$p_{i}$.

Finite numbers in this new numeral system are represented by numerals having only one grosspower $ p_0=0$. In fact, if we have a number $C$ such that $m=k=$ 0 in representation (\[3.13\]), then due to (\[3.2.1\]), we have $C=c_0
\G1^0=c_0$. Thus, the number $C$ in this case does not contain grossone and is equal to the grossdigit $c_0$ being a conventional finite number expressed in a traditional finite numeral system.

The simplest infinitesimal numbers are represented by numerals $C$ having only finite or infinite negative grosspowers, e.g., $21.3\G1^{-243.6}5\G1^{-154\mbox{\tiny{\G1}}}$. Then, the infinitesimal number $\frac{1}{\G1}=\G1^{-1}$ is the inverse element with respect to multiplication for 1: 1\^[-1]{}1=11\^[-1]{}=1. \[3.15.1\] Note that all infinitesimals are not equal to zero. Particularly, $\frac{1}{\G1}>0$ because it is a result of division of two positive numbers.

The simplest infinite numbers are expressed by numerals having positive finite or infinite grosspowers without infinitesimals. They have infinite parts and can also have a finite part and infinitesimal ones. For instance, the number $$31.5\G1^{14.8\mbox{\tiny{\G1}}}(-0.645)\G1^{5}
 7.89\G1^{0}37\G1^{-4.29}
 72.8\G1^{-360.21}$$ has two infinite parts $31.5\G1^{14.8\mbox{\tiny{\G1}}}$ and $-0.645\G1^{5}$ one finite part $7.89\G1^{0}$ and two infinitesimal parts $37\G1^{-4.29}$ and $72.8\G1^{-360.21}$. All of the numbers introduced above can be used as grosspowers, as well, giving so a possibility 