4. Prove that there exist more real numbers between zero and one than there are

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4. Prove that there exist more real numbers between zero and one than there are integers. 5. Any Turing machine may have an infinite number of different outputs. (One for each input.) Exactly how many machines do? Suppose we had a list of triples where z is the output of Turing machine k on input x. How many items would be on our list? 7. Consider the machine which receives x as input and simulates Turing machine number x in our standard enumeration until it wishes to halt. This machine then adds one to the result and halts. In other words, we are examining the machine: M(x) = Mx(x) + 1. What happens when this machine receives its own index as input?

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For question 4, you need this http://lofi.forum.physorg.com/The-Are-More-Integers-Than-Real-Numbers_22743.html Please rate :)

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