qudt:CT_COUNTABLY-INFINITE

URI: http://qudt.org/schema/qudt/CT_COUNTABLY-INFINITE

Type
Description

A set of numbers is called countably infinite if there is a way to enumerate them. Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers. The set of all fractions is also countably infinite. In other words, any set \(X\) that has the same cardinality as the set of the natural numbers, or \(| X | \; = \; | \mathbb N | \; = \; \aleph0\), is said to be a countably infinite set.

Properties
qudt:literal
countable
Annotations
dcterms:description
A set of numbers is called countably infinite if there is a way to enumerate them. Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers. The set of all fractions is also countably infinite. In other words, any set \(X\) that has the same cardinality as the set of the natural numbers, or \(| X | \; = \; | \mathbb N | \; = \; \aleph0\), is said to be a countably infinite set.
rdfs:label
Countably Infinite Cardinality Type
View as:  CSV

Work in progress

RDF/XML
<rdf:RDF
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:j.0="http://qudt.org/schema/qudt/"
    xmlns:j.1="http://purl.org/dc/terms/"
    xmlns:owl="http://www.w3.org/2002/07/owl#"
    xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="http://qudt.org/schema/qudt/CT_COUNTABLY-INFINITE">
    <rdfs:isDefinedBy rdf:resource="http://qudt.org/2.1/schema/shacl/qudt"/>
    <rdf:type rdf:resource="http://qudt.org/schema/qudt/CardinalityType"/>
    <j.1:description rdf:datatype="http://qudt.org/schema/qudt/LatexString">A set of numbers is called countably infinite if there is a way to enumerate them.  Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers.  The set of all fractions is also countably infinite.  In other words, any set \(X\) that has the same cardinality as the set of the natural numbers, or \(| X | \; =  \; | \mathbb N | \; = \; \aleph0\), is said to be a countably infinite set.</j.1:description>
    <j.0:informativeReference rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.math.vanderbilt.edu/~schectex/courses/infinity.pdf</j.0:informativeReference>
    <j.0:literal>countable</j.0:literal>
    <rdfs:isDefinedBy rdf:resource="http://qudt.org/2.1/schema/qudt"/>
    <rdfs:label>Countably Infinite Cardinality Type</rdfs:label>
  </rdf:Description>
</rdf:RDF>
TURTLE
@prefix owl: <http://www.w3.org/2002/07/owl#> .
@prefix rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#> .
@prefix rdfs: <http://www.w3.org/2000/01/rdf-schema#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<http://qudt.org/schema/qudt/CT_COUNTABLY-INFINITE>
  rdf:type <http://qudt.org/schema/qudt/CardinalityType> ;
  <http://purl.org/dc/terms/description> "A set of numbers is called countably infinite if there is a way to enumerate them.  Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers.  The set of all fractions is also countably infinite.  In other words, any set \\(X\\) that has the same cardinality as the set of the natural numbers, or \\(| X | \\; =  \\; | \\mathbb N | \\; = \\; \\aleph0\\), is said to be a countably infinite set."^^<http://qudt.org/schema/qudt/LatexString> ;
  <http://qudt.org/schema/qudt/informativeReference> "http://www.math.vanderbilt.edu/~schectex/courses/infinity.pdf"^^xsd:anyURI ;
  <http://qudt.org/schema/qudt/literal> "countable" ;
  rdfs:isDefinedBy <http://qudt.org/2.1/schema/qudt> ;
  rdfs:isDefinedBy <http://qudt.org/2.1/schema/shacl/qudt> ;
  rdfs:label "Countably Infinite Cardinality Type" ;
.
JSON
{"resource":"Countably Infinite Cardinality Type" 
 ,"qname":"qudt:CT_COUNTABLY-INFINITE" 
 ,"uri":"http:\/\/qudt.org\/schema\/qudt\/CT_COUNTABLY-INFINITE" 
 ,"properties":["description":"A set of numbers is called countably infinite if there is a way to enumerate them.  Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers.  The set of all fractions is also countably infinite.  In other words, any set \\(X\\) that has the same cardinality as the set of the natural numbers, or \\(| X | \\; =  \\; | \\mathbb N | \\; = \\; \\aleph0\\), is said to be a countably infinite set." 
    ,"informative reference":"http:\/\/www.math.vanderbilt.edu\/~schectex\/courses\/infinity.pdf" 
    ,"isDefinedBy":"&lt;http:\/\/qudt.org\/2.1\/schema\/qudt&gt;" 
    ,"isDefinedBy":"&lt;http:\/\/qudt.org\/2.1\/schema\/shacl\/qudt&gt;" 
    ,"label":"Countably Infinite Cardinality Type" 
    ,"literal":"countable" 
    ,"type":"qudt:CardinalityType" 
    ]}
JSON-LD
{
  "@id" : "http://qudt.org/schema/qudt/CT_COUNTABLY-INFINITE",
  "@type" : "http://qudt.org/schema/qudt/CardinalityType",
  "description" : "A set of numbers is called countably infinite if there is a way to enumerate them.  Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers.  The set of all fractions is also countably infinite.  In other words, any set \\(X\\) that has the same cardinality as the set of the natural numbers, or \\(| X | \\; =  \\; | \\mathbb N | \\; = \\; \\aleph0\\), is said to be a countably infinite set.",
  "informativeReference" : "http://www.math.vanderbilt.edu/~schectex/courses/infinity.pdf",
  "literal" : "countable",
  "isDefinedBy" : [ "http://qudt.org/2.1/schema/shacl/qudt", "http://qudt.org/2.1/schema/qudt" ],
  "label" : "Countably Infinite Cardinality Type",
  "@context" : {
    "isDefinedBy" : {
      "@id" : "http://www.w3.org/2000/01/rdf-schema#isDefinedBy",
      "@type" : "@id"
    },
    "description" : {
      "@id" : "http://purl.org/dc/terms/description",
      "@type" : "http://qudt.org/schema/qudt/LatexString"
    },
    "informativeReference" : {
      "@id" : "http://qudt.org/schema/qudt/informativeReference",
      "@type" : "http://www.w3.org/2001/XMLSchema#anyURI"
    },
    "literal" : {
      "@id" : "http://qudt.org/schema/qudt/literal"
    },
    "label" : {
      "@id" : "http://www.w3.org/2000/01/rdf-schema#label"
    },
    "rdf" : "http://www.w3.org/1999/02/22-rdf-syntax-ns#",
    "owl" : "http://www.w3.org/2002/07/owl#",
    "xsd" : "http://www.w3.org/2001/XMLSchema#",
    "rdfs" : "http://www.w3.org/2000/01/rdf-schema#"
  }
}

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