This article is a quick reference about how different operations on intervals are defined. Unless differently stated we use the following notation
X=[x,x]Y=[y,y] OperationX+YX−YXYX1YXDefinition[x+y,x+y][x−y,x−y][minS,maxS] where S={xy,xy,xy,xy}[x1,x1] if 0∈/X[−∞,∞] if x<0<x[x1,∞] if x=0=x[−∞,x1] if x=0=x∅ if X=[0,0]X⋅Y1 OperationX∩YX∪YDefinition[max(x,y),min(x,y)] if max(x,y)≤min(x,y)∅ otherwise[min(x,y),max(x,y)] OperationX⋚YX⊆YDefinitionx⋚y∧x⋚yy≤x∧x≤y All the following functions return NaN
if the interval is empty.
Operationinf(X)sup(X)mid(X)diam(X)rad(X)mag(X)mig(X)Definitionxx2x+xx−x2diam(X)max{∣x∣:x∈X}min{∣x∣:x∈X}