Editing Numerical tower (section)

{{Short description|Set of data types that represent numbers in a given programming language}}
In [[Scheme (programming language)|Scheme]], the '''numerical tower''' is a set of [[data types]] that represent [[number]]s and a logic for their hierarchical organisation.

[[File:NumericalTower.svg|thumb|A representation of the numerical tower with five types of numbers.]]
Each type in the tower conceptually "sits on" a more fundamental type, so an [[integer]] is a [[rational number]] and a [[number]], but the converse is not necessarily true, i.e. not every number is an integer. This asymmetry implies that a language can safely allow [[Type conversion|implicit coercions]] of numerical types—without creating semantic problems—in only one direction: coercing an integer to a rational loses no information and will never influence the value returned by a function, but to coerce most reals to an integer would alter any relevant computation (e.g., the real 1/3 does not equal any integer) and is thus impermissible.