Now that Python is beginning to embrace type annotations, is it worth revisiting the idea of having extended integers and an integer infinity?

I found myself trying to annotate this line:

events_to_do: Union[int, float] = math.inf

where I am only including float in the union to accommodate math.inf.

I'm interested in exploring this concrete proposal:

Add a class to the numeric hierarchy (https://www.python.org/dev/peps/pep-3141/) ExtendedIntegral whereby Real :> ExtendedIntegral :> Integral.

Add a sentinel math.int_inf that obeys all of the same kinds of rules as math.inf does.

Then, I could annotate more simply:

events_to_do: ExtendedIntegral = math.int_inf

With respect to Python, this is discussed somewhat here https://stackoverflow.com/questions/24587994/infinite-integer-in-python/35725065#35725065.

The name "extended integer" is discussed somewhat here https://math.stackexchange.com/questions/1442961/extended-integers. A quick search of papers shows that it is sometimes used in this sense: https://scholar.google.com/scholar?q=%22extended+integer

Best,

Neil