Infinite integer in Python
infinity, math, python, python-3.x
Solution
You are right that an integer infinity is possible, and that none has been added to the Python standard. This is probably because `math.inf` supplants it in almost all cases (as Martijn stated in his comment).
In the meantime, I added an implementation of extended integers on PyPI:
In [0]: from numbers import Integral, Real
In [0]: from extended_int import int_inf, ExtendedIntegral, Infinite
In [0]: i = int_inf
In [4]: float(i)
Out[4]: inf
In [5]: print(i)
inf
In [6]: i ** i
Out[6]: inf
In [7]: i
Out[7]: inf
In [9]: isinstance(i, Real)
Out[9]: True
In [10]: isinstance(i, Integral)
Out[10]: False
In [11]: isinstance(i, Infinite)
Out[11]: True
In [12]: isinstance(i, ExtendedIntegral)
Out[12]: True
In [13]: isinstance(2, ExtendedIntegral)
Out[13]: True
In [14]: isinstance(2, Infinite)
Out[14]: False
Problem
Python 3 has `float('inf')` and `Decimal('Infinity')` but no `int('inf')`. So, why a number representing the infinite set of integers is missing in the language? Is `int('inf')` unreasonable?