(related to Corollary: \(1^{-1}=1\))

- We have to show that inverse number of the number one is one itself, i.e. \(1^{-1}=1\).
- According to the existence of reciprocal numbers there is a number $1^{-1}$ such that \(1\cdot 1^{-1}=1\).
- Because of the existence of the number one we also find that \(1\cdot 1=1\).
- Because all inverse numbers are unique, we can compare both equations.
- This comparison leads to the conclusion that \(1^{-1}=1\).∎

**Forster Otto**: "Analysis 1, Differential- und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983