We have a serious problem with how we have been teaching computability theory, a central component of the ACM/IEEE computer science curriculum.
Let me explain. For a fair number of years, I taught a computability course. Following the standard curriculum (such as described by Hopcroft and Ullman14), and in concert with my colleagues in the field, I made claims on countless occasions that one model of computation is more powerful than another or that two models have the same power of computation. In some cases the argument appealed to ordinary set inclusion, while at other times it involved a notion of simulation via encodings. Imagine my chagrin when I came to realize these two methods of comparison are in fact incompatible!
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