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Lemma: Convergent Rational Sequences With Limit \(0\) Are a Subgroup of Rational Cauchy Sequences With Respect To Addition
Let \((M, + )\) be the commutative group of 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 subgroup of \(M\), formally \[(I, + )\subseteq (M, + ).\]
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3
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References
Bibliography
- Kramer Jürg, von Pippich, Anna-Maria: "Von den natürlichen Zahlen zu den Quaternionen", Springer-Spektrum, 2013
