f(x) = pi – 2^x Turing computable?
Hello everyone,
I have a question for anyone who is knowledgeable about computer science or has studied computer science.
Given a function f: R -> R with f(x) = pi – 2^x.
In the lecture, the question arose as to whether this function is computable. My reasoning was that this might not be the case, since (Turing) computability is usually defined only for mappings from N to N. On the other hand, one could perhaps calculate the function value approximately, similar to how "real" computers do it. However, since we are dealing with theoretical computer science, I assume that the function is formally considered uncomputable because pi cannot be calculated exactly in finite time.
I would be very grateful for answers and suggestions!
Many greetings
(1 votes)
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Right. The function cannot be predictable, because an irrational number cannot serve as an input of a TM. On the other hand, every f(x) if x rational is in turn irrational and thus impossible to calculate turbine.