document.write( "Question 517589: Prove that all subsequences of a Cauchy sequence is cauchy \n" ); document.write( "

Algebra.Com's Answer #344843 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "Hope this helps. There may be something here: \n" ); document.write( "\">MATH 138BH that will help you. Good luck.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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