This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 3.1.7 Advanced Topic: Interval Arithmetic Representations of real intervals. This represents all numbers between and . In[1]:= Interval[{-2, 5}] Out[1]= The square of any number between and is always between 0 and 25. In[2]:= Interval[{-2, 5}]^2 Out[2]= Taking the reciprocal gives two distinct intervals. In[3]:= 1/Interval[{-2, 5}] Out[3]= Abs folds the intervals back together again. In[4]:= Abs[%] Out[4]= You can use intervals in many kinds of functions. In[5]:= Solve[3 x + 2 == Interval[{-2, 5}], x] Out[5]= Some functions automatically generate intervals. In[6]:= Limit[Sin[1/x], x -> 0] Out[6]= Operations on intervals. This finds the overlap of the two intervals. In[7]:= IntervalIntersection[Interval[{3, 7}], Interval[{-2, 5}]] Out[7]= You can use Max and Min to find the end points of intervals. In[8]:= Max[%] Out[8]= This finds out which of a list of intervals contains the point 7. In[9]:= IntervalMemberQ[ Table[Interval[{i, i+1}], {i, 1, 20, 3}], 7] Out[9]= You can use intervals not only with exact quantities but also with approximate numbers. Even with machine-precision numbers, Mathematica always tries to do rounding in such a way as to preserve the validity of results. This shows explicitly the interval treated by Mathematica as the machine-precision number 0. In[10]:= Interval[0.] Out[10]= This shows the corresponding interval around 100., shifted back to zero. In[11]:= Interval[100.] - 100 Out[11]= The same kind of thing works with numbers of any precision. In[12]:= Interval[N[Pi, 50]] - Pi Out[12]= With ordinary machine-precision arithmetic, this computation gives an incorrect result. In[13]:= Sin[N[Pi]] Out[13]= The interval generated here, however, includes the correct value of 0. In[14]:= Sin[Interval[N[Pi]]] Out[14]=