ABSTRACT
Part 1 showed how to avoid rounding errors, simply by letting numbers track and express their accuracy. However, that is only half the problem with using computers to solve problems that involve real numbers. The other kind of error is variously called discretization error or truncation error or sampling error. “Sampling error” seems the most descriptive, since it is the error caused by sampling something that varies as if it did not vary and was just a constant, representable by just a single value. Whereas rounding error is replacing a correct value with a different value, sampling error is replacing a range of values with a single value. Statisticians use the phrase “sampling error” to describe the problem of observing a sample instead of the whole population. That is the way we mean it here as well, where a “population” is all real numbers in the possible variation of a quantity.
