Recall the Squeeze Theorem: Suppose that for all n, xn yn zn. If (xn) and (zn) both converge to L R, then (yn) also converges to L. Louis Reasoner gives the following proof: Using limit comparison theorems, since xn yn, for all n, then lim xn lim yn, and so L lim yn. Similarly, since yn zn, for all n, then lim yn lim zn, so lim yn L. Putting the 2 inequalities together, lim yn = L, Q.E.D. What’s wrong with this proof? Solution Nothing is wrong. It is correct..

1. Recall the Squeeze Theorem:
Suppose that for all n, xn yn zn. If (xn) and (zn) both converge to L R, then (yn) also converges
to L.
Louis Reasoner gives the following proof:
Using limit comparison theorems, since xn yn, for all n, then lim xn lim yn, and so L lim yn.
Similarly, since yn zn, for all n, then lim yn lim zn, so lim yn L. Putting the 2 inequalities
together, lim yn = L, Q.E.D.
What’s wrong with this proof?
Solution
Nothing is wrong. It is correct.