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Math Help - Real Analysis - Squeeze Theorem

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    Real Analysis - Squeeze Theorem

    Show that if xn <= yn <= zn for all n Є N, and if lim xn = lim zn = b, then lim yn = b.
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    Quote Originally Posted by ajj86 View Post
    Show that if xn <= yn <= zn for all n Є N, and if lim xn = lim zn = b, then lim yn = b.
    Let \epsilon > 0 be given. since \lim x_n = b, there exists an N_1 \in \mathbb{N} such that n > N_1 implies |x_n - b| < \epsilon. Similarly, there is N_2 \in \mathbb{N} such that |z_n - b| < \epsilon whenever n > N_2.

    now, take N = \text{max} \{ N_1,N_2 \}, and assume n > N. Note that since x_n \le y_n \le z_n, we have x_n - b \le y_n - b \le z_n - b....


    can you finish?
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