## Cauchy Sequences in Euclidean Space

Theorem

Ifis a Cauchy sequence in Euclidean- space

then each of the sequencesis a Cauchy sequence.

Proof

LetSinceis Cauchy, there existssuch that for

Hence,and each of the sequencesis Cauchy.

Theorem

Ifis a Cauchy sequence in Euclidean- space

then each of the sequencesis a Cauchy sequence.

Proof

LetSinceis Cauchy, there existssuch that for

Hence,and each of the sequencesis Cauchy.