operation, to have on hand numerals required to express both the operands and the result of the operation. The accuracy of the obtained result (i.e., how well the numeral chosen to represent the result of the operation expresses the resulting quantity) is not studied either. For the approach introduced in [@informatica; @Lagrange] both issues are crucial. Since for any fixed numeral system $\mathcal{S}$ there exist operations that cannot be executed in $\mathcal{S}$ because $\mathcal{S}$ has no suitable numerals, these marginal situations are investigated in detail. We can remind Pirahã in this occasion (see (\[Riemann29\]), (\[Riemann30\])) but even the modern powerful positional numeral systems which are not able to work with numerals having, e.g., $10^{100}$ digits. It is shown in [@informatica; @first; @Lagrange; @Sergeyev_Garro] that very often the margins of the expressibility of numeral systems are connected directly to interesting research problems.

Another important peculiarity of the new approach consists of the fact that 1 has both cardinal and ordinal properties as usual finite natural numbers have. In fact, infinite positive integers that can be viewed through numerals including grossone can be interpreted in the terms of the number of elements of certain infinite sets. For instance, the set of even 