recursive definition sentence in Hindi
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- More generally, recursive definitions of functions can be made whenever the domain is a well-ordered set, using the principle of transfinite recursion.
- In addition, it maps rational numbers to dyadic rationals, as can be seen by a recursive definition closely related to the Stern Brocot tree.
- 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.
- :Recursive definitions are used all the time, check any word in a dictionary and follow it along and you'll get a loop.
- In denotational semantics of programming languages, a special case of the Knaster & ndash; Tarski theorem is used to establish the semantics of recursive definitions.
- 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.
- 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 ).
- 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.
- 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.
- 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.
- 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.
- This comes in contrast with the direct meaning of the notion of semantic consequence, that quantifies over all structures in a particular language, which is clearly not a recursive definition.
- In a function defined by a recursive definition, each value is defined by a fixed first-order formula of other, previously defined values of the same function or other functions, which might be simply constants.
- Existence and uniqueness of the general transfinite recursive definition of sets was demonstrated in 1928 by von Neumann for both Zermelo-Fraenkel set theory and Neumann's own set theory ( which later developed into NBG set theory ).
- Therefore any recursive coding of a nonstandard model onto the natural numbers, along with a recursive definition ( acting on codes ) for the model's addition and multiplication operations will give a recursive separator, which cannot exist.
- A "'recursive definition "'( or "'inductive definition "') in mathematical logic and computer science is used to define the elements in a set in terms of other elements in the set ( Aczel 1978 : 740ff ).
- The topological recursion is then a recursive definition of infinite sequences of symmetric meromorphic n-forms \ omega _ { g, n } on \ Sigma ^ n, with poles at ramification points only, for integers ge " 0 such that 2g-2 + n > 0.
- One such function, which is provable total but not primitive recursive, is Ackermann function : since it is recursively defined, it is indeed easy to prove its computability ( However, a similar diagonalization argument can also be built for all functions defined by recursive definition; thus, there are provable total functions that cannot be defined recursively ).
- In fact, the model of " any " theory containing PA obtained by the systematic construction of the arithmetical model existence theorem, is " always " non-standard with a non-equivalent provability predicate and a non-equivalent way to interpret its own construction, so that this construction is non-recursive ( as recursive definitions would be unambiguous ).
- Normalisability is a rare feature of most non-trivial type theories, which is a big departure from the logical world . ( Recall that almost every logical derivation has an equivalent normal derivation . ) To sketch the reason : in type theories that admit recursive definitions, it is possible to write programs that never reduce to a value; such looping programs can generally be given any type.
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