DBpedia – Linked Data Fragments

Matches in DBpedia 2016-04 for { ?s ?p "In mathematics, a Gödel numbering for sequences provides us an effective way to represent each finite sequence of natural numbers as a single natural number. Of course, the embedding is surely possible set theoretically, but the emphasis is on the effectiveness of the functions manipulating such representations of sequences: the operations on sequences (accessing individual members, concatenation) can be \"implemented\" using total recursive functions, and in fact by primitive recursive functions.It is usually used to build sequential “data types” in the realm of arithmetic-based formalizations of some fundamental notions of mathematics. It is a specific case of the more general idea of Gödel numbering.E.g. recursive function theory can be regarded as a formalization of notion “algorithm”, and if we regard it as a programming language, we can mimic arrays, lists by encoding a sequence of natural numbers in a single natural number — to achieve this, we can use various number theoretic ideas. Using the fundamental theorem of arithmetic is a straightforward way, but there are also more economic approaches, e.g. using the pairing function combined with the Chinese remainder theorem in a sophisticated way."@en }

• Gödel_numbering_for_sequences abstract "In mathematics, a Gödel numbering for sequences provides us an effective way to represent each finite sequence of natural numbers as a single natural number. Of course, the embedding is surely possible set theoretically, but the emphasis is on the effectiveness of the functions manipulating such representations of sequences: the operations on sequences (accessing individual members, concatenation) can be \"implemented\" using total recursive functions, and in fact by primitive recursive functions.It is usually used to build sequential “data types” in the realm of arithmetic-based formalizations of some fundamental notions of mathematics. It is a specific case of the more general idea of Gödel numbering.E.g. recursive function theory can be regarded as a formalization of notion “algorithm”, and if we regard it as a programming language, we can mimic arrays, lists by encoding a sequence of natural numbers in a single natural number — to achieve this, we can use various number theoretic ideas. Using the fundamental theorem of arithmetic is a straightforward way, but there are also more economic approaches, e.g. using the pairing function combined with the Chinese remainder theorem in a sophisticated way.".