"""
Positive Integers
"""
from sage.sets.integer_range import IntegerRangeInfinite
from sage.rings.integer import Integer
class PositiveIntegers(IntegerRangeInfinite):
r"""
The 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 :class:`InfiniteEnumeratedSets
<sage.categories.infinite_enumerated_sets.InfiniteEnumeratedSets>`).
This set is an integer range set. The construction is
therefore done by IntegerRange (see :class:`IntegerRange
<sage.sets.integer_range.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: infinite list
sage: it = iter(PP)
sage: (it.next(), it.next(), it.next(), it.next(), it.next())
(1, 2, 3, 4, 5)
sage: PP.first()
1
TESTS::
sage: TestSuite(PositiveIntegers()).run()
"""
def __init__(self):
r"""
EXAMPLES::
sage: PP = PositiveIntegers()
sage: PP.category()
Category of facade infinite enumerated sets
"""
IntegerRangeInfinite.__init__(self, Integer(1), Integer(1))
def _repr_(self):
r"""
EXAMPLES::
sage: PositiveIntegers()
Positive integers
"""
return "Positive integers"
def an_element(self):
r"""
Returns an element of ``self``.
EXAMPLES::
sage: PositiveIntegers().an_element()
42
"""
return Integer(42)
