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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Notation for powerset with cardinality condition

Given a set $X=\{x_1, \ldots, x_n\}$ I would like to denote the set of all distinct subsets of $X$ which have cardinality $k\le n$. I am aware that the set of all subsets (of any cardinality) is referred to as the "power set" $\mathcal{P}(X)$. My…
user160623
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What is the difference between using set to make equation or not?

What is the difference between $x = a, b, c$ and $x \in \{a, b, c\}$? Which expression should I use?
Junee
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Notation for nested parenthesis?

When proving the asociativity of some operation denoted by $\bullet$ one first proves that $a\bullet(b\bullet c)=(a\bullet b)\bullet c$ for any $a$, $b$ and $c$. This automatically implies that $$a_1\bullet a_2\bullet\cdots\bullet a_n$$ is well…
augustoperez
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Degrees vs Radians (Notation)

I understand that the argument of a trigonometric function must be a pure number (a radian, if you will) and hence when we talk of 'measuring angles in degrees' we mean things such as $sin(x\frac{\pi}{180}) = sin(x^\circ)$ where $x$ is 'pure…
Nav Bhatthal
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Math notation question for an algorithm

I'm reviewing an algorithm and it all makes sense except for this line: $$ \boldsymbol{b} \leftarrow (||\boldsymbol{b}|| \_{2} - \beta)_{+} \widehat{\boldsymbol{b}} $$ $\boldsymbol b$ is an $N\times 1$ vector and $\beta$ is a constant. I'm not sure…
Arik D. Brown
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Better notation for norm

Is there a better notation for the norm of a vector? For example, if I have a set of vectors $X$, then the set of norms associated with it would be $$ \{||x|| \mid x \in X\} $$ The vertical norm lines look identical to the set builder vertical line.…
Yuxi L
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Meaning of notation concerning parameter range

I have recently seen in the context of so called doubly non-linear pde a notation concerning a parameter range where the following term $\hat{p}<\frac{n(p-1)}{(n-p)_+}$ appeared. Here $p,\hat{p}$ denote the exponents which lead to non-linearity but…
HelloEveryone
  • 449
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A notation for a variable which is insignificant in computation?

I want to explicitly show that when applying a formula certain variables on LHS of the equation are very small and will not be used in computing the RHS. I was curious if there is an actual notation for that. E.g., $A + \frac{C}{D} \approx B$ where…
Nikolai Savulkin
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Proper notation for restricting the value of a variable in an equation or inequality (not a function)

I'm sure the answer to my question here already exists, but I'm having trouble finding a clear answer using proper formal notation instead of plain English. I am aware of the notation used to place restrictions upon the domain of a function, i.e.…
Next-Door Tech
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What do the three dots mean in this problem? (Concrete Mathematics, ex. 1.9)

Exercise 1.9 in Concrete Mathematics (Knuth et al.): What does '...' between $x_1$ and $x_n$ mean? If it's multiplication, I would expect the dots to be centered. If it's saying that the inequality holds for each $x_a$ with a between $1$ and $n$…
Noah J
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Notation for choosing the minimum of a set after applying the norm

I have a function $x: \mathbb{R^+} \mapsto \mathbb{R}^n$ defined as $x(k) = \text{min}\{p \in S: \lVert p \rVert > k\}$ (where $S \subseteq \mathbb{R}^n$). I want to choose the point with the smallest norm larger than $k$, but I feel that I should…
windex123
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Notation for single condition in equation

I have an expression which can be simplified to a simpler one under the condition that two of its components are equal, and I'd like to put this fact into a single line equation. Is there a generally-accepted notation for denoting that an equality…
Zak
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What is most efficent set builder notation for a set of real values, indexed by bounded integers?

I am by trade a mechanical engineer, not explicitly trained in set builder notation. With that said, I am trying to learn to communicate information succinctly. What I am trying to express via set builder notation is the following: I have a set of…
ZaneMorris
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Is this use of product notation legal?

So I'm trying to prove something, I came across a sub-question that lead me to another question I thought of. Is the following legal? $$\prod_{k=1}^{n} \left(1-\frac{1}{2k}\right)/ \prod_{k=1}^{n} \left(1-\frac{1}{2k+1}\right) = \prod_{k=1}^{n}…
Bobby
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Meaning of a mathematical symbol

I'm reading the following Introduction to p-adic numbers by Alexa Pomeranz Towards the end of page 2, there's a symbol unknown to me. Selecting and copying it, copies a hyphen - symbol instead, so I cannot copy the actual symbol to search for it. I…
Elerium115
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