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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