Recall the Squeeze Theorem Suppose that for all n xn yn zn I

Recall the Squeeze Theorem:

Suppose that for all n, x_n y_n z_n. If (x_n) and (z_n) both converge to L R, then (y_n) also converges to L.

Louis Reasoner gives the following proof:

Using limit comparison theorems, since x_n y_n, for all n, then lim x_n lim y_n, and so L lim y_n. Similarly, since y_n z_n, for all n, then lim y_n lim z_n, so lim y_n L. Putting the 2 inequalities together, lim y_n = L, Q.E.D.

What’s wrong with this proof?

Solution

Nothing is wrong. It is correct.