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Proposition: Existence of Rational Cauchy Sequence of Zeros (Neutral Element of Addition of Rational Cauchy Sequences)

There exists a rational Cauchy sequence \((0)_{n\in\mathbb N}\) such that \[(x_n)_{n\in\mathbb N} + (0)_{n\in\mathbb N}= (0)_{n\in\mathbb N} + (x_n)_{n\in\mathbb N}=(x_n)_{n\in\mathbb N}\] for all rational Cauchy sequence \((x_n)_{n\in\mathbb N}\), i.e. \((0)_{n\in\mathbb N}\) is neutral with respect to the addition of rational Cauchy sequences.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2 3 4
Propositions: 5 6

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References

Bibliography

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