# Tagged Questions

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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### What group does $\mathbb{G}_m$ denote?

What group does $\mathbb{G}_m$ denote? I saw it used here.
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### Set notation - problem

I have problem with a notation used in an information theory course. Let $N = \lbrace 1,\dots, n \rbrace$ for $n\in\mathbb{N}$. What does $2^{N}$ mean/denote?
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### Express this mathematically

Sorry it has been a while. I have three variables, $X, Y, Z$. Every $X$ has a different number of $Y$ and every $Y$ has a different number of $Z$ so how do I express the total number of $Z$? For ...
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### How does the different use of | cause a difference between these equations?

I have the equations $$sMAPE = n^{-1}\sum_{i=1}^n\left|\frac{y_i - f_i}{(y_i+f_i)/2}\right|$$ and $$sMAPE = n^{-1}\sum_{i=1}^n \frac{|y_i-f_i|}{(|y_i|+|f_i|)/2}$$ but I don't understand what $|$ means....
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### If $\Delta$ is the Laplace operator, what are $| \Delta |$ and $|\Delta +1|$

Assuming $\Delta : H^2(\mathbb{R}^n) \to L^2(\mathbb{R}^n)$ be the Laplace operator, then: What is the exact definition of $| \Delta |$? What is $|\Delta +1|$ also? This answer to another ...
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### Question about interpreting asymptotic results

Suppose I have the following asymptotic: $$\{n \in \mathbb{Z} \cap [1, X] : f(n) \text{ is good}\} \sim cX$$ as $X \rightarrow \infty$ for some absolute constant $c$ where "good" means some desired ...
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### When using sigma notation, why is “1” put as value?

First of all, I never really learned exactly what Sigma notation is, and although I understand the basics, there are some things that are confusing me. I'm trying to convert the following algorithm to ...
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### what does the inverse membership symbol means?

I know that the symbol $$\in$$ stands for membership, but what does the symbol $$\ni$$ stand for? Because I know that in the set membership, one symbol stands for subset and the other ones for ...
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### Notation issue regarding differential equations

I am given the following problem: Find a basis of solutions for the equation: $u^{iv} + 2u'' + 3u = 0$ The notation is an exact duplicaticate of what our professor used in his notes. Does anybody ...
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### How to formally write a property of a specific coloring of a graph.

I have a doubt about how to write a statement in rigorous logical notation. I have a graph whose nodes are partitioned in some subsets $V_1,...,V_k$ and I have a function $Z:V\rightarrow \mathbb N$ ...
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### Is ∞ considered defined?

$\infty$ (Infinity) is not a number, but infinity is considered to be defined, right? There are expressions in mathematics such as: $\frac x0,0^0, \frac\infty\infty,$ which are not defined because ...
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### Notation Question: What does $\vdash$ mean in logic?

In a "math structures" class at the community college I'm attending (uses the book Discrete Math by Epp, and is basically a discrete math "light" edition), we've been covering some basic logic. I've ...
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### Is there a collection of alternative mathematical notation? (Semi-soft Question)

I'm interested in alternative systems of notation for mathematics. I've often heard how mathematical notation is illogical, inconsistent, filled with grandfather clauses that serve no purpose, and ...
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### what does $\alpha(N)$ mean in this article?

I'm trying to understand this article: http://imgur.com/a/HfJoY but I'm unsure what $\alpha(N)$ means in this context? Is it the algebraic multiplicity, that's pretty much the only $\alpha$ I have ...
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### Is $f = x^2$ or only $f(x) = x^2$ correct?

I currently study special relativity and some authors write stuff like: $$r^\mu = \left(ct, \vec x\right)$$ This is awful since $\mathsf r$ is a vector, and $r^\mu$ ist just a single component of ...
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### Is there a name or definition for this popular notation?

I'm sorry if this is a silly question. I've done quite a bit of searching and have not found any definition or name for this symbol/usage, despite immense popularity and convenience. The sources I've ...
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### “Discovering” the indefinite integral's notation

I'm currently reading Keisler's Elementary Calculus -- An Infinitesimal Approach, which develops the main results usually thought in undergrad calculus using Robinson's hyperreal numbers (instead of ...
### Strange Notation: $f(x,y) = \ln (x + \text {s} \space \overline {x^2 + y^2}$)
In a paper I'm trying to understand, from a time series $x(1),x(2),\ldots,x(n)$ a new set of time series is created: x^m_k=x(m),x(m+k),x(m+2k),...,x\left(m+\left[ \frac{n-m}{k}\right]k\right) \:\:\:...