Parentheses are overused: Difference between revisions
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Ideals: \((2)\) is the ideal generated by 2, \((a,b,c)\) is the ideal generated by \(\{a,b,c\}\). | 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: \((a,b,c,d)_2\).
