Appendix B: Formulary
2009
One-Dimensional Intervals Interval X= [ X ̱ , X¯ ] = {x ∈ ℝ : X ̱ ≤x≤ X ¯ } Degenerate interval x= [x,x] Union and intersection X∩Y= {z:z ∈ X and z ∈ Y} X∪Y= {z:z ∈ X or z ∈ Y} X∩Y≠∅⇒{X∩Y= [max ( X ̱ , Y ̱ ) ,min ( X ¯ , Y ¯ ) ], X∪Y= [min ( X ̱ , Y ̱ ) ,max ( X ¯ , Y ¯ ) ] Interval hull X ∪ ̱ Y= [min { X ̱ , Y ̱ } ,max { X ¯ , Y ¯ } ] X ∪ ̱ Y={=X∪Yif X∩Y≠∅,⊃X∪Yotherwise. Width, absolute value, midpoint w (X) = X ¯ − X ̱ , |X| =max ( | X ̱ | , | X ¯ | ), m (X) = 1 2 ( X ̱ + X ¯ )