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When we use a computer to make calculations involving real numbers, we have to use the finite set of floating-point numbers that the hardware makes available. In such a situation there are two main choices for the approximation of a real number by the floating-point number system: to use one floating-point number, or to use two. Interval Arithmetic is based on the latter choice. Whenever an operation on reals is specified, the corresponding operation on their intervals is executed. By ensuring that any rounding is outward, it is guaranteed that the computed interval contains the mathematically correct result. Thus interval arithmetic was introduced as an automatic method to keep track of the rounding errors made in computer calculations, but it has also been widely used to find upper and lower bounds for the effect caused by truncation errors and by errors (or uncertainties) in the input data to a numerical calculation. Another major application is rigorous global optimization. The science of making these ideas practical is a research programme called Interval Analysis. It was introduced in the book "Interval Analysis" by Ramon Moore, Prentice-Hall, Englewood Cliffs, NJ, 1966. An introduction to Interval Analysis and interval global optimization is given in the DTU course
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