Section 4: changed intuition for uncomputable functions, added exercise 1.5#1
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mbpereira49 wants to merge 1 commit intowburke1990:masterfrom
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Section 4: changed intuition for uncomputable functions, added exercise 1.5#1mbpereira49 wants to merge 1 commit intowburke1990:masterfrom
mbpereira49 wants to merge 1 commit intowburke1990:masterfrom
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The intuition for why uncomputable functions should exist didn't seem exactly right; the fact that there are infinitely many inputs vs. the finiteness of NAND-TM programs isn't the reason we can't compute some, since finite NAND-TM programs can still capture a restricted, but infinite, class of functions. Also added an exercise to emphasize how the uncountability of functions is why diagonalization works.