Suppose { a_n } converges to A. Choose e > 0, THere is a positive integer N such that, if(adsbygoogle = window.adsbygoogle || []).push({});

n, m >= N , then A - e < a_n < A + e and A - e < a_m < A + e

Thus for all n, m >= N we find a_n ∈ ( A - e , A + e ) and

a_m ∈ ( A - e , A +e ) . the set ( A - e, A +e ) is an interval of length 2e , hence the difference between a_n, and a_m is less then 2e

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i dont understand how they get 2e , ( a set of length 2e ?? )

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# Help with this Cauchy Proof

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