If sequence is divergent then its every subsequence must be
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A sequence is divergent if and only if for every l ∈ R there is some subsequence of (an) not convergent to l. ... If all subsequences of (an) were bounded then (an) would itself be bounded, in which case a divergent subsequence of (an) must contain two subsequences convergent to different limits.
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A sequence is divergent if one only if for every 1 € R there is some subsequence of (an) not convergent to 1...if all subsequence of (an) were bounded then (an) would itself be bounded, in which case a divergent subsequence of (an) must contain two subsequence convergent to different limits.
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