This section contains documents which might help instructors understanding this new approach.

• Teacher's manual (short version) (pdf file)

This document has been used to help visiting instructors understand proofs and exercises without necessarily providing enough information to be able to solve problems by themselves.

• Teacher's manual (longer version) (pdf file)

• Equivalence of the definitions of limits (pdf file)

A reasonable question is whether the theorems proved using ultrasmall numbers or proved using the classical epsilon-delta-limit definition are really the same.

One can go from using ultrasmall numbers to classical definitions that do not use the concept of observability by "forgetting" the extra structures provided.

This paper shows that the two definitions of the limit are equivalent.