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Proposition: Existence of Inverse Rational Cauchy Sequences With Respect to Addition

For every rational Cauchy Sequence $(x_n)_{n\in\mathbb N}$ there exists an inverse rational Cauchy Sequence $(-x_n)_{n\in\mathbb N}$ such that the sum of both sequences equals the Cauchy sequence of rational zeros:

$$(x_n)_{n\in\mathbb N}+(-x_n)_{n\in\mathbb N}=(0)_{n\in\mathbb N}.$$

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