About: S map   Sponge Permalink

An Entity of Type : owl:Thing, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

S map is a function which maps "a pair of a natural number and a function" to "a pair of a natural number and a function". It was defined by Japanese googologist Fish in 2002 and used in the definition of Fish number 1 and Fish number 2. It is defined as \begin{eqnarray*} S:[m,f(x)]→[g(m),g(x)] \end{eqnarray*} which means that when a pair of \(m \in \mathbb{N}\) and a function \(f(x)\) is given as input variables of S map, a pair of \(g(m) \in \mathbb{N}\) and a function \(g(x)\) is obtained as return values, where \(g(x)\) is defined as and \(g(m)\) is calculated by substituding \(x=m\) to \(g(m)\).

AttributesValues
rdfs:label
  • S map
rdfs:comment
  • S map is a function which maps "a pair of a natural number and a function" to "a pair of a natural number and a function". It was defined by Japanese googologist Fish in 2002 and used in the definition of Fish number 1 and Fish number 2. It is defined as \begin{eqnarray*} S:[m,f(x)]→[g(m),g(x)] \end{eqnarray*} which means that when a pair of \(m \in \mathbb{N}\) and a function \(f(x)\) is given as input variables of S map, a pair of \(g(m) \in \mathbb{N}\) and a function \(g(x)\) is obtained as return values, where \(g(x)\) is defined as and \(g(m)\) is calculated by substituding \(x=m\) to \(g(m)\).
dcterms:subject
dbkwik:googology/p...iPageUsesTemplate
abstract
  • S map is a function which maps "a pair of a natural number and a function" to "a pair of a natural number and a function". It was defined by Japanese googologist Fish in 2002 and used in the definition of Fish number 1 and Fish number 2. It is defined as \begin{eqnarray*} S:[m,f(x)]→[g(m),g(x)] \end{eqnarray*} which means that when a pair of \(m \in \mathbb{N}\) and a function \(f(x)\) is given as input variables of S map, a pair of \(g(m) \in \mathbb{N}\) and a function \(g(x)\) is obtained as return values, where \(g(x)\) is defined as \begin{eqnarray*} B(0,n) & = & f(n) \\ B(m+1,0) & = & B(m, 1) \\ B(m+1,n+1) & = & B(m, B(m+1, n)) \\ g(x) & = & B(x,x) \end{eqnarray*} and \(g(m)\) is calculated by substituding \(x=m\) to \(g(m)\). \(B(m,n)\) is similar to Ackermann function except \(B(0,n) = f(n)\).
is wikipage disambiguates of
Alternative Linked Data Views: ODE     Raw Data in: CXML | CSV | RDF ( N-Triples N3/Turtle JSON XML ) | OData ( Atom JSON ) | Microdata ( JSON HTML) | JSON-LD    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 07.20.3217, on Linux (x86_64-pc-linux-gnu), Standard Edition
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2012 OpenLink Software