SOLUTION: Prove that all subsequences of a Cauchy sequence is cauchy

Question 517589: Prove that all subsequences of a Cauchy sequence is cauchy
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you can show that all subsequences of a Cauchy sequence are convergent then you can use: Every convergent sequence (with limit s, say) is a Cauchy sequence, since, given any real number ε > 0, beyond some fixed point, every term of sequence is within distance ε/2 of s, so any two terms of the sequence are within distance ε of each other.

Hope this helps. There may be something here: MATH 138BH that will help you. Good luck.

John

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