In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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. > http://www.encyclopediaofmath.org/index.php/Isomorphism
Which might have been relevant if WM had claimed existence of only a bijection rather than a linear mapping. Linear mappings are specific kinds of mappings of a type that WM has not shown can exist between the set of binary sequences and the set of paths of a Complete Infinite Binary Tree.
> > And here you have seen such an extension.
Here in WM's la-la-land have seen claims of all sorts of things but rarely any valid justification for any such claims, and certainly no justification for any claims not valid in ZF or NBG. > > Should you really be unable to understand this, then use Hilbert's > model , in my case suppressing integer parts larger than 0.
That still does not make either set into a linear space or any mapping between them into a linear mapping, both of which would be required if WM's claim were valid.
Note that while everyone is capable of error, WM is incapable of 'fessing up when caught in one. --