Assertion: real number | /r/DefinedAs | ordered field
Facets:
value: axiomatically
type: MANNER
value: synthetically
type: MANNER
Source sentences:
text: The real numbers can be defined synthetically as an ordered field satisfying some version of the completeness axiom.
text: The real numbers can either be defined axiomatically as a complete ordered field, or can be reduced by set theory as a set of all limits of Cauchy sequences of rational numbers (a completion of a metric space).