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    Quote Originally Posted by flower3 View Post

    We may as well assume the sequence is not bounded above.
    \left( {\exists x_{n_1 } } \right)\left[ {x_{n_1 }  > \max \left\{ {1,x_1 } \right\}} \right].
    \left( {\forall j > 1} \right)\left( {\exists x_{n_j } } \right)\left[ {x_{n_j }  > \max \left\{ {j,x_{n_{j - 1} } } \right\}} \right].
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