define cauchy sequence
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sequence of real numbers {an} is a Cauchy sequence provided that for every ϵ > 0, there is a natural number N so that when n, m ≥ N, we have that. ... Given any real number ϵ > 0, there is an N(ϵ) so that 10−N(ϵ) < ϵ. Thus we have shown that the sequence {tn(x)} is a Cauchy sequence
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sequence of real numbers {an} is a Cauchy sequence provided that for every ϵ > 0, there is a natural number N so that when n, m ≥ N, we have that. ... Given any real number ϵ > 0, there is an N(ϵ) so that 10−N(ϵ) < ϵ. Thus we have shown that the sequence {tn(x)} is a Cauchy sequence
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