In context it looked like you meant something like numbers described by Knuth arrow notation or something similar.
Taking your clarification- note that just because something is complicated does not mean it is complex in the technical sense. There are many other generalizations of the reals such as the surreal numbers. In this particular context, ordinal lists of reals (which can be thought of vector spaces of the reals with a privileged basis) seem to work pretty well. Beware the superficial similarity of words.
In context it looked like you meant something like numbers described by Knuth arrow notation or something similar.
Taking your clarification- note that just because something is complicated does not mean it is complex in the technical sense. There are many other generalizations of the reals such as the surreal numbers. In this particular context, ordinal lists of reals (which can be thought of vector spaces of the reals with a privileged basis) seem to work pretty well. Beware the superficial similarity of words.