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 $x$ represent?

$x$ can mean: A defined value in $x = 5$ An unknown, TBD. value, in $3x = 2+4$ A variable in $y(x) = x+4$ A sum of numbers in $\int_0^2 \mathrm{d}x$ Are there any other examples?
Frank Vel
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How to call simple expressions in a paper which do not need any proof?

I am using an expression in a paper which doesnt need a proof at all such as $$\sum_{i=k}^K\binom{K}{i}p^i(1-p)^{K-i}$$ is a decreasing function of $k$ and $$\sum_{i=0}^{k-1}\binom{K}{i}p^{K-i}(1-p)^i$$ is an increasing function of $k$. However I…
Seyhmus Güngören
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What does $\mathbb{R}^{[0,1]}$ stand for?

What does $\mathbb{R}^{[0,1]}$ stand for in the following expression? $\Phi: C[0,1] \to \mathbb{R}^{[0,1]}$, where $C$ is the space of all the continuous function in $[0,1]$ and $\Phi$ is an operator. EDIT 1 Considering the notation…
user3889486
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Notation for "there exists at least 2"?

Let $S = \langle 1,3,5,7,9 \rangle$ be a sequence of a numbers. Then let $Q = \{ 1,2,4 \}$ and $R = {1,2,3}$ be two sets of numbers. Then I have a function $exists(Q,S)$ that should return true if there is at least two elements $q \in Q$ such that…
af194
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What's the notation of the one-sided differential of a function?

Assume $$f(x)=\left \{\begin{matrix} x-1 & x \leq 0\\ x+1 & x > 0 \end{matrix} \right.$$ Obviously, $df(x)/dx$ do not exists at $x=0$ but the one-sided differential exists. What's the notation of one-sided differential? $$d_-f(x)/d_-x$$,…
iuradz
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Subscript plus and negative sign

What is the precise mathematical definition of the positive and negative subscript signs as in the following function? $f(\mu) = \displaystyle\sum_{i=1}^n \alpha (x_i - \mu)_{+} + (1- \alpha)(x_i - \mu)_{-}$
pyrrhic
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Different use of approximate equality symbols

I have been wondering for a long time whether there is a unequivocal way to define and use the symbols commonly adopted for an approximate equality between two quantities. I am a physicist, and I often see them used interchangeably and more or less…
usumdelphini
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Notation question. How to write the set of all polynomials (over $ \mathbb{R}$) of degree at most $p$.

The question is pretty much in the title. I have been using $\mathrm{poly}_p$ but I don't like it.
fred
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Difference between Gamma and partial Omega to describe a domain boundary

Is there a difference between referring to the boundary of a domain $\Omega$ as $\Gamma$ or $\partial \Omega$ ? Or is this just preference or synonyms of the same thing? From my experience, they seem to be used arbitrarily, but I feel like I might…
Charles
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Notations for array operations

There are some common array operations that are used in programming, which I have a difficult time writing out in mathematical notation without using explicitly-indexed scalars. Some include: Element-wise products of two arrays. Sum of all elements…
hatmatrix
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What does $\therefore$ mean

Question: I recently read the symbol $\therefore$ in a couple of posts. Unfortunately i can't find the posts anymore. Does this have any special mathematical meaning?
math635
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Need help understanding notation

The textual description of the space $G$ is as follows: $G(\mathbb{R}^2)$ is the Banach space composed of the distributions $f$ which can be written as $f = \mathrm{div}(g)$, where $\mathrm{div}:Y\rightarrow X$. Later on in the paper, a discrete…
AnonSubmitter85
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Calculator mode. ENG mode?? (SCI vs. FLO vs. ENG)

When I type 8*6 FLO = 48 SCI = $4.8 * 10^1$ ENG = $48 * 10^0$ 1) What is the point of ENG mode?? 2) What are situations where you want answers in SCIentific notation?
JackOfAll
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Significant figures: Trailing Zeros in Scientific Notation.

I'm wondering how you determine the number of significant figures of a number in scientific notation with trailing zeros. For example: $3100.0*10^2$ (which is not in correct scientific notation) has how many significant figures? On first guess…
theideasmith
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Does $\sin(2x)^2 = \sin(2x^2)$ or $(\sin(2x))^2$

In the notation $\sin(x)^2 $ Does this equal $\sin(x^2) $ or $(\sin(x))^2 $ ? I'm sorry this is such a simple question but Google is unhelpful. There are plenty of sources illustrating $\sin^2(x) $ = $(\sin(x))^2 $ but nothing about $\sin(x)^2…
Sam Sabin
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