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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Do we have this symbol in mathematics?

It is the symbol I used to show left hand side of inequality isn't greater than right hand side. More precisely I used this to show the below matrix is not diagonally dominant: $$\begin{bmatrix}5&6&7\\ 2&-4&2\\ 3&2&-5\\ \end{bmatrix}$$ So at the…
Etemon
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Is there a notation for repeatedly applying a function?

There is notation for applying both multiplication and addition a set amount of times (can be infinite): $\sum$, $\prod$ but there is no notation (to my knowledge) of repeating a function. Whenever I need this I use this notation: $R_{n}^{k} f(a) $…
fastMath
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Does ⋮ mean "is divisible by" in mathematical notation?

For example, $5(2+3m)⋮5$ if $m$ is an integer. My teacher said yes, but I can't find anything about this triple colon ⋮ online.
user71207
  • 1,543
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The meaning of $f\colon \mathbb R^2 \times \mathbb R \to \mathbb R^2 \times \mathbb R^2$

I know $f \colon \mathbb R^2 \to \mathbb R$ mean that f maps each ordered pair (which contains two numbers as input) to a single number (as output). What about the $f\colon \mathbb R^2 \times \mathbb R \to \mathbb R^2 \times \mathbb R^2$?
Đặng Huy Hoàng
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How would you write a set that contains all the reals for a solution and an empty set?

My teacher wants me to write solution sets like: solution set $= \{x:x \in \mathbb{ℝ}, \}$, but he didn't go over how to write a set that contains all reals and how to write a set that is empty.
Astin Lu
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Can we combine set notation and interval notation?

Is it possible for us to combine set notation and interval notation, e. g. $x \in \{3, 10\}$?
my2cents
  • 387
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Interpretation: existence of $2$ elements in a set. Simple question.

I'm ask to decide if there exists $2$ elements $a$,$b$ in a set such that $a+b =8$. It seems to me that many understand that $a$ and $b$ need to be two different elements. How should I understand "$2$" in this case? The assumption $a\neq b$ is not…
user11775
  • 333
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What does $(x, y)$ $\in [10,-10] \times [0,0]$ mean - Multiple of two domains?

I tried to search online but I can't find the right definition. Does the first square bracket represent the domain of $x$ and the second square bracket the domain of $y$? Therefore: does $(x, y)$ $ \in [10,-10] \times [0,0] $ mean a line from…
underdisplayname
  • 1,240
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What is the function $E(x)$?

When reading Problems in Calculus of One Variable (a translated Russian book), I came across unfamiliar notation "$E(x)$". It is neither expected value nor $\exp(x)$. Here is a picture of the function used in context, which I hope someone can deduce…
twentyyears
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What does the curly x symbol "$\mathcal{X}$" mean in "$\;x_i\in\mathcal{X}\;$"?

If you need more context, this equation is on the second page of this document. My guess is it just means "whatever value $x$ can have" or "all values of $x$", but I just wanted to check.
slim
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Is this notation for a domain standard?

I guess they are defining domain in a very general way. So you can say a function $f: \mathbb{R} \rightarrow \mathbb{R}$ is taking values (as a function) in $\mathbb{R}^{\mathbb{R}}$. Is this a common thing? I read a lot of mathematics (applied…
mathtick
  • 147
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Change (or increment) raised to some power

After some shallow research, I've found no results of anyone asking the same question as me. Please feel free to refer me to wherever this has been discussed previously. When expressing a change with the letter delta: $\Delta x$ for example and…
sware
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Successive "approximately equal" signs

Which is notation is stylistically preferred? $$\Delta U = mg \frac{R^2h}{R^2 + R h} \approx mg \frac{R^2 h}{R^2} = mgh$$ or $$\Delta U = mg \frac{R^2h}{R^2 + R h} \approx mg \frac{R^2 h}{R^2} \approx mgh$$ And does the rule change if you are…
Max
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Help with Notation

Let $S_{1},S_{2},S_{3},....$ be a sequence of mathematical statements, each of which is dependent on the same variable, such that, at any given moment exactly one and only one of the statements can be true, while the others must be false. What's a…
Ethan Splaver
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How to denote that an integer doesn't have zero digit?

I wanted to know if there is a mathematical notation to say verbally "it does not include the digit zero in the number". For example, $86$ is (conjectured to be) the largest integer $n$ such that $2^n$ does not include zeros. (FYI: $2^{86} =…
Francesco
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