# Parentheses are overused

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 :

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