[@Tarski], staring from e.g: $-1$, and constructing all other integers as follows: $$1 = (-1) \times (-1), \; 0 = 1 + (-1), \; 2=1+1, \ldots$$ In calculators, ten digits are present: 0,1,2,3,4,5,6,7,8,9 and integers are entered in sequence using standard positional numeral system. RIES [@RIES] follow similar way, except for 0 and 1. Use of positional base-10 numerals is simple reflection of human anatomy/history, and difficult to include in our virtual calculator. Therefore we restrict to really small magnitude integers, $-1,0,1,2$ in particular. All other integers must be constructed from above four. Noteworthy, these integers are also among essential mathematical constants included in famous [@e] Euler formula: $$\label{euler}
e^{i \pi} + 1 = 0, \qquad e^{2 \pi i} - 1 = 0.$$ Two is also smallest possible integer base for logarithm $\log_2$. Binary system is now used in virtually all modern computer hardware.

The same reasoning applies to rationals. One might enumerate them using Cantor diagonal method, Stern-Brocot tree, or generate unambiguously by repeated composition[^3] of a function: $$\operatorname{next}(x) = \left(1 + 2 \lfloor x \rfloor -x  \right)^{-1},$$ starting from zero: $$0,1,\frac{1}{2},2,\frac{1}{3},\frac{3}{2},\frac{2}{3},3,\frac{1}{4},\frac{4}{3},\frac
   {3}{5},\frac{5}{2},\frac{2}{5}, \ldots$$ Usually the best is to leave language without explicit rationals, and let them appear by 