If someone asks me right now, what a number is, I would say 1,2,3,-1,1+i,2.13, etc. But what I have essentially stated are just symbols. I tried to explore a bit what a number exactly is. What are these symbols pointing to?

As I got to know the answer is not that simple, we cannot have an all-encompassing definition of numbers. Accepting this, I can also not find peace with just treating them as symbols.

So I just wanted to ask, is there a way I can somehow construct natural numbers, then fractions, then integers, real numbers, and so on, so that I at least have some notion attached to these numbers, rather than treat them just as symbols with which I'm playing.