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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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Is it okay to write $f(x)^2$?

As far as I understand we write $\cos^2 x$ just to not mix up $(\cos x)^2$ with $\cos(x^2)$. But it is difficult to associate $f(x)^2$ with anything else but $(f(x))^2$. Is it correct to use such a notation?
faleichik
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Notation: for $x$ not much less than $a$

"Everybody knows" that $a\ll b$ means a quite vague thing, something like $a$ is very much less than $b$. (And on math.stackexchange.com, it may be observed that not everybody knows the difference in MathJax and LaTeX code between $a\ll b$ and…
Michael Hardy
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The order of equalities

First note that I am not a mathematician. I do use it for my studies, but I am not reading anything remotely complicated in regards to maths. That said, here is my question: Today I found myself wanting to write a probability, first in terms of a…
Thorkil Holm-Jacobsen
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Order of precedence of "()", "implies", "forall" and "and"

I would like to know the order of precedence of $()$, $\implies$, $\forall$ and $\wedge$. For instance, how many "$()$" possibly could we remove for the following formula: $(\forall a, ((b_0 \wedge b_1) \implies c)) \wedge (\forall d, (e \implies…
SoftTimur
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What does this huge X mean that is written like the sigma notation?

I hope that you will not mind if I do not explain the background of this formula. The problem which I encounter is probably a simple one: What does the huge $\large \times$ mean and why is it written like a sigma? I had no clue how to search for…
Xiphias
  • 709
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Is there a symbol for "is of the form"

Is there a logical symbol for "is of the form" which can be used as a shorthand in a statement like: "Any even natural number is of the form $2n$" ?
Nat
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Conventional set notation for integers between m,n CS Theory/Math literature

This is a pretty simple, straightforward question. I've seen in the literature $[n]=\{0,1,2,\dots,n-1\}$ and $[n]=\{1,2,3,\dots,n\}$. Is there a similar convention for $[n]\backslash[m]=\{n,n+1,\dots,m\}$? Maybe [n,m] or something? I can't seem to…
Michael Jarret
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Is there a symbol for "as long as" in math?

Let's say we have the expression $$∀,∈ℤ:=⟹=$$ Which means "for all values of and in the set of integers, if equals then must equal ." For example, if 4×6=4×6, then 4=4. However, this does not apply to 0. For example, 7×0=6×0, but 6≠0. Is…
The_Animator
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Is there an "and" symbol?

I was wondering if there was a symbol for "and"? For example, I want to say something like $\therefore a = b \, \text{and} \, c = d $ Then can I replace "and" with a symbol? Thanks!
Jeel Shah
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What does the notation $\sup_{x\in X}\inf_{y\in Y}d(x,y)$ mean?

Say you have two disjoint closed sets $X$ and $Y$ in a metric space. I'm trying to interpret what $$\sup_{x\in X}\inf_{y\in Y}d(x,y)$$ means. Does it mean that you pick a fixed $x\in X$, and then compute $\inf_{y\in Y}d(x,y)$ for this fixed $x$ as…
Bear
  • 33
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What is this expression?

I saw this nice relief on the University of Warsaw's library building, but I'm left wondering what the line beneath $\pi$ and above Collatz is saying. I'm not familiar with the arrow notation. Can anyone identify it or give a reference for it?
Will Vousden
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Notation about n choose k permutations

I'm stuck on how to write the notation formally and clearly for the set over all the product in the form of $\lambda_{i_1}\lambda_{i_2}\dots\lambda_{i_r}$, where each $i_j$ could be $1,2,\dots,$ or $n$, and $n$ is greater than $r$. Note that…
Thinkpad
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What is the difference between the notations $j \in \{1, 2, ..., p\}$ and $j=1,2,...,p$?

first of all, I am very grateful for any help! Please don't take offense if the question is trivial. However, I am primarily a business student and therefore have little prior experience in neat notation of mathematical formulas. I am currently…
Desperate_undergraduate
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What does $x \in \langle0, 1\rangle$ mean?

I know what $x \in \{0, 1\}$, $x \in [0, 1]$, and $x \in (0, 1)$ mean. But recently I encountered $x \in \langle0, 1\rangle$. What does it mean? Source: Problem 4760, Crux Mathematicorum 48.6, June 2022, pg 349. (PDF link via cms.math.ca).…
Occe1998
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What does $R_{0}^{+}$ mean?

I'm reading this paper: http://www.aaai.org/Papers/KDD/1996/KDD96-027.pdf, and the authors used the symbol $R_{0}^{+}$ in the definition of Exact Exception Problem, such as $D: P(I) \rightarrow R_{0}^{+}$. Could anyone please help me understand what…
user87094
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