Sequence of minors of the modules

Question

I want to prove the following fact:

If a real sequence $(x_n)_n$ converges to $0$, then the sequence $(y_n)_n$ defined by $y_n=\min \{ |x_1|,|x_2|,\dots , |x_n| \}$ also converges to $0$.

I have tried to use the fact that if a sequence converges to $0$ then there is a finite number of terms outside of $(- \epsilon, \epsilon), \ \forall \epsilon >0$, but I don't know if this is the best way. Can someone help me, please?

Answer 1

Hint : use the fact that for every $n$, we have $0 \leq y_n \leq \lvert x_n \rvert$.