[math-fun] Axioms for mean

--- "Schroeppel, Richard" <rschroe@sandia.gov> wrote:

Wrt Means, Gosper's objection was a bit more subtle: should we require that

avg( avg(a,b), avg(c,d) ) = same thing with b and c swapped?

This *is* true for ordinary averages, and geometric, harmonic, etc. means.

Rich

This fails for the AGM. So if we accept the AGM as legitimate, then we must reject this as an axiom. Gene __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com