More generally, recursive definitions of functions can be made whenever the domain is a well-ordered set, using the principle of transfinite recursion.
22.
In addition, it maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern Brocot tree.
23.
Variants of interchangeability of code and data together with the treatment of functions lend themselves extremely well for a recursive definition of a variadic compositional operator.
24.
:Recursive definitions are used all the time, check any word in a dictionary and follow it along and you'll get a loop.
25.
In denotational semantics of programming languages, a special case of the Knaster & ndash; Tarski theorem is used to establish the semantics of recursive definitions.
26.
In Dedekind's work, this approach appears as completely characterizing natural numbers and providing recursive definitions of addition and multiplication from the successor function and mathematical induction.
27.
In mathematical logic and computer science, the least fixed point is related to making recursive definitions ( see domain theory and / or denotational semantics for details ).
28.
Note that string projection is well-defined even if the rank of the monoid is infinite, as the above recursive definition works for all strings of finite length.
29.
The syntax of a member of the description logic family is characterized by its recursive definition, in which the constructors that can be used to form concept terms are stated.
30.
That recursive definitions are valid-meaning that a recursive definition identifies a unique function-is a theorem of set theory, the proof of which is non-trivial.
