The reciprocal of an interval

### 5.40.6 The reciprocal of an interval

The reciprocal of an interval the interval determined by the reciprocals of the end points.
Input:

1/i[2,3]

Output:

[0.333333333333333..0.500000000000000]

Input:

1/i[-6,-3]

Output:

[-0.333333333333333..-0.166666666666667]

If the original interval has zero as an end point, then the reciprocal interval will have infinity or minus infinity as one of the end points.
Input:

1/i[0,2]

Output:

[0.500000000000000..+infinity]

Input:

1/i[-1,0]

Output:

[-infinity..-1.00000000000000]

If one end point is positive and the other is negative, then the reciprocal will simply be the interval from -infinity to infinity.
Input:

1/i[-2,3]

Output:

[-infinity..+infinity]