Mathematics Stack Exchange
Mathematics Stack Exchange

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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Correct way for writing domain of a function

When writing the domain of a function, in set builder notation, how does one correctly write the set of all real numbers? E.g. for $f(x) = 3x+2$, which of the following would correctly state the domain? Are they all OK, just some better than…
n1010
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Cleaner notation for cardinality of set instead of |{⋅}|

I feel it's a little ugly to use the normal "absolute value" notation for the size of an anonymous set-builder set: $$ N = |\{ x \in \mathcal{X} : f(x) \geq 0 \}| $$ Is there a preferred replacement? I feel like I've seen $$ N = \# \{ x \in…
japreiss
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$y$ as coefficient for $5xy$ in the term $5y^2x$

In this text book, it was mentioned that we generally use the term coefficient in two ways 1) The numerical coefficient of a term in an algebraic expression 2) A variable as a coefficient for rest of the term But didn't comment anything on splitting…
hanugm
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How do we address this $p(v_0+h)$ in mathematics?

Consider a differential equation $\frac{dp}{dv}=f(v,p)$ and solving the differential equation yield $g(v,p)=$ constant and initial condition $p(v_0)=p_0$ implies $g(p_0,v_0)$=constant so i use this equation to find the value of p at point $(v_0+h)$…
chuackt
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Equation-to-Text Converter

I was just thinking today... I was reading a book called "Forecasting: Principles and Practice", and found myself reading mostly the theoretical paragraphs, and skipping most of the mathematical equations due to lack of time (and also a bit of…
Hassaan
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Meaning of pre-superscript in group theory

Is pre-superscript a standard notation for something? I've encountered it in the following: $$(a,g)(b,h) = (a + {}^gb + f(g,h), gh).$$ This was given in relation to a formula for the multiplication on the abelian set $A$ with extension $G$ as $A$ X…
zhanmusi
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Help with math notation (noob question)

I'm teaching myself math and I can't figure out what the below symbols mean in a textbook: I did figure out that $\Bbb Z$ = integer set and $\Bbb N$ = natural, and $\Bbb R$ = real. But what do all the pluses and dots and $\{0\}$ mean? Eg how is…
ilmoi
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Learning what $\{a_{k}\}^{n}_{0}$ means

Somewhere I saw the notation $\{a_{k}\}^{n}_{0}$ used. I believe it was used for a summation, but I'm not sure. What does this actually mean and can also use it to describe the set $\{a_0,a_1,...,a_n\}$?
Spador Yedi
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Is there a shorthand notation to $frac(x) = x - \lfloor x \rfloor $?

In old Hewlet Packard calculators, it was common to have an int and a frac function, which were giving the integer and the fraction part of a number. Nowadays, the floor function is quite common and noted $ \lfloor x \rfloor $ but to get fraction…
Camion
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What is the correct notation to define a vector in $\mathbb{R}^n$ within the interval $[0,1]$?

If I can can define a binary string with $n$ bits as a vector in the space $\{0,1\}^n$; how can I define a vector in $\mathbb{R}^n$ for the interval $[0,1]$? Can I just write $[0,1]^n$?
Gus Kenny
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What does the semicolon (";") mean in "$a\in(2;3)$"?

I'm working on a linear program and I have the following constraint: I'm wondering what does the ";" mean? At first I thought it meant the variable $a$ can only be $2$ or $3$, but that's what $(2, 3)$ is for, right?
AlfroJang80
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Best way to denote tuples and sets?

When writing a research paper, what is the best way to denote a tuple and a set? The problem is the following: I have a set of geometric intersections $\{s_1,s_2,s_3,...\}$ and then I order them. So I can say that I have a tuple of intersections…
Jake B.
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Is there an equivalent of arg max for equality conditions?

I want to know if there's a way of saying: "The price that sets the output of a function equal to a constant" in a way that resembles $\arg \max$. What I'm trying to express is close to saying: "x is part of the set of arguments that maximize a…
Arturo Sbr
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the difference between t = 1 and ∆t = 1

for example , when i want to see how fast is time , i see the longest hand in clock , the first time i start to observe , the clock hand is pointing at 12 , then after few moment the clock hand moved once , which mean i passed 1 second , and then…
user6668201
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The meaning of $\int\limits_\mathbb{R}$

Which of $\lim_{a\to\infty} \int_{-a}^{a}$ and $\lim_{r\to-\infty} \lim_{s \to \infty} \int_{r}^{s}$ does $\int_{\mathbb{R}}$ mean?
user27182
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