How to make an integer larger than any other integer?

Since python integers are unbounded, you have to do this with a custom class:

import functools

@functools.total_ordering
class NeverSmaller(object):
    def __le__(self, other):
        return False

class ReallyMaxInt(NeverSmaller, int):
    def __repr__(self):
        return 'ReallyMaxInt()'

Here I’ve used a mix-in class NeverSmaller rather than direct decoration of ReallyMaxInt, because on Python 3 the action of functools.total_ordering would have been prevented by existing ordering methods inherited from int.

Usage demo:

>>> N = ReallyMaxInt()
>>> N > sys.maxsize
True
>>> isinstance(N, int)
True
>>> sorted([1, N, 0, 9999, sys.maxsize])
[0, 1, 9999, 9223372036854775807, ReallyMaxInt()]

Note that in python2, sys.maxint + 1 is bigger than sys.maxint, so you can’t rely on that.

Disclaimer: This is an integer in the OO sense, it is not an integer in the mathematical sense. Consequently, arithmetic operations inherited from the parent class int may not behave sensibly. If this causes any issues for your intended use case, then they can be disabled by implementing __add__ and friends to just error out.