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3 . 6 In Theorem 3 . 2 1 , we showed that a language is Turing - recognizable iff some enu - merator enumerates

3.6 In Theorem 3.21, we showed that a language is Turing-recognizable iff some enu-
merator enumerates it. Why didn't we use the following simpler algorithm for the
forward direction of the proof? As before, s1,s2,dots is a list of all strings in **.
E= "Ignore the input.
Repeat the following for i=1,2,3,dots.
Run M on si.
If it accepts, print out si."
3.21 Let c1xn+c2xn-1+cdots+cnx+cn+1 be a polynomial with a root at x=x0. Let
cmax be the largest absolute value of a ci. Show that
|x0|(n+1)cmax|c1|
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