# Proposition: Multiplication Of Rational Cauchy Sequences

Let $$(x_n)_{n\in\mathbb N}$$ and $$(y_n)_{n\in\mathbb N}$$ be two rational Cauchy sequences. The multiplication of rational Cauchy Sequences can be defined based on the multiplication of rational numbers as follows: $\begin{array}{cclc} (x_n)_{n\in\mathbb N}\cdot (y_n)_{n\in\mathbb N}&:=&(x_n\cdot y_n)_{n\in\mathbb N}\\ \end{array}$ i.e. the product of two rational Cauchy sequences is a new rational sequence, whose sequence members are the products of rational numbers being the corresponding members of the original two rational Cauchy sequences.

Moreover, the new rational sequence $$(x_n\cdot y_n)_{n\in\mathbb N}$$ is also a rational Cauchy sequence.

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9
Propositions: 10 11 12 13 14 15

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### References

#### Bibliography

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