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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.

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Meaning of notation $v \mapsto ( x \mapsto f(x,v) )$

I came across this notation in this wiki article. Can anyone tell me the meaning of this notation? What exactly is happening here? $v \mapsto ( x \mapsto f(x,v) )$ What I understand here is $x, v \in V$ and $V^*$ is its dual. Am I correct, if I say,…
Prashanth
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Notation for sum of products.

I have a set of sucessive elements $\{a_1, a_2, a_3, a_4\}$ from an arithmetic progression and I need to sum all the possible product-combinations of two elements, i.e. $$ a_1\cdot a_2+a_1\cdot a_3+a_1\cdot a_4 +a_2\cdot a_3+a_2\cdot a_4+a_3\cdot…
Neves
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Shorthand notation for "increases" and "decreases"

I want to write out something like: "As $x$ increases, $y$ decreases." Is there a standard symbolic notation for this, such as an up arrow and a down arrow? (And if you can tell me how to write it in latex, that would be awesome, too). Thanks!
Angada
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Is there a symbol for integrating and setting $C=0$?

Too often it's useful to just set $C$ to $0$ after integrating, so I was wondering if there is a symbol for that? Formally this would mean a shorter way of writing: $\int_{t_0}^x f(t)\,\mathrm{d}t = F(x), (F(t_0) = 0)$ This is useful when…
Frank Vel
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Is there any reason I can't use the $\cdot$ (dot product sign) instead of $\times$ (multiplication sign)?

Do note that I have read this question. However, I don't think it's quite the same question. When dealing with simple number multiplication, I actively try to use $\cdot$ instead of $\times$. Take the following example: 3 $\times$ 4 as opposed to: 3…
someonewithpc
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What is the meaning of the notation $\mathbb{R}^3/\mathbb{Z}^3$?

In Terence Tao's piece on Kolmogorov's Law (http://terrytao.wordpress.com/2014/05/15/kolmogorovs-power-law-for-turbulence/) he uses the notation for the fluid velocity $$u: \mathbb{R} \times \mathbb{R}^3/\mathbb{Z}^3 \to \mathbb{R}^3 $$ What is the…
James P
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What does "wedge" mean?

In Allen Hatcher's Algebraic Topology, $X\vee Y$ means the "wedge sum" of two (topological) spaces $X$ and $Y$. However, in $\LaTeX$, \wedge is the notation for $\wedge$, while $\vee$ is wirtten \vee. Where does this inconsistency come from?
Gaussler
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Meaning of : Set is closed under finite intersections and arbitrary unions

I have been working through "Set theory for working mathematician" and near the end of chapter about real numbers there is a small bit of topology. Namely the natural topology $\tau$ on euclidean space $\mathbb{R}^n$ is defined as set of all open…
Vanio Begic
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Notation for rounding function

The Wikipedia article http://en.wikipedia.org/wiki/Nearest_integer_function mentions the following notation for the rounding or "nearest integer" function. (That is, the function that corresponds to the ordninary rounding where you go up if the…
DavidButlerUofA
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Usage of capital and small letters

Are there rules for when small, capital and greek symbols are used? Simple example: The volume left in a cube with a sphere in it is V=C-S with capital standard latin letters, meaning "if you don't know who I am, you have to do the equations first.…
Mr.Mund
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Difference between $\sqrt [q]{x^p}$ and $x^{p/q}$?

Is there difference between $\sqrt [q]{x^p}$ and $x^{p/q}$ ? There seems to be no difference when just dealing with positive reals, but what about when $x$ is negative (or even complex)? p.s. Maybe there's in fact no difference but I'm too…
JSCB
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Difference between $f(x) \neq 0$ and $f(x) \not\equiv 0$

What is the difference between the statements $$ f(x) \neq 0 $$ and $$ f(x) \not\equiv 0? $$
Jason Schmidt
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"Scoping" rules in mathematics

I've been having a discussion with my friend about scoping rules in mathematical syntax. By scoping I mean a set of rules that define how variable and function names could be chosen so that at any given point no name used is ambiguous. As I'm a…
Krotton
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Notation of Hessian?

I looked here, and couldn't find an answer: http://en.wikipedia.org/wiki/Hessian_matrix I am looking for a way to denote the Hessian at a certain value. I have a function $f(x)$ where $x \in \mathbb{R}^d$, and I want to somehow denote the second…
linalg
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Why do some people place the differential at the beginning of their integral?

I've seen several times on this site people writing integrals like $ \int \! dxf(x) $. This seems confusing to me, especially in an iterated integral or next to a long integrand and it's nonstandard compared to my own personal experience. I'm…
R R
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