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A long ray is a one-dimensional shape made from gluing an uncountably infinite number of half-open line segments together in the order given by ω1. This makes it longer than the ray, which is made from gluing a countably infinite number of half-open line segments in the order given by ω0. It can be considered as being the nonnegative part of a number line which enumerates all countable ordinals. A long ray has a boundary comprising the single point on the closed end. If this point is removed, the open long ray can be constructed.

AttributesValues
rdf:type
rdfs:label
  • Long ray
rdfs:comment
  • A long ray is a one-dimensional shape made from gluing an uncountably infinite number of half-open line segments together in the order given by ω1. This makes it longer than the ray, which is made from gluing a countably infinite number of half-open line segments in the order given by ω0. It can be considered as being the nonnegative part of a number line which enumerates all countable ordinals. A long ray has a boundary comprising the single point on the closed end. If this point is removed, the open long ray can be constructed.
dcterms:subject
dimensionality
  • 1(xsd:integer)
dbkwik:verse-and-d...iPageUsesTemplate
Vertices
  • 1(xsd:integer)
edges
  • 1(xsd:integer)
equivalent manifold
  • Long ray
abstract
  • A long ray is a one-dimensional shape made from gluing an uncountably infinite number of half-open line segments together in the order given by ω1. This makes it longer than the ray, which is made from gluing a countably infinite number of half-open line segments in the order given by ω0. It can be considered as being the nonnegative part of a number line which enumerates all countable ordinals. A long ray has a boundary comprising the single point on the closed end. If this point is removed, the open long ray can be constructed.
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