Repeatability and numerical analysis

The discrete nature of the systems that I consider in most of this book makes it almost inevitable that computer experiments on them will be perfectly repeatable. But if, as in the past, one tries to do computer experiments on continuous mathematical systems, then the situation can be different. For in such cases one must inevitably make discrete approximations for the underlying representation of numbers and for the operations that one performs on them. And in many practical situations, one relies for these approximations on "machine arithmetic"—which can differ from one computer system to another.