Assertion: real number | /r/HasProperty | complete
Facets:
value: to the open interval
type: TEMPORAL
value: more technically
type: DEGREE
value: often
type: TEMPORAL
Source sentences:
text: This is formally defined in the following, and means that the reals are complete (in the sense of metric spaces or uniform spaces, which is a different sense than the Dedekind completeness of the order in the previous section).
text: (This limit exists because the real numbers are complete.)
text: This property of the real numbers is expressed by saying that the real numbers endowed with the standard metric, ( R , | ⋅ | ) {\displaystyle (\mathbb {R} ,|\cdot |)} , is a complete metric space.
text: The real numbers are often described as "the complete ordered field", a phrase that can be interpreted in several ways.
text: More technically, the reals are complete (in the sense of metric spaces or uniform spaces, which is a different sense than the Dedekind completeness of the order in the previous section ).
text: That is, the reals are complete.
text: An example is given by the real numbers, which are complete but homeomorphic to the open interval (0,1), which is not complete.