* Dan Asimov <dasimov@earthlink.net> [Nov 18. 2012 08:36]:
I'm not very familiar with the n-adic numbers, but I think that
...999.0... = -1
is true in the 10-adic numbers, where the reasoning Marc uses can be justified rigorously.
(Alternatively, just add 1 to ...999.0... to get 0.)
--Dan
[...]
For me the left side of ...999999.0 = -1.0 is just ten's complement, a neat way to write negative numbers without the minus sign. In general, to negate a (non-negative) number, first complement the digits ( d --> 9-d ), then add 1. Example: 123 --> ...9999876 --> ...9999877 == -123 Check (negate again): ...9999877 --> ...0000122 --> 123 Omit the "add 1" step to get nine's complement (with two zeros, 0 and ...9999999 ). Engineers learn that for base 2, and about every computer in existence uses two's complement for integers.