 An infinitesimal number is one which, while not coinciding with zero, is in some sense smaller than any finite number. This sense has often been taken to be the failure to satisfy the Principle of Archimedes, which amounts to saying that an infinitesimal number is one that, no matter how many times it is added to itself, the result remains less than any finite number. In the engineer’s practical treatment of the differential calculus, an infinitesimal is a number so small that its square and all higher powers can be neglected. In the theory of limits the term “infinitesimal” is sometimes applied to any sequence whose limit is zero.