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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A little question on notation of integral

On Wikipedia articles, I often see $$\frac{dx}{x}$$ where the $\frac{1}{x}$ can often be absorbed into powers of $x$ in the integrand. For example, the Mellin transform is expressed as $$\int_0^\infty x^s f(x) \frac{dx}{x}$$ instead of…
Szeto
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Correct mathematical expression

I am a biologist. My apologies if I my question is too basic. I am writing a scientific manuscript and I would like to express the following with a correct mathematical expression: for a list of numbers (from $x_1$ to $x_n$) calculate the product of…
mike_
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Notation in set theory applied to counters

I have written a notation representing a counter for a condition: $M \leftarrow \displaystyle \sum_{i =1}^{|X|} [B_j = X_i]$ So far this gives me a number for a specific j (the counter), but I want to turn this into a set for all values of j in…
sfelixjr
  • 145
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Why is [a,b] notion for cross product very common in post-USSR countries and seemingly isn't used in others at all?

Seems that same holds for dot product. I suppose, this is due to notions of Lie bracket and inner product in Hilbert space which are generalizations of cross and dot product and denoted in same manner in Russia as dot and cross products. But maybe…
Oleksandr Kulkov
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Elementary math notations per culture or country

I cannot find a place listing the mathematical notations per country. The symbols listed in wikipedia refer to english notations. (Even the french page for instance, reproduces the english symbol for parallelism). This question is very similar but…
zezollo
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What does $(\nabla \psi)^2$ mean?

This is a question about notation. I know that for a function $\psi(x,t)$ $$\nabla\psi=\left(\frac{\partial\psi}{\partial x},\frac{\partial\psi}{\partial t}\right)$$ (the gradient of $\psi$) and $$\nabla^2 \psi=\frac{\partial^2\psi}{\partial…
AzJ
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A question regarding case notation

Consider the parameter $P$ and a property $S$ associated with this parameter represented as $P_S$. For example, consider that the height of a tree (“H”) is my parameter and the property is the tree’s name. Therefore, $H_{T1}$ refers to the height of…
limp
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Notation of remainder for a series expansion

I am writing something and met a notational conflicting. Is there any alternative notation for the remainder for a series, e.g. Taylor, expansion? It is typically denoted as R, but is there anything else and used before (I don't want to invent my…
Ethan
  • 21
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Question about "Formal notation of function"

The inputs of function $f$ are a set $A$ and one natural number $n$. Plus, its outputs are $n$ 3-dimensional coordinates. For example, $A$ is defined by ~~~. Then, $f(A, 4) = \{(x_1, y_1, z_1), \ldots, (x_4, y_4, z_4)\}.$ In this case, is it correct…
Danny_Kim
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Short notation for a set.

Let we have the following set $$ \{y_1, y_2, ..., y_L\} $$ My question: For short should I use $\{y_k\}$, $\{y_k\}_k$ or $\{y_k\}_{k=1,..,L}$? My idea: $\{y_k\}$ is a one member set, so it is incorrect. $\{y_k\}_{k=1,..,L}$ is correct.…
user153245
  • 800
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vague $\forall$ notation

Many times I find myself wondering exactly how to separate the conditions of a $\forall$ statement and its conclusions, for example: $$\forall x,y\in S, x\circ y\not\in S, x=y.$$ This could mean: $$\forall x,y\in S, (x\circ y\not\in S,…
Austin Weaver
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Double or nested "such that" notation

I have searched the questions regarding notation of "such that" in this forum but only encountered discussions on the use of : vs. | and less common alternatives. In some cases I find myself in need of using two "such that" formulations in a nested…
mrclng
  • 121
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Do right-to-left language speakers write expressions right-to-left too?

This is a very simple question. I am almost embarrassed to ask, and I'm even a bit unsure whether this is the right place to post it. I would like to know whether native right-to-left language speakers write mathematical equations left-to-right or…
Luciano
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What is $W_n ?$

I'm trying to solve an equation for B where $2 B e^{(1-B)}=1$ I plugged it into wolfram alpha and got: What is that $W_n$ mean? How do I intrepret this answer? (Feel free to retag it, I wasn't entirely sure what it falls under!)
corsiKa
  • 586
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In set notation, how do I "read" the following: "f : Z -> R"

In words, how would I express this notation? "Given a random variable $f:Z\rightarrow \mathbb R$, its expected value is denoted by $\mathbb{E}_{z \sim \mathcal{D}}[f(z)]$" This is from the first chapter of "Understanding Machine Learning" by…
Clay
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