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Computer Science

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  • $\begingroup$ I am a bit confused when you say all programs $z$ isn't it true that if $P$ is a program then $z = \#(P)$ and therefore every program has a unique $z$ number? $\endgroup$ Commented Sep 4, 2013 at 16:15
  • $\begingroup$ Your set $B$ includes a program $z$ iff $z$ halts on some input. On the other hand, $P$ is a predicate, not a program. Since $P$ is computable, it is computed by some program. $\endgroup$ Commented Sep 4, 2013 at 16:28
  • $\begingroup$ Perhaps you would like to review basic logic and basic set theory first, as well as mathematical English. $\endgroup$ Commented Sep 4, 2013 at 16:29
  • $\begingroup$ Oops... I understand your remark and thank you for your explanation, but I did a poor letter choice, I didn't mean to refer to the predicate mentioned in my question, I was just considering a generic program $P$. $\endgroup$ Commented Sep 4, 2013 at 16:31