Positive Integers

class sage.sets.positive_integers.PositiveIntegers

Bases: IntegerRangeInfinite

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 InfiniteEnumeratedSets).

This set is an integer range set. The construction is therefore done by IntegerRange (see IntegerRange).

EXAMPLES:

Sage

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

Python

>>> 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

an_element()

Return an element of self.

EXAMPLES:

Sage

sage: PositiveIntegers().an_element()
42

Python

>>> from sage.all import *
>>> PositiveIntegers().an_element()
42