
Re: Does a nonlinear additive function on R imply a Hamel basis of R?
Posted:
Apr 20, 2013 8:50 PM


<lugita15@gmail.com> wrote in message news:5c7453d4234e40b99aba608bd69e99eb@googlegroups.com... > On Saturday, April 20, 2013 12:38:48 PM UTC4, Mike Terry wrote: > > No  how about defining f as: > > > > > > > > f(x) = 0 if x/PI is irrational > > > > f(x) = x if x/PI is rational > > > > > > > > Then f is additive and not linear... > That's not an additive function. f(pi + 1) = 0, but f(pi) + f(1) = pi.
Indeed not, my bad. And it seems to construct an f which works along the lines I intended, I would want to use AC at some point, which is no help!
Mike.

