Calculus and Infinity

It is argued that both Newton and Leibnitz invented Calculus. However, despite its practical uses there were

some analysts/mathematicians/philosophers, who were critical of the foundation of calculus, for example the

use of Infinitesimals and the limiting processes involved in obtaining the final results.

Analyse the criticism given by either George Berkeley or Karl Marx and the solution offered to these criticisms by either Cauchy et al with the limits or Robinson with the use of hyperreal numbers.

You may wish to give the notation used by Newton and/or Leibnitz and the modern notation used to study calculus.