with some Euler’s results from the new methodological positions. The first remark we can make is that the records of the type

[rl]{} f\_1(x)= \_[i=1]{}\^ a\_i(x), & f\_2(x)=\_[-]{}\^ a\_i(x),\
&\
f\_3(x)= \_[a]{}\^ g(t,x) dt,& f\_4(x)= \_[-]{}\^ g(t,x) dt,

\[Riemann23\] and similar are sufficiently precise to define a function only if one uses the traditional language. As it has been shown in the previous section, the accuracy of the answers one can get with this language is lower with respect to the new numeral system using 1.

Thanks to this numeral system, we know now that the only symbol $\infty$ and the absence of numerals allowing us to express different infinite numbers just did not give us the possibility to distinguish many different functions in each of the objects present in (\[Riemann23\]). We can say that we are now in the situation similar to a physicist who first observed a black dot in a weak lens and then had put a stronger one and has seen that that the black dot consists of many different dots. When we have changed the lens in our mathematical microscope we have seen that within each object of our study viewed as one entity with 