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Proof

(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 \(1^{-1}=1\).
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References

Bibliography

1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983