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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Mathematical notation - cummulative summation

The Mertens function can be calculated in Mathematica by: Accumulate[Table[MoebiusMu[k], {k, 1, n}]] and is written as $$M(n)=\sum_{k=1}^n\mu(k)$$ Could someone please tell me how I would write Table[Mean[Accumulate[Table[MoebiusMu[k], {k, 1,…
martin
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Why are superscripts used instead of subscripts in this example?

A snippet from Marcus du Sautoy's The Number Mysteries, Chapter 3, in the section called HOW GOOD ARE YOU AT RANDOMNESS is shown below. My question is, why does the author use superscripts instead of subscripts here?
I. J. Kennedy
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Meaning of Clo(A), Int(A), Rint(A)

I've just stumbled upon this notation in a text about optimalisation with no explanation as to what they mean (suggesting they are widely used and well known?). $A$ is a set (a convex set in this case) and the notation I am not sure of is: $$clo(A),…
Dahn
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Set notation, what does it mean

Can sonbody explain to me what does set notation of $$ C_NM\\ $$ means. The C in given notation is not letter C, it is some kind of very narrow C. I Could not find the alternative, to write. Thanks
depecheSoul
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Notation for a defining a grid of points

I evaluated a function over a grid of points in three-dimensions. I would like to know what the standard notation is to define my grid of points? In matlab notation the grid is defined by: [x,y,z] =…
okj
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Tensor product symbol and convolution

The convolution of $f$ and $g$ is sometimes written as $f\ast g$ and sometimes as $f \otimes g$. Is convolution denoted by both of these symbols because the operations are related, or is it just historically determined? Wikipedia and Google dont…
Leo
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Comma after equation

ps: I have asked this question on https://tex.stackexchange.com/ (here) but is regarded as off-topic. So I moved it here. I have seen different ways in papers to put comma after equation. right after the equation: right before where: no comma at…
herohuyongtao
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Notation for quadratic form

My book states the following for a generalisation on $\mathbb{R}^k$: $\displaystyle\sum_{i,j=1}^{k} a_{ij}x_ix_j$ Is this the same notation as $\displaystyle\sum_{i\leq j=1}^{k} a_{ij}x_ix_j$ or is it a mistake in the book?
Aqancake
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Is $\epsilon _{X_i}(I_n) $ an other notation for the indicator function?

My book uses both of the functions $\epsilon _{X_i}(I_n)$ and $1_{X_i\in I_n}$ once with an equality sign, otherwise just the first one. Is this different notation for the same function? Thanks in advance!
Alexander
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Definitions of sets

How would I define the set $\Omega_2(x)\ =\ \{4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, 38, 39\dots\}$, where $\Omega_2$ is the set of semi primes (ie - numbers with $2$ not necessarily distinct prime factors)? I would like to define…
martin
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Is there a standard shorthand for the set $\{0, 1, \dots,k-1,k+1,\dots,n-1,n\}$?

The question title pretty much says it all. In derivations where there's some fancy footwork being done with indices, I find expressions like $$\sum_{i \neq k} x_i$$ a bit too vague. On the other hand, this is explicit enough, but just too unwieldy…
kjo
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Notation for "Nested" Sequences?

Let $X$ and $Y$ be two ordered pairs $X = (A,B)$ and $Y = (A,B)$. Then let $A$ and $B$ be two sequences "nested" in the pairs $A = \langle A_1,A_2,...,A_n \rangle$ and $B = \langle B_1,B_2,...B_n \rangle$ (the elements of the sequences in $X$ and…
copenhagen
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Other shortcuts similar to $\pm$?

In writing proofs, I'll sometimes end up with two separate but similar results, such as $[a] + [b] = [a + b]$ and $[a] \times [b] = [a \times b]$. Out of curiosity, is there some standard notation to denote two operations at once, besides the $\pm$…
Cisplatin
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Braket notation

$\def\pd#1#2{\frac{\partial#1}{\partial#2}}\def\braket#1#2{\langle#1|#2\rangle}\def\bra#1{\langle#1}\def\ket#1{#1\rangle}$I am given that $$\bra{\theta,\phi}|L_+|\ket{l,m} = \hbar e^{i\phi} \left(\pd{}{\theta}+i\cot{\theta}\pd{}{\phi}\right)…
O. P.
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Mathematical notation - defining sets

Building on this question, if the cubeful numbers were defined as follows: $$\Bbb Z_{\{3+\}} = \{a \in \Bbb Z \mid \not\exists b \in \Bbb Z \text{ s.t. } a \neq b^3 \}$$ Would it suffice to say that: $$\text{ If }\ \Bbb Z_{\{3+\}} = \{a \in \Bbb Z…
martin
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