In fact there are a plethora of conflicting formal systems in use. In certain applications of numerical differentiation and integration, it is, for example, convenient to have signed zeroes. A simple reason has to do with the converse of {displaystyle lim _{x o 0^{-}}{x^{-1}}=-infty } lim_{x o 0^{-}}{x^{-1}} = -infty, namely, it is convenient for {displaystyle lim _{x o -infty }{x^{-1}}=-0} lim_{x o -infty}{x^{-1}} = -0 to be considered true. Such zeroes can be seen as an approximation to infinitesimals.