Empty Interval

3.4.1 Empty Interval

An empty Kaucher interval $X = ∅$ for $X ∈ KR$ is defined as an interval where at least one of the bounds is undefined:

- - X= {[x,x]|x=∅ ∨ x= ∅}= ∅.

Here, $∅ ∉R$ , meaning the empty interval is not a real-valued interval. Consequently, no arithmetic operations can be performed on an empty interval.

In computational implementations, the empty interval is typically represented using qNaN (Quiet-Not-a-Number) values. Any arithmetic operation involving a qNaN will propagate the qNaN, ensuring that invalid or undefined operations do not yield misleading results.

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