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Lemma: Convergent Rational Sequences With Limit \(0\) Are Rational Cauchy Sequences

Let \((M , + , \cdot)\) be the unit ring of all rational Cauchy sequences. The set \(I:=\{(a_n)_{n\in\mathbb N}~|~a_n\in\mathbb Q,\lim a_n=0\}\) of all rational sequences convergent to \(0\) is a subset of \(M\), formally \(I\subseteq R\).

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References

Bibliography

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