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Analysis using ultrasmall numbers


This website is a repository for documents linked to Analysis using ultrasmall numbers: a mathematical theory developed by Prof. Karel Hrbacek, Dr. Olivier Lessmann and Dr. Richard O'Donovan and published under the title "Analysis with ultrasmall numbers" by CRC Press.

Most documents are in pdf format and are all open content.

Documents for teachers, which can be used in the classroom, may come with the LaTeX source code and can be freely used, modified and distributed.

Articles are in several categories (and some documents may appear in more than one place).


The interval [0,1] contains infinitely many real numbers so some of them must be really very close to each other. So close that without a microscope they cannot be distinguished from one another: their difference is not observable.

Why teach this way?

Why not use another theory containing infinitesimals?

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