Stable Numerics Subroutine Library
Programming Reference Manual
Version 1.1 DD-00006-011

3.4.1 Empty Interval

An empty Kaucher interval X = ∅  for X ∈ KR  is defined as:

X = {[x,x]|x =∅ ∨ x=∅}= ∅

where ∅̸∈ R  . 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.