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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How can I specify a function object without naming it?

I would like a notational way of referencing a particular function object, without naming it anything in particular. For example, the statement $f:\mathbb{R}\rightarrow \mathbb{R}, f(x) = x^2$ Makes the name f an identifier for the function object…
extremeaxe5
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$x_\varnothing$ interpretation

Reading a miniature 16 in the book "Thirty-three miniatures" by Jirí Matoušek I can understand the proof only by writing $x_\varnothing = 1$. In that proof you observe a linear combination $\sum_{I \subseteq \{1,2,...,d\}}\alpha_Ix_I $ of…
jupiter_jazz
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Notation: how to construct a set with upper bound and lower bound?

For example, set $A = \left \{ 1, 5, 10, 30 \right \} \in \mathbb{R}^N$ r = $10$ How do I write down a set which takes $A - r$ as lower bound, and $A + r$ as upper bound, containing ranges? like: set $C = (A - r)?(A+r) = \left \{ [-9,11], [-5,15],…
null
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Why is the standard deviation always positive?

I wondered why the standard deviation always has to be positive. I found the following answers: answer 1, answer 2. There's a lot of people saying that the standard deviation is positive because it's the root of a positive number, and hence by…
Mr. President
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Should you write $a_1^2$ or ${a_1}^2$?

I originally posted this on TexStackExchange, but someone advised me to post it here. I apologize in advance if this is a duplicate, but I have looked and found no similar question. We consider a $n$-tuple $(a_1,\ldots,a_n)$, and we want to…
E. Joseph
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Formula with functions named $i_x$ and the imaginary constant together

In writing up a report that includes the modified spherical Bessel functions, the standard notation I've seen is to write them as \begin{align} i_n(r) &= \sqrt{\frac{\pi}{2r}} I_{n+1/2}(r) \\ k_n(r) &= \sqrt{\frac{\pi}{2r}}…
Hooked
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Number of elements in a set and notation

I have a notational question. In a formal proof, suppose I'm making some statements about a finite set $B$, such that $|B| = n$, for some $n \geq 3$, $n$ belonging to the naturals. Supposed that in some part of the proof, I must write the subset…
jpugliese
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Notation for half-integers

I'm wondering if there is any sort of colloquial notation for the set of half integers (i.e. $\{ \frac{n}{2} \mid n\in \mathbb{Z}\}$), or any sort of set of fractions of integers, (i.e. $\{\frac{n}{a}\mid $ $n\in \mathbb{Z}$ and $a$ is some…
PatEugene
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should the 2 in L-2 norm notation be a subscript or superscript?

I'm currently taking an online course where the professor has a habit of writing norms like this: $||a^{[l](C)} - a^{[l](G)} ||^2$ Since I don't have a great amount of experience in math or the concepts of deep learning, I was often confused whether…
Stephen
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Correct notation for multiple intervals for a function's range

I'm hoping that this isn't an obvious question, but I was curious about possible notations for what interval a piecewise function is defined on. For example, consider the following function (where $x \in \mathbb{R}$): $$\begin{cases} x & 0…
EJoshuaS - Stand with Ukraine
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Understanding int() and mod() functions as used in this formula

Context: SCOM metric to measure software class cohesion Paper: A SENSITIVE METRIC OF CLASS COHESION by Luis Fernández and Rosalía Peña. The equation in question is on page 86: $S(m,a) = \frac 12[1 + int(\frac {m-1}a)][mod(\frac {m-1}a) + m…
George Aristy
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What does $\mathbb{R}^ {\times}$ mean?

What does $\mathbb{R}^ {\times}$ mean? I cannot seem to find it anywhere.
James Woodward
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Phrase to describe numbers which are powers of a common base

I'm looking for a succint phrase to describe the set of numbers $$S_b = \{i\in\mathbb{Z}: b^i\}. $$ That is, the numbers which are all powers of a (specific) common base $b$. I've played with "exponent-b numbers", "base-b power" numbers, etc. but…
Anti Earth
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Is there a way to notate {there exists infinitely many integers $n$} in symbols?

If I wanted to write, there exists an integer $n$ then in symbols this would be written as $$\exists n\in\mathbb{Z}.$$ If I wanted to write, there exists only one integer $n$ then in symbols would be written as $$\exists!n\in\mathbb{Z}.$$ Sometimes…
Mr Pie
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Meaning of notation on the sum of two sets

The sum of two sets of numbers $S,T$ is defined as: $$ S+T=\big\{z \mid \exists x \in S \quad\exists y \in T \text{ such that } x+y = z\big\} $$ I'm not really sure what $S+T$ is. If $S=\{s_1,s_2,\ldots,s_n\}$ and $T = \{ t_1, t_2, \ldots,t_n\}$…
Yos
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