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Proposition: Existence of Rational Cauchy Sequence of Ones (Neutral Element of Multiplication of Rational Cauchy Sequences)
There exists a rational Cauchy sequence \((1)_{n\in\mathbb N}\) such that \[(x_n)_{n\in\mathbb N} \cdot (1)_{n\in\mathbb N}= (1)_{n\in\mathbb N}\cdot (x_n)_{n\in\mathbb N}=(x_n)_{n\in\mathbb N}\] for all rational Cauchy sequence \((x_n)_{n\in\mathbb N}\), i.e. \((1)_{n\in\mathbb N}\) is neutral with respect to the multiplication of rational Cauchy sequences.
Table of Contents
Proofs: 1
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Proofs: 1 2
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References
Bibliography
 Kramer Jürg, von Pippich, AnnaMaria: "Von den natürlichen Zahlen zu den Quaternionen", SpringerSpektrum, 2013