## Saturday, April 13, 2013

### Interval analysis

The set of all rational intervals is countable. We can develop analysis in terms of this intervals firstly through interval arithmetic:
(= (add-intervals [1 2] [3 4]) [4 6])
(= (multiply-intervals [1 2] [3 4]) [3 8])

We can express any continuous real function as a function of intervals using its set of extrema. For example, the square of the interval [-2,2] is [0,4] and the square of the interval [2,3] is [4,9].