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.

12848 questions
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Question on Notation (Set theory)

I'm working on a problem set. The class is called 'Algorithms for Inference'. In the definition of the problem, it says $V$ is a set of vertices. An "independent set" can be represented as a binary vector of dimension $n=|V|$ with $I=[I_i]\in…
user3884723
  • 85
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2 answers

Some notation regarding "::"

I'm reading through some geometry proofs, and I can see something like $AB^2:PM\times EB::BC^2\ :CD\times PQ$ So I understand that $A:B$ is equivalent to $\frac{A}{B}$, but what does the $::$ mean?
Trogdor
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Help on mathematical notation and formalisation for the following description

I would like to describe a hypothesis, formally. So I have defined $p = {t_1,t_2,t_3, \cdots, t_n}$ and I would like to say "A pattern $p_i$ is more important than $p_j$, if $t \in p_i$ is more important than $t \in p_j$", I know that it is a bit…
drhanlau
  • 157
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1 answer

What is difference between ≈ and ~?

I'm reading a quantum mechanics book, and it has the following equation: $$ \Delta x \approx \frac{\lambda}{\sin\alpha} \sim \frac{h}{mc\sin\alpha} $$ What is the difference between $\approx$ and $\sim$?
daviewales
  • 523
2
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2 answers

Notation for an integer being square-free

An integer $n \neq 0$ is square-free if $n$ is divisible by no prime square. Can you figure out any notation for simplifying this long description? It may be guessed that $p^{2} \nmid n$ for any prime $p$ is okay, but this is still a bit long.
Yes
  • 20,719
2
votes
1 answer

Formally correct way to define asymptotic notations

I found an algorithm book which tries to define asymptotic notations as sets and then used notations like $n=O(n^2)$. Is there a mathematically correct way to define asymptotic notations like $O(n), \Omega(n), \Theta(n), o(n)$ and $\omega(n)$? And…
computerenthusiastic
  • 33
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Two integers with the same prime factors notation

Let $m,n\in \mathbb{Z}$, what is the notation usually used to say that $m,n$ have the same prime factors, i.e. $m=p_1^{m_1}p_2^{m_2}\cdots p_2^{m_r}$, $n=p_1^{n_1}p_2^{n_2}\cdots p_r^{n_r}$ for some primes $p_1,p_2\cdots,p_r$. I think about…
user80225
2
votes
3 answers

Is there another meaning of this notation?

In a book I found the following notation: Let $c,d\in \mathbb{Z}$ such that $c\mathbb{Z}+d\mathbb{Z}=\mathbb{Z}$. For me, this means that $\gcd(c,d)=1$. If $\gcd(c,d)=1$, then there is $z,u\in \mathbb{Z}$ such that $cz+du=1$. Then any integer…
user80225
2
votes
2 answers

Notation for "first $x$ where $f(x)$ greater than $t$"?

What is the preferred notation for expressing the first $x$ where $f(x)$ is greater than a threshold $t$. This is similar to $\arg\max$ notation but instead of max, I want the first $x$ where $f(x)$ is greater than $t$.
Jakob
  • 21
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1 answer

How to denote a set of nested tuples?

I want to define a set that elements that are nested tuples, like this one: $$a =((1, 2), (1, 2, 3), (1, 2))$$ I want this so I can index elements and write $a_{2,3} = 3$. My first idea was simply writing: $\mathbb{R}^2 × \mathbb{R}^3 ×…
Calmarius
  • 903
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0 answers

Manifolds and Varieties

In my language, spanish, the word for (topological) manifold and (algebraic) variety is the same: "Variedad". This happens also in some other languages, like french (variété) or portuguese (variedade). Is there a mathematical link between these two…
Marco Flores
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3 answers

What is the name of this notation?

What is the name of a notation that looks as follows: "1 2 9 8 4 6 + * / + *" But is evaluated as "1 + 2 * 9 / 8 + 4 * 6" EDIT: I do think it's RPN now and my eval above is incorrect (as it's supposed to be evaluated in the stack on the first…
jsanc623
  • 123
2
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1 answer

Notation: Difference between $C$ and $C^0$

Lately I have been running into the following notation fairly often: $f\in C^0(\Omega)$, $g\in C^0(B,\mathbb R^3)$ etc. I always thought this was just some peoples' way of saying that a function is simply continuous, but lately I am confused about…
dinosaur
  • 2,252
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1 answer

Is there a recommended symbol for "equal by abuse of notation"?

Can anyone suggest a good candidate for a symbol to be used for "equal by abuse of notation"? I can only think of "$\stackrel{\text{def}}{=}$", but it does not seem to be quite appropriate. For example, in "$m = m\otimes 1$", are there any…
Alexey
  • 2,124
2
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2 answers

How to write a counter in proper notation?

I have made a system where I count every hour that meets a certain condition. I would now like to express this in a simple formula but sadly can not come up with a solution. This is what I need. For each hour where $\theta_{dp} > \theta_{crit}$ add…
MatoBehr
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