We are most interested in finding a graphing algorithm which we may program a modern computer to perform. One immediate concern is the representation such machines use for real numbers. The representation often used is analagous to scientific notation, keeping a fixed number of digits for any given quantity. This can lead to further difficulties. It is equally clear that so that .
Most calculations introduce some numerical round-off.
With complicated equations, there will be long sequences of calculations, which allows numerical round-off to accumulate. For such equations, the generated graph may differ significantly from the actual graph.