Number sets

Not all numbers are of the same kind. Starting from the naturals, every time an operation takes us “outside” the starting set, we are pushed to widen it: this is how the integers, the rationals and the reals are born, in a chain of inclusions $\mathbb{N}\subset\mathbb{Z}\subset\mathbb{Q}\subset\mathbb{R}$. The section closes with the history of zero, the number that made positional notation possible.

• The number sets N, Z, Q, R
• Zero and positional notation