To represent the integers that he called p-adic numbers, Kurt Hensel introduced, in 1897, formal series to base p:
∑i−0+∞aipi  with  0≤ai≤p−1.\sum_{i-0}^{+\infty}a_ip^i~~ \text{with}~~ 0\leq a_i\leq p-1.
Although these series do not converge and therefore have no meaning in classical analysis, we can still perform all sorts of operations on them. Let's see what happens when p = 10—that is, with 10-adic numbers.
A 10-adic chimera ==============================================================================================================================================================================================================
More than a thousand years passed after the Pythagoreans—masters of number—and the "invention" of zero before positional notation became established in India. In this notation, 2019 is shorthand for the number 2 × 103 + 0 × 102 + 1 × 101 + 9 × 100 in base 10. The position of each digit indicates the corresponding power of the base—10 in our decimal system—hence the importance of zero as a placeholder for missing powers. The Babylonians did arrange powers of 60 in increasing order, but without a distinct symbol for "nothing," a unit in their base-60 system could represent 1, 60 or 3,600.