Proposition: Addition of Rational Cauchy Sequences
Let \((x_n)_{n\in\mathbb N}\) and \((y_n)_{n\in\mathbb N}\) be rational Cauchy sequences. The addition of rational Cauchy Sequences is defined as:
\[\begin{array}{cclc}
(x_n)_{n\in\mathbb N}+(y_n)_{n\in\mathbb N}&:=&(x_n+y_n)_{n\in\mathbb N}\\
\end{array}\]
where the result \((x_n+y_n)_{n\in\mathbb N}\) is also a rational Cauchy sequence, called the sum of the rational Cauchy sequences \((x_n)_{n\in\mathbb N}\) and \((y_n)_{n\in\mathbb N}\). The sum exists and is welldefined.
Table of Contents
Proofs: 1
 Proposition: Addition of Rational Cauchy Sequences Is Associative
 Proposition: Addition of Rational Cauchy Sequences Is Commutative
 Proposition: Existence of Rational Cauchy Sequence of Zeros (Neutral Element of Addition of Rational Cauchy Sequences)
 Proposition: Existence of Inverse Rational Cauchy Sequences With Respect to Addition
 Proposition: Addition of Rational Cauchy Sequences Is Cancellative
Mentioned in:
Proofs: 1 2 3 4 5 6 7 8 9 10 11
Propositions: 12 13 14 15 16 17
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References
Bibliography
 Kramer Jürg, von Pippich, AnnaMaria: "Von den natürlichen Zahlen zu den Quaternionen", SpringerSpektrum, 2013