 There are two competing mathematical strategies that are used in connection with physical theory; one emphasizes rigor and the other pragmatics. The pragmatic approach often compromises mathematical rigor, but offers instead expediency of calculation and elegance of expression. A case in point is the notion of an infinitesimal, a non-zero quantity that is smaller than any finite quantity. Infinitesimals were used by Kepler, Galileo, Newton, Leibniz and many others in developing and using their respective physical theories, despite lacking a mathematically rigorous foundation, as Berkeley clearly showed in his famous 1734 treatise The Analyst criticizing infinitesimals. Such criticisms did not prevent various 18th Century mathematicians, scientists, and engineers such as Euler and Lagrange from using infinitesimals to get accurate answers from their calculations. Nevertheless, the pull towards rigor led to the development in the 19th century of the concept of a limit by Cauchy and others, which provided a rigorous mathematical framework that effectively replaced the theory of infinitesimals. A rigorous foundation was eventually provided for infinitesimals by Robinson during the second half of the 20th Century, but infinitesimals are rarely used in contemporary physics. For more on the history of infinitesimals, see the entry on  continuity and infinitesimals.