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|=|N|=0, is said to be a countably infinite set.

Properties
dtype: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|=|N|=0, is said to be a countably infinite set.
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|=|N|=0, is said to be a countably infinite set.
rdfs:label
Countably Infinite Cardinality Type
View as:  CSV

Work in progress

RDF/XML
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    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/"
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    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">
    <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>
    <rdfs:isDefinedBy rdf:resource="http://qudt.org/2.1/schema/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.2:literal>countable</j.2:literal>
    <j.0:informativeReference rdf:datatype="http://www.w3.org/2001/XMLSchema#anyURI">http://www.math.vanderbilt.edu/~schectex/courses/infinity.pdf</j.0:informativeReference>
    <rdfs:isDefinedBy rdf:resource="http://qudt.org/2.1/schema/shacl/datatype"/>
    <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://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://www.linkedmodel.org/schema/dtype#literal> "countable" ;
  rdfs:isDefinedBy <http://qudt.org/2.1/schema/qudt> ;
  rdfs:isDefinedBy <http://qudt.org/2.1/schema/shacl/datatype> ;
  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":"\n  A set of numbers is called countably infinite if there is a way to enumerate them.\n  Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers.\n  The set of all fractions is also countably infinite.\n  In other words, any set $X$ that has the same cardinality as the set of the natural numbers,\n   or $| X | \\; =  \\; | \\mathbb N | \\; = \\; \\aleph0$, is said to be a countably infinite set.\n  " 
    ,"description":"\n  A set of numbers is called countably infinite if there is a way to enumerate them. \n  Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers.\n  The set of all fractions is also countably infinite.\n  In other words, any set $X$ that has the same cardinality as the set of the natural numbers,\n   or $| X | \\; =  \\; | \\mathbb N | \\; = \\; \\aleph0$, is said to be a countably infinite set.\n  " 
    ,"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\/datatype&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" : [ "\n  A set of numbers is called countably infinite if there is a way to enumerate them. \n  Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers.\n  The set of all fractions is also countably infinite.\n  In other words, any set $X$ that has the same cardinality as the set of the natural numbers,\n   or $| X | \\; =  \\; | \\mathbb N | \\; = \\; \\aleph0$, is said to be a countably infinite set.\n  ", "\n  A set of numbers is called countably infinite if there is a way to enumerate them.\n  Formally this is done with a bijection function that associates each number in the set with exactly one of the positive integers.\n  The set of all fractions is also countably infinite.\n  In other words, any set $X$ that has the same cardinality as the set of the natural numbers,\n   or $| X | \\; =  \\; | \\mathbb N | \\; = \\; \\aleph0$, is said to be a countably infinite set.\n  " ],
  "informativeReference" : "http://www.math.vanderbilt.edu/~schectex/courses/infinity.pdf",
  "literal" : "countable",
  "isDefinedBy" : [ "http://qudt.org/2.1/schema/qudt", "http://qudt.org/2.1/schema/shacl/datatype" ],
  "label" : "Countably Infinite Cardinality Type",
  "@context" : {
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      "@id" : "http://purl.org/dc/terms/description",
      "@type" : "http://qudt.org/schema/qudt/LatexString"
    },
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      "@type" : "@id"
    },
    "literal" : {
      "@id" : "http://www.linkedmodel.org/schema/dtype#literal"
    },
    "informativeReference" : {
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      "@type" : "http://www.w3.org/2001/XMLSchema#anyURI"
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  }
}

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