I think an important distinction is that in those "old days", people were largely working in what we now know to be subsets of real numbers, and the same conclu

I think an important distinction is that in those "old days", people were largely working in what we now know to be subsets of real numbers, and the same conclusion applies there. If you want to go to supersets of real numbers, you may be interested in https://en.wikipedia.org/wiki/Surreal_number https://en.wikipedia.org/wiki/Surreal_number