Infinite integer in Python

Question

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?

Answer 1

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 

Answer 2

Taken from here: https://www.gnu.org/software/libc/manual/html_node/Infinity-and-NaN.html

IEEE 754 floating point numbers can represent positive or negative infinity, and NaN (not a number)

That is, the representation of float and Decimal can store these special values. However, there is nothing within the basic type int that can store the same. As you exceed the limit of 2^32 in an unsigned 32-bit int, you simply roll over to 0 again.

If you want, you could create a class containing an integer which could feature the possibility of infinite values.