for 
is defined as:
An empty Kaucher interval for is defined as:
![X = {[x,x]|x =∅ ∨ x=∅}= ∅](StabNumRef_PG136x.png)
where 
. Hence no arithmetic can be performed on an empty interval. On a computer 
is represented by qNaNs
(Quiet-Not-a-Number) hence causing any arithmetic to yield further qNaNs.