observation and the tool used for this observation. The latter is directly related to interrelations between numeral systems[^2] used to describe numbers and numbers (and other mathematical objects) themselves. Numerals that we use to write down numbers, functions, etc. are among our tools of investigation and, as a result, they strongly influence our capabilities to study mathematical objects.

ii\) Both standard and non-standard Analysis study mainly functions assuming finite values. In [@informatica; @Dif_Calculus], functions and their derivatives that can assume finite, infinite, and infinitesimal values and can be defined over finite, infinite, and infinitesimal domains have been studied. Infinite and infinitesimal numbers are not auxiliary entities in the new approach, they are full members in it and can be used in the same way as finite constants.

In the next section, we present very briefly the new methodology for treating infinite and infinitesimal quantities indicating mainly the facts that are used directly in this paper. A comprehensive introduction and numerous examples of its usage can be found in [@informatica; @Lagrange] while some applications can be found in [@De_Leone; @D'Alotto; @Margenstern; @informatica; @Korea; @Dif_Calculus; @Num_dif; @Sergeyev_Garro].

Accuracy of mathematical languages and a new numeral system for dealing with infinity {#s2_riem}
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