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Proposition: Existence of Real One (Neutral Element of Multiplication of Real Numbers)

There exists a real number \(1\in\mathbb R\) such that \[x\cdot 1=1\cdot x=x\] for all \(x\in\mathbb R\), i.e. \(1\) is neutral with respect to the multiplication or real numbers.

Table of Contents

Proofs: 1

Mentioned in:

Corollaries: 1
Lemmas: 2
Proofs: 3 4 5 6 7 8 9 10 11
Propositions: 12 13
Sections: 14

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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
  2. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013