We may employ several domain description functions
within a single number system.
The number system
, with 
,
allows an interval to describe its domain with any particular member of 
.
Interval inclusion and extension are defined as before.
This is possible since the definitions rely indirectly
upon 
, via the definition of domain membership.
For 
,
,
.
The demotion operators 
and 
depend
upon the function chosen to describe the interval whose domain description
is being demoted. A valid 
demotion operator is a valid
demotion operator for any 
.
Similarly for 
and .
| Jeff Tupper | March 1996 |