> The halting problem may have been mathematically disproven by finding one highly convoluted counter example, but it's more significant failing is that it is i

> The halting problem may have been mathematically disproven by finding one highly convoluted counter example, but it's more significant failing is that it is infinite and thus can not be implemented on a machine with finite limits. I agree that would be a better way to teach it, but Turing machines have infinitely-long tapes -- the really unexpected result is that you couldn't solve the Halting Problem even if you had (countably) infinite tape and infinite time to do it. The same probably holds for uncountably-infinite tapes too (the "burrito" counterexample still breaks it), though you can't really address a tape that long for obvious reasons.