eg, $\sum_i\sum_j\frac{\rho_1^i}{i!}\frac{\rho_2^j}{j!}$

I have a basic question, and I haven't found a confirmation if this is correct: If we have the notation $\sum_n n$, means the same as $\sum_{i=1}^{n} i$ so $i$ runs from its minimum value until its ...
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### Is it proper integral notation to use “x=” in the bounds of a definite integral?

So, several years ago I skimmed through a calculus textbook and some of it stuck, some of it didn't. Now several years later I'm finishing up my second Calculus class at university, and I'm a little ...
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### Big-Omega, how do I prove or contradict?

How do I prove or contradict the following: $$\alpha\cdot n^k-b\cdot n^{k-1}=\Omega(n^k)$$ where $a,b>0$ and $k\ge1$
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### What is notation “$1_{\text{something}}$”? eg, $E(1_{\{X\leq t\leq X+Y\}})$

In this mathStackExchange here, use notation $E(1_{\{X\leq t\leq X+Y\}})$. What is this notation?
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### Best notation for $\mathbb{Z}_m^n$ [closed]

This is an easy question. Which notation do you think is better for the set: $A:=\left\{x=[x_1,\dots,x_n]: x_i\in \mathbb{Z}_m\right\}$, where $\mathbb{Z}_m=\left\{i:0\leq i < m \right\}$. I've ...
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### Distance Formula in Regression Context / Support Vector Machines

I am studying data science via "introduction to statistical learning in R". In chapter 9, we are learning about support vector machines and the maximal margin classifier. I generally ...
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### How do I prove that $f(n)=o(g(n))$ if and only if $g(n)=\omega(f(n))$

I don't know how can I prove this: prove that $f(n)=o(g(n))$ if and only if $g(n)=\omega(f(n))$
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### Double bars around poset?

Given a poset X that is contractible, I have a document that says: "If $H : \|X\| \times I \rightarrow \|X\|$ is a homotopy to the constant map" What does the $\|-\|$ signify? I have no idea ...
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### Different vector notations

I've encountered at least the following vector notations: $\overline{a}, \ \underline{a}, \ \vec{a},$ and a. Are they alternative notations for the same thing, or is $\vec{a}$ only for physical ...
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### Integral with set in the differential

I encountered several integrals by now that integrate over a "set of differentials" or is with respect to a set respectively, like the (physicist) partition function of a polymer with ...
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### Typesetting a covector

I understand the notation of upper and lower indices for components of vectors and covectors, but when I write a vector not in component form I use an over-arrow notation e.g. $\vec r$. Is there a ...