real_number

:= x : x = n + 0.d₁d₂d₃d₄… where n is an integer and d_i is a decimal digit.

This means that $$n + \frac{d_1}{10} + \frac{d_2}{100} + \ldots \frac{d_k}{10^{k}} \le x < n + \frac{d_1}{10} + \frac{d_2}{100} + \ldots \frac{d_k}{10^{k}} + \frac{1}{10^{k}}, \forall k \in \mathbb{Z}_{1}^{+}$$