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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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Difference between $\land$ and braces

I was wondering what are the difference between the $\land$ and $\begin{cases} \\ \\ \end{cases}$ symbol. As I know, they both mean "and". So far, I've noticed the $\land $ on statements (not sure if it's the correct word) like : $$\forall…
moray95
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What does $\mathbb{\bar C}$ denote in complex analysis?

What does $\bar A$ denote when $ A \subseteq \mathbb{C}$? I've seen it used in some places as the algebraic closure, other places as $\bar A = A$ \ $ \partial A $ and other places again as $\bar A = A$ \ $\{0\}$. I should probably add that I don't…
user27182
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If $\lim f(x)$ can theoretically be anywhere on the interval $0$ up to and including $\infty$, is the interval written $(0,\infty]$?

Let's take $f(x)=a^x+b$ where $a\in\mathbb R$ and $b\in\mathbb R^+$. clearly $L=\lim_{x\to\infty}f(x)>0$, but is the interval written $L\in(0,\infty)$ because limits only approach infinity or is $L\in(0,\infty]$ because infinity is one of the values…
Jacob Claassen
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Does $a≠b≠c$ imply $c≠a$?

Is $a≠b≠c$ a shorthand for ($a\neq b$ and $b\neq c$), or is it a shorthand for ($a\neq b$ and $b\neq c$ and $c\neq a$)? I want to know the "correct and formal" answer, rather than the "most commonly used" answer.
cr001
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How to recognize letters in curly style (eg, $\mathfrak{S}$, $\mathfrak{A}$, $\mathfrak{I}$) for mathematical notations?

Ebbinghaus' Mathematical Logic uses some notation in curly style, and I can't tell which letter is which. For example: What is the letter ($\mathfrak{S}$) for sequent calculus? and what are the letters ($\mathfrak{A}$ and $\mathfrak{I}$) and for an…
Tim
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Summing pairs from a sequence

Suppose we have an arbitrary sequence $$\{a_k\} = \{a_1, a_2, ..., a_k\} $$ and use it to a create a set as follows $$A = (a_i+ a_j : a_i, a_j \in \{a_k\})$$ and we wanted to sum over all of the members of this set, would we denote it as $\sum A$…
Brad Graham
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Operation meaning in set theory

When reading a set theorem, there is a part that: Defined a sequence $S_{n}$. Let $N = \inf\{n:S_{n}=0\}$ and let $X_{n} = S_{N \land n}$ I could not understand the operation $ \land$ in $S_{N \land n}$. Is this "and" operation? If it's true so…
M.bara
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Notation: sin and cos without brackets

Recently I read an equation that was formated like the following one: $f = \sin x y + \cos z$ Since $x$, $y$, and $z$ are different variables, and there are not brackets (), is $y$ inside the sin-operator or not? Does there exist some kind of rule…
Lemonbonbon
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Help with notation for tuples

How would I represent a set of tuples $(a_1,a_2,a_3,...)$, where each element $a_i$ is a positive integer in the interval $1\leq a_i \leq A_i$ The only thing I can think of is defining the set of integers $S_i=\{1\leq k\leq A_i\}$, and then just…
Ethan Splaver
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Notational question on generalized scalar product

Maybe not precisely a math question, but certainly related, and apparently there even is a notation tag :) We can think of the standard vector scalar product, $$ \langle \vec{x}, \vec{y} \rangle := \sum_i x_i y_i $$ as being a special case of…
Lagerbaer
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Semicircle law theorem (Math notation)

I will put part of the sentence here because I am interested in something very specific. It follows that Let $I\subset \mathbb{R}$ be an interval. Define the random variables $$ E_n(I)=\frac{\#\left(…
Odds'n'Ends
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What does it mean when a variable is defined with a subscript but used without one in equations?

This article defines $x_i ,i=1,\dots,n$ where $x$ has a subscript. However succeeding the definition, the formula contains only $x$. How am I supposed to interpret this generic notation in terms of math?
Thelonious Monk
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What is meant by observation i and i'?

In 'Elements of Statistical Learning' Chapter 14 (p. 503), objects $i$ and $i'$ and further $x_i$, $x_i'$ are commonly referred to. However I don't think they are explicitly defined. What could be the meaning of this symbol: $'$ I think it could…
Thelonious Monk
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How to describe all points with coordinates that are permutations of sets of values for x and y using notation correctly

Suppose I have a set of values for x: something like {1, 2} and another set for y: {3,4}. If I need to list all the possible points which coordinates are permutations of those sets and I don't want to list them explicitly, how would I do it? Best I…
PupaLupa
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Can the following conditional value be expressed using the min and max functions?

For example, consider $y$ such that $$ y=\cases{c, & if $c\le0$,\\0, & if $c>0$.} $$ Then, it can be easily expressed as $$y=\min\{c, 0\}.$$ Using the above trick, can I express the following $y$ using $\max$ or $\min$ ? $$ y = \cases{c, & if $c\le…
Danny_Kim
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