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Here's one thing i noticed. In Elementary Real Analysis, when we say that a sequence $s_n$ converges to a point $s$, we first set an $\epsilon > 0$ such that for large $N \in \mathbb{N} $ $| s_n - s | < \epsilon. $

Why don't we set up the convergence of loss functions that way? i. e. We don't have a hyperparameterhyperparameter $\epsilon$ to ensure our convergence.

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