Why is this proof incorrect? (limit product is product of the limits) – math.stackexchange.com

I want to prove that if: $$\lim_{n \to \infty}s_n = L_1, \lim_{n \to \infty}t_n = L_2$$ then $$\lim_{n \to \infty}(s_n t_n) = L_1L_2$$ Wrong (?) proof: Fix $\epsilon >0$. By definition, there ...

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