Date: Mar 1, 2013 4:49 PM
Subject: Re: WM's Mytheology § 222 Back to the roots
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.
The concept of an isomorphism arose in connection with concrete
algebraic systems (initially, with groups) and was extended in a
natural way to wider classes of mathematical structures.
And here you have seen such an extension.
Should you really be unable to understand this, then use Hilbert's
model , in my case suppressing integer parts larger than 0.