A further extension of interval arithmetic allows better
models of ``bumpy'' functions. A function is 
-bumpy
if it is partial or discontinuous. In general, a function g
is 
-bumpy if a better model exists
for g in 
than in .
Bumpy functions are formally defined in section 
.
This extension also allows for natural models of multi-functions;
multi-functions are functions that may return multiple results,
such as 
.
Throughout this section, let denote 
,
for a fixed choice of f.
Each number in is specified as a
set of numbers from :
A real number x is contained in interval j if x is contained by any member of j:
| Jeff Tupper | March 1996 |