Comments about the halting problem
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If you are interested in learning about the importance of halting problem, I would suggest reading (at least parts of) Gödel, Escher, Bach, a wonderful book that won the Pulitzer Prize. GEB discusses so many different ideas and areas of human thought and creativity that it is impossible to really summarize, but one of the motifs is "What does Computability Mean? What problems are 'uncomputable'?"
