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## Main Question or Discussion Point

The general definition for a sequence to diverge is the negation of what it means for a sequence to converge: ##\forall L\in\mathbb{R}~\exists\epsilon>0~\forall N\in\mathbb{N}~\exists n\ge N##, ##|a_n - L| \ge \epsilon##. How does this general definition of divergence relate to the definition of a sequence diverging specifically to infinity, which is ##\forall M \in \mathbb{R} ~ \exists N \in \mathbb{N} \forall n \ge N##, ##a_n > M##?