Joachim Faulhaber wrote:
What is the meaning of the cardinality of a continuous interval? It seems to be defined to be 0? Why not make it only available for discrete domains?
Try this:
interval<double> x(0.0, 1.0); if(x.cardinality() == numeric_limits<interval<double>::size_type>::infinity()) cout << "cardinality is infinite\n";
for doubles a, b with a < b: [a,b).cardinality() == infinity but {[a,a],[b,b]}.cardinality() == 2
Function cardinality() has been introduced to make clear: This function yields the number of *elements*, and not the number of iteratable entities in the interval container. For continuous domain_types the cardinality of an interval container can be infinite but it can be finite as well.
This seems to make the cardinality of empty intervals infinite! I get this output from the code below: empty interval cardinality is 0 empty interval cardinality is infinite unit interval cardinality is 0 unit interval cardinality is infinite singleton interval cardinality is 1 { const interval< double > empty_interval; cout << "empty interval cardinality is " << empty_interval.cardinality() << "\n"; if( empty_interval.cardinality() == numeric_limits< interval< double
::size_type >::infinity() ) cout << "empty interval cardinality is infinite\n"; }
{ const interval< double > unit_interval( 0.0, 1.0 ); cout << "unit interval cardinality is " << unit_interval.cardinality() << "\n"; if( unit_interval.cardinality() == numeric_limits< interval< double
::size_type >::infinity() ) cout << "unit interval cardinality is infinite\n"; }
{ const interval< double > singleton_interval( 0.0 ); cout << "singleton interval cardinality is " << singleton_interval.cardinality() << "\n"; if( singleton_interval.cardinality() == numeric_limits< interval< double >::size_type >::infinity() ) cout << "singleton interval cardinality is infinite\n"; } Do you agree this is potentially confusing?