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You would need to show how to use length to implement halt and that is the part you will not be able to do. If you did, then yes, length would not be computable

You would need to show how to use length to implement halt and that is the part you will not be able to do. If you did, then yes, length would not be computable. Reductions in complexity theory work like this. An explicit algorithm invokes a black box and this shows that either the black box does not exist or you can solve the original problem. Typically you care about the complexity of the reduction to establish that the problem is inside a given complexity class (e.g. NP complete).

constantcrying 4y ago
You didn't answer the question. The statement is obviously false by the way, as you can see in the article where the author does exactly that. You rephrasing the statement to make it true, is just ignoring the point. I would encourage you to engage in some studying of reading comprehension. It is an important skill in mathematics and related disciplines.
- dellamonica 4y ago
  You are the one failing basic logic. Your statement is logically true but vacuous because your conditional is false! If <absurd condition> then <some even more absurd thing> is a perfectly sound logic statement. I explained already how reduction proofs work. Why don't you read on that instead of posting non sense?
  - constantcrying 4y ago
    You are arguing against a completely fictional point which you have made up in your head. None of what you are saying is even remotely a response to my criticism. You can tell me that I failed basic logic all you want, but your reading comprehension sucks so much that you still have not been able to figure out what I am even talking about. I think you still haven't understood that I never said his intended reasoning was wrong. But that his statement as written is plainly false. There is no argument against the logic by me, so the fact that you keep going on and on about "logic" just shows that you haven't even understood yet that nobody disagrees with the logic. I know how a proof by contradiction works, you do not seem to want to understand that "computes" and "implements" are different words. And that by repeatedly arguing that the authors reasoning is valid if you change the statement to make it correct you are proving my point again and again.
    - dellamonica 4y ago
      I'll bite, what is the false statement that you keep alluding to? Because the vacuous "if" statement that you claimed to be false is absolutely a truth in logic. Compute and implements are different words, nobody is arguing that. To me and everyone literate in math/cs, the role of "implementing" here is in the proof by reduction, which in the case of computability is used to establish by contradiction that some other problem is not computable by reducing a known incompatible problem to it. Just like when you show an algorithmic implementation that maps any SAT instance to another problem using a polynomial time algorithm, then it follows that this other problem is NP-complete.
      - constantcrying 4y ago
        >I'll bite, what is the false statement that you keep alluding to? Read the first post. You should have done that before responding I think.
        dellamonica 4y ago
        Right... have a good day.

constantcrying 4y ago

You didn't answer the question. The statement is obviously false by the way, as you can see in the article where the author does exactly that. You rephrasing the statement to make it true, is just ignoring the point. I would encourage you to engage in some studying of reading comprehension. It is an important skill in mathematics and related disciplines.

dellamonica 4y ago
You are the one failing basic logic. Your statement is logically true but vacuous because your conditional is false! If <absurd condition> then <some even more absurd thing> is a perfectly sound logic statement. I explained already how reduction proofs work. Why don't you read on that instead of posting non sense?
- constantcrying 4y ago
  You are arguing against a completely fictional point which you have made up in your head. None of what you are saying is even remotely a response to my criticism. You can tell me that I failed basic logic all you want, but your reading comprehension sucks so much that you still have not been able to figure out what I am even talking about. I think you still haven't understood that I never said his intended reasoning was wrong. But that his statement as written is plainly false. There is no argument against the logic by me, so the fact that you keep going on and on about "logic" just shows that you haven't even understood yet that nobody disagrees with the logic. I know how a proof by contradiction works, you do not seem to want to understand that "computes" and "implements" are different words. And that by repeatedly arguing that the authors reasoning is valid if you change the statement to make it correct you are proving my point again and again.
  - dellamonica 4y ago
    I'll bite, what is the false statement that you keep alluding to? Because the vacuous "if" statement that you claimed to be false is absolutely a truth in logic. Compute and implements are different words, nobody is arguing that. To me and everyone literate in math/cs, the role of "implementing" here is in the proof by reduction, which in the case of computability is used to establish by contradiction that some other problem is not computable by reducing a known incompatible problem to it. Just like when you show an algorithmic implementation that maps any SAT instance to another problem using a polynomial time algorithm, then it follows that this other problem is NP-complete.
    - constantcrying 4y ago
      >I'll bite, what is the false statement that you keep alluding to? Read the first post. You should have done that before responding I think.
      - dellamonica 4y ago
        Right... have a good day.