Convergent Sequence is Cauchy Sequence
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Theorem
Metric Space
Let $M = \struct {A, d}$ be a metric space.
Every convergent sequence in $M$ is a Cauchy sequence.
Normed Division Ring
Let $\struct {R, \norm {\,\cdot\,}} $ be a normed division ring.
Every convergent sequence in $R$ is a Cauchy sequence.
Normed Vector Space
Let $\struct{X, \norm{\,\cdot\,} }$ be a normed vector space.
Every convergent sequence in $X$ is a Cauchy sequence.