Rational Cauchy sequence/Ring/Null sequences/Ideal/Exercise

Let $C$ be the set all Cauchy sequences in $\mathbb{Q}$.

a) Show that $C$ is a commutative ring with the componentwise addition and multiplication.

b) Show that the subset $N\subseteq C$, consisting of all null sequences is an ideal.

c) Show that $C/N$ is a field.

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