Editing Fixed-point combinator (section)

===Values and domains===
Many functions do not have any fixed points, for instance <math>f : \N \to \N</math> with <math>f(n)=n+1</math>. Using [[Church encoding]], natural numbers can be represented in lambda calculus, and this function ''f'' can be defined in lambda calculus. However, its [[domain of a function|domain]] will now contain ''all'' lambda expressions, not just those representing natural numbers. The Y combinator, applied to ''f'', will yield a fixed-point for ''f'', but this fixed-point won't represent a [[natural number]]. If trying to compute ''Y f'' in an actual programming language, an infinite loop will occur.