Parentheses are overused: Difference between revisions

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[[Category:Conflicting definitions]]
[[Category:Ambiguities]]


Parentheses are used to represent all sorts of operations and objects, many of which conflict with each other.
Parentheses are used to represent all sorts of operations and objects, many of which conflict with each other.
Grouping parts of an expression: \( (x+1)(x+2) \)
Argument of a function: \(f(x)\) is "\(f\) applied to \(x\)". ([[There is no function application symbol]])


Greatest common divisor: \((a,b) = \gcd(a,b)\)  
Greatest common divisor: \((a,b) = \gcd(a,b)\)  
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Vectors or one-column matrices: \( \begin{pmatrix} a \\ b \end{pmatrix} \)
Vectors or one-column matrices: \( \begin{pmatrix} a \\ b \end{pmatrix} \)
Ideals: \((2)\) is the ideal generated by 2, \((a,b,c)\) is the ideal generated by \(\{a,b,c\}\).
Tuples: \((a,b)\)
Cycle notation for permutations: \((a,b)\) or \((a \; b)\)
Legendre/Jacobi symbol: \( \left(\dfrac{a}{b}\right) \)
[[Intervals]]: \((a,b)\) is open at both ends, \((a,b]\) is open at one end.
== Less standard notations, local to a document ==
These are many and varied, one motivating example
<ref>[https://www.sas.rochester.edu/mth/undergraduate/honorspaperspdfs/caten2017.pdf "The toplogy of magmas", by Charlotte Aten]</ref>:
The set of all 2-faces of the simplex with vertices a,b,c and d: \((a,b,c,d)_2\).
==References==
<ref>[https://karendcampe.wordpress.com/2016/04/28/problems-with-parentheses/amp/ "Problems with parentheses", by Karen Campe]</ref>

Latest revision as of 13:02, 31 July 2021


Parentheses are used to represent all sorts of operations and objects, many of which conflict with each other.

Grouping parts of an expression: \( (x+1)(x+2) \)

Argument of a function: \(f(x)\) is "\(f\) applied to \(x\)". (There is no function application symbol)

Greatest common divisor: \((a,b) = \gcd(a,b)\)

Counting combinations: \( {n \choose k} = \frac{n!}{k!(n-k)!} \)

Repeated differentiation : \( f^{(n)}(x) = \frac{\mathrm{d}^nf}{\mathrm{d}x^n} \)

Vectors or one-column matrices: \( \begin{pmatrix} a \\ b \end{pmatrix} \)

Ideals: \((2)\) is the ideal generated by 2, \((a,b,c)\) is the ideal generated by \(\{a,b,c\}\).

Tuples: \((a,b)\)

Cycle notation for permutations: \((a,b)\) or \((a \; b)\)

Legendre/Jacobi symbol: \( \left(\dfrac{a}{b}\right) \)

Intervals: \((a,b)\) is open at both ends, \((a,b]\) is open at one end.


Less standard notations, local to a document

These are many and varied, one motivating example [1]:

The set of all 2-faces of the simplex with vertices a,b,c and d: \((a,b,c,d)_2\).


References

[2]