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Proposition: Multiplication of Rational Cauchy Sequences Is Associative

The multiplication of rational Cauchy sequences is associative, i.e. for any rational Cauchy sequences \((x_n)_{n\in\mathbb N}\), \((y_n)_{n\in\mathbb N}\) and \((z_n)_{n\in\mathbb N}\) the following law is valid:

\[[(x_n)_{n\in\mathbb N}\cdot (y_n)_{n\in\mathbb N}]\cdot (z_n)_{n\in\mathbb N}=(x_n)_{n\in\mathbb N}\cdot [(y_n)_{n\in\mathbb N}\cdot (z_n)]_{n\in\mathbb N}.\]

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