### Navigation

- index
- modules |
- next |
- previous |
- Basic Structures »

# Positive Integers

class `sage.sets.positive_integers.``PositiveIntegers`

  Bases: `sage.sets.integer_range.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: 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()

  `an_element`()

    Returns an element of `self`.

    EXAMPLES:

        sage: PositiveIntegers().an_element()
        42

### Navigation

- index
- modules |
- next |
- previous |
- Basic Structures »