  We describe in dialogue form a possible way of discovering and investigating
10-adic numbers starting from the naive question about a `largest natural
number'. Among the topics we pursue are possibilities of extensions to
transfinite 10-adic numbers, 10-adic representations of rational numbers, zero
divisors, square roots and 10-adic roots of higher degree of natural numbers,
and applications of 10-adic number representation in computer arithmetic. The
participants of the dialogue are idealized embodiments of different
philosophical attitudes towards mathematics. The article aims at illustrating
how these attitudes interact, in both jarring and stimulating ways, and how
they impact mathematical development.
