Go backward to Example Go up to Top Go forward to Example

Function Applications

Definition: function application

apply(f, x) := such y: <x, y> in f.

Notation: we write f(x) instead of apply(f, x).

Notation: we write f(x₀, ..., x_n-1) to denote f(<x₀, ..., x_n-1>).

Proposition: a function maps every argument in its domain to a well-defined result.

forall f: f is function =>

forall x in domain(f):

f(x) in range(f) /\  <x, f(x)> in f.