One of the major triumphs of early twentieth-century logic was the formulation of several (equivalent) precise definitions for what it means to say that a function f:ℕ→ℕ is computable. In our current age, many people have an intuitive sense of this concept through experience with computer programming. However, it is challenging to turn such intuition into a concise formal mathematical treatment that is susceptible to a rigorous mathematical analysis.
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