If we post a program and try to construct a Turing machine to solve it but are not successful, does this prove that no Turing machine exists? If not, why would prove this?
Fill in the blank(s) with the appropriate word(s).
If we pose a problem and try to construct a Turing machine to solve it but are not successful, that alone does not prove that no Turing machine exists. What we must do is actually prove that no one can ever find such a Turing machine—that it is not possible for a Turing machine to exist that solves this problem.
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