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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Notation for a composite function with the same function

If I have some composite function $g$, defined as $$g(x)=(k\:\circ\:k\:\circ\:...\:\circ\:k)$$ where $k(x)$ is essentially put into itself $n$ times, is there any compact notation I could express $g(x)$ with?
Maj Zobrani
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Notation of min with i

Ive seen an unfamiliar notation of min. Min Notation: $$\min_{i=1,\dots,N}\left|\langle w,x_i\rangle\,+\,b\right|\,=\,1.$$ What do they mean with it? Does it mean: Choose $x_i$ that $\left|\langle w,x_i\rangle\,+\,b\right|\,=\,1?$ They want me to…
Hans Mustermann
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What do the letters below $\max$ mean?

In the following example, I have a question about the meaning of the letter $y$ below the $\max$ symbol. I know that $\max P(y\,|\,x)$ is simply to find the maximum value of $P(y\,|\,x)$, probability of $y$ given $x$. What is the role of the letter…
dreamer58
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Need help with nested array notation

I have ben looking at one specific research paper (here's the link if you would like to see http://mrob.com/users/chrisb/Beyond_Nested_Arrays_V.pdf) and I am having trouble understanding some stuff. the symbols ● , /, and › have not been giving me…
Blue
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Can a function be a part of $R(\sin x,\cos x)$ if it only contains elements of $\sin x$ or $\cos x$

My textbook says that integrals of the form $\int R(\sin x,\cos x)$ can be simplified using some substitutions (like $\tan \frac{x}{2}=t $. My question is would those substitutions be applicable if R is just a function of $\sin x$ without any term…
Tatai
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How to mathematically represent a missing element in a set so that it is summed as 0?

I currently have a fixed set of length $5$ denoted with elements $A = \{s_1,\ldots,s_5\}$. I have a function that takes each element and cubes it, then sums across all elements, so that $$ S = \sum_{i=1}^5 s_i^3 $$ However, sometimes the set may be…
user321627
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Representing the set which contains integers each of which is a subset of certain interval(segment?).

I've read the book of cyber security and saw the notation below. $$ \mathbb{Z_{n}} ~~\leftrightarrow~~ \text{set of integers which satisfy }~ 0 \leq i < n $$ And what I want to represent is the set of natural integers equal or greater than 1 and…
electrical apprentice
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What is the origin of the inverse function notation?

I know that $f^{-1}$ denotes the inverse of the function $f$. Like many others, I find this notation bizarre and ambiguous. But my question is: where does this notation come from? Who used this notation first? In what context and what was their…
jameshfisher
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Is it clear enough if I remove -external-parentheses in $\sin ( (x-y)\pi )\; \cos ( (x+y)(a-\pi )) $?

I have this expression $$\sin ( (x-y)\pi )\; \cos ( (x+y)(a-\pi )) \qquad (1)$$ Is it clear if I omit those external parentheses and write it like this? $$\sin (x-y)\pi \;\cos (x+y)(a-\pi ). \qquad (2) $$ In general, which one is preferred?
math2021
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$\forall a > 0$, can $\{ x < -a \text{ or } x > a \}$ be rewritten as $\{ -a > x > a \}$?

While studying about inequalities, I came across the following definition ($\forall a > 0)$: $$ \begin{alignat}{1} & |x| > a \iff \{ x \mid x < -a \text{ or } x > a \} \\ & |x| < a \iff \{ x \mid -a < x < a \} \end{alignat} $$ Naturally, as $\{…
Luiz Felipe
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What is the set denoted by $\mathbb{K}$?

Wikipedia's article on the Leibniz determinant formula states there exists one and only function $F:M_n(\mathbb{K})\mapsto\mathbb{K}$ which is alternating, multilinear and $F(1)=1$. I assume $M_n$ is the set of $n\times n$ square matrices, build…
FShrike
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History and current usage of this symbol for "corresponds to"?

Encyclopedia.com lists the following symbol for "corresponds to": The source they give is "Oxford University Press", although I am not sure which exact work they used. But they list the symbol, and the stated meaning of "corresponds to" is the one…
user583837
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Are there any rules about when to write or drop grouping symbols mathematical expressions? eg, "$\sin cxyz$" vs "$\sin(cxyz)$"

I am curious whether there exists one, like an extension to the PEMDAS rule. I am referring to trigonometric, logarithmic, and other functions similar. This is because I am confused about when to drop grouping symbols. For instance, we understand…
soupless
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what does $L_{2}^{1}(0)[0,\infty )$ mean?

The following is from Reproducing kernel Hilbert space section "Connection between RKHS with ReLU function". We will work with the Hilbert space ${\displaystyle {\mathcal {H}}=L_{2}^{1}(0)[0,\infty )}$ of absolutely continuous functions with…
yllgl
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"Dictionary" notation for definitions

Many mathematical definitions have the following form using real numbers as an example: A real number is called X iff it is integer and greater than $2$. As we know definitions serve only as abbrevations. Could we define "X" in the following…
user599310
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