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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.

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Function Notation with "|"

What does that following notation mean in english? In this case, J is a set, but I am not sure how the "|" relates the set to the function f.
Doug Beach
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Interpreting statement notation

I have statement $$ \forall x \in \mathbb{Z} : \exists y \in \mathbb{Z} : xy=1 $$ I would translate this into English as: for all x and for some y integers it is true that: $$ xy=1 $$ Problem is i don't understand $:$ in this notation. To my…
Tuki
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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 property. Does this mean there are infinitely many…
user60194
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Meaning of $\Bbb Q[√2]$

I know that $\Bbb Q[x]$ is the set of all polynomials in $x$ with rational coefficients. And that $\Bbb Q[√2]$ is the smallest field containing $\Bbb Q$ and $√2$. But the other day our professor denoted by $\Bbb Q[π]$ the set of all polynomials in…
Not Euler
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Set notation meaning

When you write $x\in R$, this reads $x$ is an element of $R$. This specifies a domain for $x$ which is simply a variable. When you define a set $X = \{x\}$ , the set of all $x$, or $X = \{x\in R\}$ it seems as though to define the set you are…
Carlos Bacca
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Is it legal to write $A_\mu = (a, b, c, d)$?

In special relativity (theoretical physics), one uses a lot of four-vectors. With regular vectors, I would say the following is okay: $$ \vec A = \begin{pmatrix} a \\ b \\ c \end{pmatrix} \qquad A_1 = a \qquad A_2 = a \qquad A_3 = c $$ It would be…
Martin Ueding
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A question on the interval notation used in a Mechanism Design text book

I'm working on understanding a textbook on Mechanism Design and I came across a part that I didn't quite understand, which is underlined in RED: What does the underlined part refer to? I know it's an interval of some sort, but I'm clueless beyond…
Joebevo
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I have a sphere $S^2$, how can I define it?

I'm not sure how to say, using proper mathematical notation, a sphere $S^2$ is equal to the basic unit sphere $1=x^2 + y^2 + z^2$. Just looking for a quick answer, thank you.
John Miller
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What is the correct way to write "for all other values of x"

I wish to write a piecewise function with several cases, where it has a certain definition for one set of specified $x$ values, another definition for another set of $x$ values, etc, then one final definition for all remaining values of $x$. It…
Ulysses
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notation for set of indexed functions instead of braced functions?

Sorry for the vague title. We sometimes write functions as: $$f(2)=5$$ and sometimes as $$f_2 = 5$$ and sometimes with multiple variables, as $$f_2(2)=5$$ instead of $$f(2,2)=5$$ In principle these are the same, but they allow for different…
user56834
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Conventions for function notation with multiple variables

Consider the following expression: $x\cdot a\cdot b$ In programming you could define a function $f(x,a,b)$ to assign values to all the variables. However, since I cannot remember seeing such notation being used in purely mathematical context, I am…
Milo Wielondek
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notation for cartesian product with dependent types?

Normally, for a cartesian product between sets $A$ and $B$, we have the notation $$A\times B$$ But what if the set $B$ depends on the first element of the cartesian product? i.e., for each $a\in A$, we have a set $B_a$, such that for all elements of…
user56834
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Represent recurrent digit in numbers

I have try google and this website search engine, didnt find anything. Let's say that I have a number like this : 111118883458888. Is there a way to express this number like this (reg exp) : ('1'^5) ('8'^3) '345' ('8'^4), but in a mathematical…
ThisIsAName
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The cone $\mathbb R_+^n$ of all vectors in $\mathbb R^n$

In a paper I've been studying it says: Let $x$ in the cone $\mathbb R_+^n$ of all vectors in $\mathbb R^n$ with nonnnegative components ($n\in\mathbb N$) Somebody tell me what does it means, please? $\mathbb R_+^n$ should be…
Mark
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Is the set of all sequences of positive integers of unlimited length denoted $\Bbb N^\infty$?

Is the set of all sequences of positive integers of unlimited length denoted $\Bbb N^\infty$? I think that's most probably not right as it seems to imply the set of infinitely long sequences of integers but it's all I can come up with. I want the…
it's a hire car baby
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