Number theory discussion regarding floats, ints and NaN/Inf

This sentence is meaningless. Infinity is a floating point number. And finite floating point numbers are also concepts. float('inf') is one element of the structure of floating point numbers, just as 1.0 and float('nan') are.

Note that x + 1 = x has also as solution sys.float_info.max and many other finite (and moreover elements for which is_integer() returns True) float.