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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.

12848 questions
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What is the meaning of $\Sigma_n, \Pi_n, \Delta_n$ without superscript symbols?

Sometimes I see the $\Sigma_n, \Pi_n, \Delta_n$ notation without superscript symbols (for example, in this answer on Mathoverflow; another example is hypermachines ($\Sigma_n$-machines)). But when I read articles on Wikipedia (Descriptive set…
lyrically wicked
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Is adding a plus before a positive number a mistake?

I had a simple problem to find out the function equation from a sinusoidal graph. $$F(x)= -2\sin(2x)$$ Would it be considered a "mistake" to write it down the following way? $$F(x)= -2\sin(+2x)$$ Or, would it simply be an unnecessary additional…
Mikolaj Marcisz
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Need help with notation for objective function

I am reading the paper about Generative Adversarial Nets and there is the equation: $$ \min_{G}\max_{D}V(D,G) = \mathbb{E}_{\mathbf{x} \sim p_{data}(\bf{\mathbf{x}})}[\log D(\mathbf{x})] + \mathbb{E}_{\mathbf{z} \sim…
MegaNightdude
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What is the meaning of $\mathbb{R}_{++}$?

From [1], on page 9, one can find the following expression. $$L:\mathbb{R}\setminus\mathcal{A}\rightarrow\mathbb{R}_{++}$$ What is $\mathbb{R}_{++}$ is meant to be? The $\mathbb{R}_{+}$ symbol seems to usually mean positive real numbers or…
Bernardo Sulzbach
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Matrix of the form $E_{ij}$ where $i$ and $j$ are positive integers

I am trying to solve Problem 15 on page 107 of Brešar's Uvod v Algebro. The question translates into English as: Explain why any endomorphism of the algebra $M_2(\mathbb{R})$ can't map the matrix $E_{11}$ to the matrix $E_{12}$. In this question,…
InsertNameHere
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What does "8.5070592e+37" mean?

When Google calc gives me numbers like this: 8.5070592e+37 How do I convert this back into a large number again. i.e…
user66430
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Is there accepted notation for this remainder function

I have a use for a function that represents the least amount that must be added to an integer $x$ to make it a multiple of $y$. I.e., if we call that function $\Delta$, then $\Delta(\frac{x}{y}) = y\lceil\frac{x}{y}\rceil-x$ If there isn't an…
Joe Slater
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Is there a common notation for a matrix with one entry equal to one and zero otherwise?

Kind of like a unit vector, but it's a matrix. For example, if the notation is $A_{ij}$, then this matrix has all zero elements, except $a_{ij} = 1$. Is there a common notation/term for this kind of matrix? The goal is to write something like: for a…
smörkex
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Notation for element of a set on which some function is minimal

This is a simple notation question about something I seem to have forgotten, have a complete mental block to remembering, and can't find online. I think there's an equally simple answer. Suppose I have (for instance) a set $S$ and some injective…
j0equ1nn
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Is there a notation for a given order-preserving bijection?

Let $A,B$ be sets and $G,H$ be order-relation for $A,B$ respectively. Say, i proved existence of an isomorphism $\psi$ such that [$(x,y)\in G$ iff $(\psi(x),\psi(y))\in H$]. However, "$A\cong B$" gives no information about which order relations…
Jj-
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What is the meaning of this product symbol?

What is the meaning of the above symbol (the circle with the cross)? I frequently come across it, but as I am learning mathematics on my own, I wasn't able to figure out where it comes from and what it means ($\mathcal{A}_i$ are $\sigma$-algebras…
AlphaOmega
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Is 'set' over an equal sign correct?

Recently friend of mine showed me a way to write $f(x)=0$, however I could not find anything about that in the Internet. Is it correct? $f(x)=x^2-1\stackrel{set}{=}0 \\ x = 1 \lor x = -1$
kezc
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How to distinguish argument parentheses and grouping parentheses?

$$s(a+b)$$ Does it mean s times a+b, or is s a funtion and take a+b as arguments? $$(s(a+b))(c+d)$$ Does it mean s(a+b) times (c+d), or is s a high order function and s(a+b) return a function which then take c+d as arguments? As a reader, how do I…
Gqqnbig
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What does this notation mean: $C([a,b], \mathbb{R})$, $C([a,b], \mathbb{R^m})$?

I know $C$ is for continuous functions, and I assume $([a,b], \mathbb{R})$ means an interval on the real number line, and for $([a,b], \mathbb{R}^m)$ I assume this means that you have some vector in $\mathbb{R}^m$ whose components can assume any…
goblinb
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If {$a_n$} is a sequence of natural number, can we write {$a_n$} $\in\mathbb N$?

If {$a_n$} is a sequence of natural numbers, can we write {$a_n$} $\in\mathbb N$ ? Thanks. ${}{}{}{}{}{}{}{}{}{}{}$
JSCB
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