Assertion: isomorphism's inverse | /r/HasProperty | surjective
Facets:
value: both
type: DEGREE
value: onto the positive cones
type: TRANSITIVE-OBJECT
value: onto order
type: MANNER
Source sentences:
text: a bijection always has an inverse (being surjective and injective); and that inverse is also a monotone, because it will always map right back to the original ordering (being bijective)
text: For what it's worth, his definition does not use the phrase "order embedding" but rather requires that a function and its inverse are both surjective onto the positive cones and order preserving/monotonic/isotonic...