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Was (wer) ist finitely computable - definition
GROUP G THAT HAS SOME FINITE GENERATING SET S SO THAT EVERY ELEMENT OF G CAN BE WRITTEN AS THE PRODUCT OF FINITELY MANY ELEMENTS OF THE FINITE SET S AND OF INVERSES OF SUCH ELEMENT
Finitely-generated group; Finitely-generated subgroup; Finitely generated groups; Finitely Generated Group; Finitely generated subgroup
![The six 6th complex roots of unity form a [[cyclic group]] under multiplication.](https://commons.wikimedia.org/wiki/Special:FilePath/Cyclic group.svg?width=200 "The six 6th complex roots of unity form a [[cyclic group]] under multiplication.")
Computable number
![π]] can be computed to arbitrary precision, while [[almost every]] real number is not computable.](https://commons.wikimedia.org/wiki/Special:FilePath/10,000 digits of pi - poster.svg?width=200 "π]] can be computed to arbitrary precision, while [[almost every]] real number is not computable.")
REAL NUMBER THAT CAN BE COMPUTED TO WITHIN ANY DESIRED PRECISION BY A FINITE, TERMINATING ALGORITHM
Computable numbers; Recursive number; Recursive numbers; Uncomputable number; Non-computable numbers; Noncomputable number; Non-computable number; Computable real; Computable real number; Computable reals; Uncomputable numbers; Uncomputable real number
In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, effective numbers or the computable reals or recursive reals.
Incomputable
BASIC OBJECTS OF STUDY IN COMPUTABILITY THEORY
Non-computable function; Total computable function; Partial computable function; Computable predicate; Incomputable; Effectively computable; Turing computable; Uncomputable function; Incomputable function; Noncomputable function; Provably total; Turing-computable; Uncomputable
·adj Not computable.
Computable function
BASIC OBJECTS OF STUDY IN COMPUTABILITY THEORY
Non-computable function; Total computable function; Partial computable function; Computable predicate; Incomputable; Effectively computable; Turing computable; Uncomputable function; Incomputable function; Noncomputable function; Provably total; Turing-computable; Uncomputable
Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithms, in the sense that a function is computable if there exists an algorithm that can do the job of the function, i.
Wikipedia
Finitely generated group
In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of S and of inverses of such elements.
By definition, every finite group is finitely generated, since S can be taken to be G itself. Every infinite finitely generated group must be countable but countable groups need not be finitely generated. The additive group of rational numbers Q is an example of a countable group that is not finitely generated.
