Symbolic perturbation by infinitely small values removes degeneracies in geometric algorithms and enables programmers to handle only generic cases: there are a few such cases, whereas there are an overwhelming number of degenerate cases. Current perturbation schemes have limitations, presented below. This paper proposes to use an epsilon-arithmetic, i.e. to represent in an explicit way infinitely small numbers, and to define arithmetic operations (+,-,*,/,<,=) on them.