of inadequate numeral systems that we use to work with infinity, more precisely, to express infinite numbers.*

Recently, a new numeral system has been developed in order to express finite, infinite, and infinitesimal numbers in a unique framework (a rather comprehensive description of the new methodology can be found in [@informatica; @Lagrange]). The main idea consists of measuring infinite and infinitesimal quantities by different (infinite, finite, and infinitesimal) units of measure. This is done by using a new numeral.

An infinite unit of measure has been introduced for this purpose in [@informatica; @Lagrange] as the number of elements of the set $\mathbb{N}$ of natural numbers. It is expressed by a new numeral 1 called *grossone*. It is necessary to emphasize immediately that the infinite number 1 is neither Cantor’s $\aleph_0$ nor $\omega$ and the new approach is not related to the non-standard analysis.

One of the important differences with respect to traditional views consists of the fact that the new approach continuously emphasizes the distinction between numbers and numerals and studies in depth numeral systems. In general, neither standard analysis nor non-standard one pay a lot of attention to the necessity, in order to be able to execute an arithmetical 