Assertion: real number | /r/HasProperty | ordered
Facets:
value: totally
type: DEGREE
value: as with the natural numbers
type: OTHER
Source sentences:
text: Just as with the natural numbers that we learn first as children, the real numbers are ordered, which we can intuitively define as the concept that given a pair of unique real numbers, one of them is greater than the other (and, conversely, one is less than the other).
text: The well-ordering theorem implies that the real numbers can be well-ordered if the axiom of choice is assumed: there exists a total order on R with the property that every non-empty subset of R has a least element in this ordering.
text: First, since the real numbers are totally ordered, they carry an order topology.