The set of natural numbers is not closed to subtraction (additive inverse). We expand it to Z.
Z is not closed to division. We get Q or rational numbers.
Rational numbers are not closed to limit!
So, we invent real numbers to deal with them (for example, the definition of e).
The root of negative is not defined in R. If we also expand our set of numbers to include this, we get Complex Numbers.
I suppose after that we have a set that is closed to all of our operations.
https://en.wikipedia.org/wiki/Complex_number
Mathematics of Machine Learning
Rational numbers - representations