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A solution to the halting problem is an algorithm H that computes the following mapping:To be more precise, it is proven that /universal/ halt deciders don't exist. There is nothing stopping us writing a halt decider that works correctly for /some/ inputs.
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly
And it is proven that halt deciders don't exist
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