Chapter 8. Classes

In mathematics, when we write sin, we refer to a mathematical object for which we know many methods from elementary calculus. For example:

  • We might want to evaluate sin x at x=0.5, that is, compute sin(0.5), which returns a real number
  • We might want to compute its derivative, which gives us another mathematical object, cos
  • We might want to compute the first three coefficients of its Taylor polynomial

These methods may be applied not only to sin but also to other sufficiently smooth functions. There are, however, other mathematical objects (for example, the number 5) for which these methods make no sense. Objects that have the same methods are grouped together in abstract classes, for example, functions. Every statement and every ...

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