Can we compute
? No. Since
applied to
is
it would appear that
However,
is undefined.
applied to
would have the form
which is undefined. Even worse,
is false! At
this equation gives
.
Referring back to their definitions, we see
,
,
, and
applied to
are defined if
,
,
and
is distinct from all
, and
and
is distinct from all
, respectively. Here,
.
Definition.
A pair
is a
suitable origin
if
(1)
and
are free of nonpositive integers
(2)
and
are disjoint
(3) Integer elements of
are
(
and
)
Definition.
A pair
is
accessible
from a pair
if there exists a proper sequence
of shift and inverse shift operators
,
,
, and
such that
