Calculus Theory: Decidability, Halting Problem

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This lecture delves into the concepts of calculability, decidability, and the Halting Problem. It explores the questions that computational theory seeks to answer, such as what can be solved with an algorithm and the nature of decision problems. The lecture discusses the countability of pairs of positive integers, the enumeration of programs, and the uncountability of functions. It also explains the distinction between decidable and undecidable problems, using examples to illustrate these concepts. The demonstration of self-reference as a tool to showcase the undecidability of the Halting Problem is a key highlight of the lecture.

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