This tower can be viewed as a sort of “Postnikov tower” of (although it is of course not a Postnikov tower in the usual sense). Note that it is not “convergent”: the limit of the tower is the ring of -adic integers. This makes perfect sense in terms of carrying: the -adic integers can be identified with “decimal numbers” that can be “infinite to the left”, with addition and multiplication defined using the usual carrying rules “on off to infinity”.
Dan Isaksen, A cohomological viewpoint on elementary school arithmetic, The American Mathematical Monthly, Vol. 109, No. 9. (Nov., 2002), pp. 796-805. (jstor)
Revised on December 7, 2015 19:46:20
by Commettee for the Abolition of the Notation Z_p for Denoting?