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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What does do double vertical bars with numerical parameters on the right hand side mean?

In the following equation, $$\large R(Y) = \lambda \left\| \frac {x^\top Y} {\|x\|} \right\|^2_2$$ What do the double bars with range $2$ to $2$ on the right hand side mean? I need to work with this equation, but I don't understand what it is doing.…
Adam
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Regarding notation, for $f(x,y)$ are $f_x(x,g(x))$ and $\frac{\partial}{\partial x}f(x,g(x))$ interpreted differently?

More specifically, I see $\frac{\partial}{\partial x}f(x,g(x))$ as meaning take the derivative of $f(x,g(x))$ w.r.t $x$. On the other hand, I see $f_x(x,g(x))$ as meaning the partial derivative of $f(x,y)$ evaluated at $(x,g(x))$ Do these notations…
user106860
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Having trouble notating an equation determining how much XP is to be given to players while referencing variables found in our database.

In the game being developed, players will be playing best-of-three matches against one another. XP will be given out depending on their score vs the average score and will receive a bonus for whether or not they win or lose. Given the nature of our…
Tenkster
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Meaning of symbol $\looparrowright$ in math

Is there a conventional meaning for the symbol $\looparrowright$ when used in math. I came across this symbol in here (see slide 2 for e.g.).
Likely
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Is this notation feature a kind of "variable shadowing"?

I'm a programmer, hence the term "shadowing" in the title. In C++ programming, you can do the following: void foo() { int i = 5; { int i = 6; } } The two is here are separate variables. The i in the inner scope is said to…
Stefan Monov
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Notation for meta-variable or placeholder variable

I have an ODE model for a biological system which has state variables named $A, B, C, \dots$, and the expressions for their derivatives contain the unknown functions $f_A, f_B, f_C, \dots$. I was typing up a description for each but it ended being…
JaredL
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Is ${\rm mod}(x,m)$ recognizable notation for $\,x\bmod m\,$?

From my understanding the standard notation for modulus is $\,x \bmod m$, but using that notation expressions like $(((x-.5) \bmod 7) -y)^2$ become quite clumsy. The Desmos graphing calculator uses the aformention notation of $\,{\rm mod}(x,m)$…
Aaron Quitta
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Notation for "Defined as proportional to"

If I say $x$ is defined as $y+z$ then I can say $x := y+z$. If I want to say $x$ is defined as proportional to $y+z$, then how can I say that? Would I say $x :\propto y+z$?
Shrey Joshi
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How to understand this summation notation?

The documentation for OpenCV provides the following convolution explanation Assume you want to know the resulting value of a particular location in the image. The value of the convolution is calculated in the following way: Place the kernel…
Startec
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"shorthand notation" for $x^{-1}$

I had a student write "$x^-$" as a "shorthand" for $x^{-1}$. Is anyone aware of a context where this is standard notation? Edit: Since it appears that as far as anyone knows he did just make it up, it seems unlikely that anyone will ever have the…
David C. Ullrich
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Best notation for interval with scientific notation?

I am giving a value $\alpha$ and its confidence interval in a table. All numbers are very large so I ought to use scientific notation. But what is the best and neatest way to present this? Some options: $5\times10^6 (9\times10^5,9\times10^6)$ -…
thlpswm
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What does "$:[$" mean in $q_{(i,d,j)} ≜ P(S_{[t+1:t+d]}=j\;|S_{[t+1:[}=j)$?

I am reading through some math on a paper, and I am trying to properly understand some of the proofs / equations. In particular, $$q_{(i,d,j)} ≜ P(S_{[t+1:t+d]}=j|S_{[t+1:[}=j)$$ is fairly confusing to me. I know that the function q is being…
squirvel
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How can I notate the assignment of each variable in a tuple to a specific value?

Assume I have a tuple of variables, i.e. $\mathcal{T} = (x_1,...,x_n)$. Now I would like to assign each of those elements in the tuple to the same value $c$. How I can I denote this in a formally correct way? Maybe using the $\forall$ symbol?
Chris
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How best to denote an elementwise function of a vector?

Consider a vector $\pmb{v}=(v_1, v_2...,v_n) \in \mathbb{R}^n$ and a function $f: \mathbb{R} \to \mathbb{R} $. What is the best way to denote the vector $(f(v_1), f(v_2)....,f(v_n))$? Writing $f(\pmb{v})$ isn't exactly correct as $f$ is not…
ste_kwr
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Is there a difference between $g(x,y)$ and $g(x;y)$?

Is there a reason that the second notation uses a semicolon? Here's the definition: we say $g(x;y)$ is a Green's function $$g(x;y) = \left\{ \begin{array}{lr} \sin(kx)\sin(k(y-1)/k\sin(k) & : x \lt y\\ …
user29418
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