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I know that computability is the proof of existence of an algorithm to solve a particular function in a infinite time but I can not understand how to decide that it is computable.

  • How can we know that that this is computable, if pi is infinite and checking all digits would require infinite time? This is not about pi being infinite and all numbers will occur at some point etc.

    f(n) := { 
              1, if Decimal number n exists somewhere in pi
              0, else
            }
    

This was an example of a computable function, although I do not understand this one either, the question is not about that at all, I want to know sources and methods and tips about how can I understand that

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