There have proved to be many places throughout analysis where there are distinctive inconsistent insights. The examples in the remainder of this section are drawn from Mortensen (1995). For example: (1) Robinson’s (1974) non-standard analysis was based on infinitesimals, quantities smaller than any real number, as well as their reciprocals, the infinite numbers. This has an inconsistent version, which has some advantages for calculation in being able to discard higher-order infinitesimals. Inter