Vercongence?

Calculus Level 3

Consider the following strange definition:

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

Which of the following conclusions is wrong?


Inspired by Abbot's Understanding Analysis
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