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.

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Question for the default notations in mathematics to represent variables, such as $n$ for an integer and $z$ for a complex number.

I just read an article about the notations in mathematics. There are some articles like this one about the mathematical notations. Furthermore, here gives another further advise about writing. In many places (textbooks, math contests, the questions…
JetfiRex
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On "def" notation

I've been perplexed by the notation of writing def above an equal sign, even though it seems rather trivial. So, in the example below, is this the correct usage of def? $f'(x) \stackrel{\text{def}}{=} \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$ Also, is…
Alexander
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How to express equation of line in set builder form?

I found set builder form of writing equation of straight line like $\left\{(8t+8,2t+5)∣t∈R\right\}$ on this answer. I found this way of the equation of line unique. I'm seeing this first time and interested in knowing how to convert any linear…
user983440
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What does the notation $\circ$ mean?

I can't search it on google, because it doesn't support symbols like these. It might have to do with binary operations, I think.
Mohamed Ayman
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Is it common to use (for example) "Obviously $a \leq b$..." is equivalent to "Let $a \leq b$..."?

I am reading several works of an author. I have identified in one of the works, what he meant by "Obviously $a \leq b$..." is the same as "Let $a \leq b$...", since (I think) it is absurd if the construction given implies $a \leq b$. In another work…
AyamGorengPedes
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What's the notation for "up to an affine transformation"?

Suppose y=ax+b, where a and b are constants. This is to say that y is equal to x up to an affine transformation. Is there any notation to express the relationship between y and x that is similar to $\propto$ (the notation for proportional to)?…
ExcitedSnail
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Is there a concise word for nth largest that is a generalisation of "maximum"?

$$ \max_{x \in {X}} f(x) $$ Means I want the maximum value of $f$ under all possible values of $x \in X$ Is there a way to say the above but for the second maximum (ie once you remove the $x$ that gives the maximum, what is the new maximum)? What…
Alexander Soare
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Proper notation for equation solving.

What is the proper notation when solving one equation by inserting another known relationship? $$y=x^2, y+2x^2=1$$$$y+2x^2=1\Leftrightarrow x^2+2x^2=1 \Leftrightarrow x=\pm\sqrt{\frac{1}{3}}$$ I assume the first $\Leftrightarrow$ is wrong since we…
Erik Eriksson
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Limiting the scope of an operator

With the product rule, one has to limit the scope of operators (without using $f'$ or $\partial f/\partial x$): $$ \frac\partial{\partial x} u(x) v(x) = \left(\frac\partial{\partial x} u(x)\right) v(x) + u(x) \frac\partial{\partial x} v(x) $$ I have…
Martin Ueding
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Can we consider $\tan^{-1}x$ as an angle in degree?

When we write $\tan^{-1}x , \sin^{-1}x,...$ is it automatically considered as an angle in radian or it can be considered as degree as well? For example, we have$\;\;\pi-(\tan^{-1}(2)+\tan^{-1}(3))=\frac{\pi}4$ But can we…
Etemon
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Difference between $f(a)=b$ and $f:a\mapsto b$?

From what I understand, these two notations are exactly the same. Can they be used interchangeably?
Ruochan Liu
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What does this grid notation mean?

I read the below notation from a machine learning paper. $G_d$ is called a grid in $[0,1]^{d \times n}$ by the author. My understanding is: the vector entries are now restricted on the grid points instead of arbitrary values within the continous…
Yiwei Jiang
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Equivalence of Notation for Momentum Continuum

This wikipedia page for Magnetohydrodynamics lists the conservation of momentum in a continuum as: \begin{equation} \rho \left( \frac{\partial}{\partial t} + \vec v \cdot \nabla \right) \vec v = \vec J \times \vec B - \nabla p \end{equation} I was…
helloworld922
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What is meant by the notation complex numbers with superscript cross: $\mathbb{C}^{\times}$

The context I'm seeing it in says it's isomorphic to the automorphisms on $\mathbb{C}$. Thanks for your help.
fuqnuts
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Regarding the little oh, $o$ notation.

What I have come to understand is that $f(n)$ is said to be $o(g(n))$ if and only if for every $c>0$, there exists $n_0\in\mathbb{N}$ such that $f(n)
user948104
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