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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

1. Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013