I was told many times a story. Indeed a fascinating one to me as a student learning mathematics.
First there were natural numbers. People started adding things and finding solutions to finding the unknowns when the results of the addition are known.
The intriguing "non-existent" solutions to certain additive equations involving natural numbers, lead to finding negative numbers and zero. Complementing the set such that there is a solution to every problem of simple addition.
Then came the extensive use of multiplication to ease the laborious addition operations. Leading to problems asking to find the unknowns when the results of multiplication are known.
Extending the story, what lead to the discovery of rationals is to solve any equations involving simple multiplication.
And what lead to the discovery of irrationals is the solutions to equations involving simple exponents, and even more. (such as?)
Finally, the exciting polynomials gave birth to complex numbers in a way that every polynomial equation has all solutions within complex numbers.
My question is simply this.
Is it the end of the story?
Can we expect anything more?
Is there a set of numbers that is sufficient for every operation that we can imagine?
Or, is it a never ending story?