> As an analogy, consider the average numerical computer program. We often derive the underlying math in terms of real-valued vector spaces. However, when imple

> As an analogy, consider the average numerical computer program. We often derive the underlying math in terms of real-valued vector spaces. However, when implementing the program on a computer system, all variables are ultimately discrete. A reason for not thinking about our problems in terms of discrete objects is that math just tends to get incredibly complicated as soon as objects are discrete; and that the computational substrate is fine-grained enough (in most cases). When doing computations that require a lot of precision, one actually needs to consider the fact that floats/doubles are discrete and with limited precision, and handle that in the code. Typical examples may be numerical analysis, physical simulations, game world code (for assuring consistent state for all connected players), and geometrical algorithms. Fortunately for most programmers, they do not need that level of precision in their code.