This one is from "A Programming Approach to Computability" , by A.J. Kfoury, Robert Moll, & Michael Arbib (1982), on page 77. How do they get all that out of [itex]\sigma \leq \mu [/itex] ??? [This section continues as follows: Are these guys kidding, or what? In every previous instance that I have found in this book, they used [itex]\leq[/itex] to represent "less than or equal to". Here, I guess maybe they are using it to signify "is a subset of". But even if that's the case, how do they conclude (in the second paragraph), that "if [itex]\sigma(y)[/itex] is defined, it equals [itex]\mu(y)[/itex]"? I can't say that I like this stuff, but I'm determined to understand it if I can, so any suggestions will be appreciated.