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Topic: Does a nonlinear additive function on R imply a Hamel basis of R?
Replies: 8   Last Post: Apr 21, 2013 7:59 PM

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Mike Terry

Posts: 653
Registered: 12/6/04
Re: Does a nonlinear additive function on R imply a Hamel basis of R?
Posted: Apr 20, 2013 8:50 PM
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<lugita15@gmail.com> wrote in message
news:5c7453d4-234e-40b9-9aba-608bd69e99eb@googlegroups.com...
> On Saturday, April 20, 2013 12:38:48 PM UTC-4, 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.







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