Worried about going over his storage limit, Connor monitored the number of undeleted voicemail messages stored on his phone each
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Recall that a sequence 
is convergent if and only if is also a Cauchy sequence, which means to say that for any 
, we can find a sufficiently large 
for which
whenever both
and 
exceed .
But this never happens if we choose
and 
; under these conditions, we have
Therefore is not a Cauchy sequence and hence does not converge.
whenever both
But this never happens if we choose
Therefore
