Vercongence?

Calculus Level 3

Consider the following strange definition:

We say a sequence (xn)(x_n) verconges to xx if there exist an ϵ>0\epsilon>0 such that for all NNN\in \Bbb{N}, nN    xnx<ϵn\ge N \implies |x_n-x|<\epsilon

Which of the following conclusions is wrong?


Inspired by Abbot's Understanding Analysis
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