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Vor
Vor
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By your definition, all problems with defined finite solutions are effectively solvable. Just set the algorithm A(P_i)$A(P_i)$ to be "output x"$x$", where x$x$ is the solution to P_i$P_i$. For example, the algorithm you would use to solve the instance of IS_PRIME on 37 is "output yes."

Now the algorithm picking algorithms to apply is uncomputable, but you said you didn't care about that.

By your definition, all problems with defined finite solutions are effectively solvable. Just set the algorithm A(P_i) to be "output x", where x is the solution to P_i. For example, the algorithm you would use to solve the instance of IS_PRIME on 37 is "output yes."

Now the algorithm picking algorithms to apply is uncomputable, but you said you didn't care about that.

By your definition, all problems with defined finite solutions are effectively solvable. Just set the algorithm $A(P_i)$ to be "output $x$", where $x$ is the solution to $P_i$. For example, the algorithm you would use to solve the instance of IS_PRIME on 37 is "output yes."

Now the algorithm picking algorithms to apply is uncomputable, but you said you didn't care about that.

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Xerxes
Xerxes
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By your definition, all problems with defined finite solutions are effectively solvable. Just set the algorithm A(P_i) to be "output x", where x is the solution to P_i. For example, the algorithm you would use to solve the instance of IS_PRIME on 37 is "output yes."

Now the algorithm picking algorithms to apply is uncomputable, but you said you didn't care about that.