Positive Integers¶
- class sage.sets.positive_integers.PositiveIntegers[source]¶
Bases:
IntegerRangeInfiniteThe enumerated set of positive integers. To fix the ideas, we mean \(\{1, 2, 3, 4, 5, \dots \}\).
This class implements the set of positive integers, as an enumerated set (see
InfiniteEnumeratedSets).This set is an integer range set. The construction is therefore done by IntegerRange (see
IntegerRange).EXAMPLES:
sage: PP = PositiveIntegers() sage: PP Positive integers sage: PP.cardinality() +Infinity sage: TestSuite(PP).run() sage: PP.list() Traceback (most recent call last): ... NotImplementedError: cannot list an infinite set sage: it = iter(PP) sage: (next(it), next(it), next(it), next(it), next(it)) (1, 2, 3, 4, 5) sage: PP.first() 1
>>> from sage.all import * >>> PP = PositiveIntegers() >>> PP Positive integers >>> PP.cardinality() +Infinity >>> TestSuite(PP).run() >>> PP.list() Traceback (most recent call last): ... NotImplementedError: cannot list an infinite set >>> it = iter(PP) >>> (next(it), next(it), next(it), next(it), next(it)) (1, 2, 3, 4, 5) >>> PP.first() 1