On 1 Mrz., 22:28, Virgil <vir...@ligriv.com> wrote: > In article
> > If you believe that the real unit interval together with + and * is > > not isomorphic to the real unit interval with + and * then you may do > > so . I call them isomorphic. > > What I said was that the real with interval with + is not a group. > > > If ax + by is in the unit interval, then f(ax + by) is in the tree. > > But ax + by is NOT always in the unit interval, so accordingly f(ax + > by) need not be in the tree. > > > If ax + by is not in the unit interval, then f(ax + by) is not in the > > tree. > > But for a mapping to be linear on the unit interval requires that for > any x and y in the unit interval and any a and b in the field of scalars > ax+by also be in the interval. Otherwise the interval is not a linear > space at all and there cannot be any linear mappings from it to anything.