What will happen if the choice of $N$ in the definition of convergence doesn't depend on epsilon ?
2026-03-27 08:57:14.1774601834
About the definition of convergence of a sequence.
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It means that from $N$, all the terms of the sequence are equal to the limit $\ell$ ! Indeed, forall $n \geqslant N$, you can make $\varepsilon \rightarrow 0$, which leads to $u_n = \ell$ forall $n \geqslant N$ (with usual notations).