# 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 $g(n)=\omega(f(n))$
1answer
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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 ...
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### Are there any standards we can use to communicate math, e.g. ISO standards, does Category Theory aim eventually to be something like this?

I'm finding it difficult to read and express ideas in a standard way, I'm working in Computer Science and there are so many different math languages ways of communicating ideas. Is there a standard ...