For a sequence a_1, a_2, ... in R^n to be convergent there are (at least) 2 theorems, as follows:(adsbygoogle = window.adsbygoogle || []).push({});

if for all epsilon>0 there exists an M such that when m>M, then |a_m-a|<epsilon

and also:

If u(epsilon) is a function such that u(epsilon)-->0 as epsilon-->0, then

the sequence is convergent if

for all epsilon>0 there exists an M such that when m>M, then |a_m-a|<epsilon

~~~~~~~~~~~~

I can understand this intuitively, because u(epsilon) and epsilon behave similarly .. but how I prove that they are equivalent? Do I simply take the limit of both definitions, and then set them equal? help!

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# Theorems of convergence for sequences?

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