On 2011-01-23, Ilmari Karonen <email@example.com> wrote: > > It also turns out that the otherworldly addition as we have defined it > corresponds in a simple way to ordinary addition. In particular, > > x & y = g( f(x) + f(y) ), > > where > > f(0) = 0, f(o) = 1, f(~o) = -1, f(x) = x+1 and f(~x) = -(x+1) > > for all positive integers x, and g is the inverse of f, i.e. > > g(0) = 0, g(1) = o, g(-1) = ~o, g(x) = x-1 and g(-x) = ~(1-x) > > for all integers x > 1.
Of course, there's a typo here: that should be g(-x) = ~(x-1) for all x > 1.
-- Ilmari Karonen To reply by e-mail, please replace ".invalid" with ".net" in address.