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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In what context are these mathematical symbols used?

I just noticed that the Unicode character set contains an entire block (256 characters) of math symbols. I've got no idea how some of them should be used. For example: U+22DA (⋚) and U+22DB (⋛): less-than-equal-to-or-greater-than, and…
wchargin
  • 1,802
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3 answers

"Such that" symbol "$\mid$"

I know the "such that" symbol $\mid$ from the definition of sets: $$\{x \mid x \in \Bbb N \land x < 3\}$$ Is it OK to use this symbol outside of sets. For instance, if I want to define a function that takes a non-empty set of natural numbers and…
Hyperboreus
  • 341
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2 answers

What is the meaning of $\bigvee$ (bigvee) operator

What do mean $\bigvee$ operator in page 6 of this document. It is a Variable-sized Math Operator. What about $\bigwedge$?
Secret
  • 111
11
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2 answers

Notations: use of parentheses with "mod" and the "|" symbol

I'm working through a practice test with no available solutions, and I came across this question. Let $a,b,c,d,e$ be integers with $c>0$. Suppose that $a\equiv b\pmod c$, and that $d\equiv e\pmod c$. Determine whether each of the following…
stett
  • 369
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2 answers

Notation for “should be equal to”

Suppose I have some (possibly complicated) expression depending on one or more parameters, and a value which this expression should have for the solution I'm interested in. How do you write that, in particular if you want to distinguish it from a…
MvG
  • 42,596
10
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3 answers

Notation for all permutations of a set

Suppose I have a finite set $X$. Is there a standard notation to denote the set of all possible permutations of the elements of $X$? P.S. something like the power set notation for all subsets.
user3761729
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5 answers

What does a tilde underneath an inequality mean?

I've recently come across an expression of the form $$\large x \lesssim y$$ What does this expression mean?
Optional
  • 692
10
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3 answers

Correct notation or operator to remove elements from sequence

I'm currently using the following notation to denote a sequence (i.e. ordered list of elements): $\langle x_n | x \in \mathbb{N} \rangle$ E.g. $S = \langle 1,3,5,7 \rangle$ and $S_2 = 3$ I know other notations exist, such as…
Macuyiko
  • 103
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6 answers

Why do some people use $+\infty$ instead of $\infty$?

Why do some people use $+\infty$ instead of $\infty$? Because we usually denote minus infinity as $-\infty$, I think it is sufficient to denote plus infinity as $\infty$. Are there any reasons for this notation? I saw that many people majoring…
Kamon
  • 127
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9 answers

What does a hat or star means in math?

What are the general uses of the hat and star symbol in math? Or could you please point me to a page that discusses this? Thanks.
Martin08
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1 answer

Order of operations / Precedence in Sigma notation

given this equation: $$A^t_j=f(k^i_1 \sum_{i=0,i\neq j}^n A^{t-1}_i W_{ij}+k^j_2 A^{t-1}_j)$$ and these two infos: Notation: What is the scope of a sum? https://people.richland.edu/james/lecture/m116/sequences/sequences.html (bottom) It seems to me…
Col. Cool
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3 answers

What does $\mathbb{R}_{++}$ stand for?

What does $\mathbb{R}_{++}$ mean? I know $\mathbb{R}_+$ means all non-negative real numbers, but I have no clue what $\mathbb{R}_{++}$ means.
HELP
  • 117
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4 answers

Which parentheses are implied by $\prod$?

Which is correct? $$ \prod_a ab = \left[ \prod_a a\right]b $$ or $$ \prod_a ab = \prod_a \left[ ab \right] $$ I'd say the latter, but with $\sum$ we have $$\sum_a a + b = \left [ \sum_a a \right ] + b $$ Do they work differently, or did I guess…
Peter
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2 answers

How to denote domain and range

Is there a common way to denote the domain or range of a function? I've seen things like $ \cal{D}\left(f\right) $ and $ \cal{R}\left(f\right) $ for the domain and range, respectively, but I wasn't sure if there was a more explicit syntax for this…
brianmearns
  • 837
9
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3 answers

Notation for integer between two values

This may be a silly question, but it has been a long time since I have used set notation to any real extent. How would I write that $i$ is an integer ranging from $1$ to $N$? My (possibly faulty) recollection is that this is expressed as $i \in \{…
codeAndStuff
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