What is the proof that the limit of a Cauchy sequence of integers is an integer?

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prove that limit of a cuachy sequence of integers is an integer
 
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First think about what would have to be true for a sequence of integers to be a Cauchy sequence - then do some work and present it here.
 
a sequence of integers which is cauchy is eventually constant. is the constant term the limit?
 
Try to show "a sequence of integers which is cauchy is eventually constant" and the answer for the limit will become apparent.
 
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