Somewhere in a discussion here (I think it was on the "Thinking like a Theorist: Number Systems") someone said that all of mathematics can be built up from 1, -1, addition, and multiplication. I found this statement to be fundamentally correct (in fact, multiplication can be removed as it is repeated addition) and rather intellectually exciting and decided to explore it a bit. Clearly from this concept we can produce the integers, and from addition we can produce multiplication. We can produce the rational numbers if we conceptualize two integers and what factor one must be multiplied by in order to produce the other. Through Euclid's proof of the existence of irrationals we can produce them, and so on. The list is endless. The point is, it's amazing how fundamentally simple concepts have produced all of...this, the beautiful world of mathematics that we delve into every time we visit Brilliant.
Any thoughts on this from more experienced mathematicians and theorists?