In fact, my motivation was the way that Frege defined the natural numbers:
>From the paper: "We shall define an algorithm analogously to the way that Gottlob Frege defined a natural number. Basically Frege says that that the number 42 is the equivalence class of all sets of size 42. He looks at the set of all finite sets and makes an equivalence relation. Two finite sets are equivalent if there is a one-to-one onto function from one set to the other. The set of all equivalence classes under this equivalence relation forms the set of natural numbers. For us, an algorithm is an equivalence class of programs. Two programs are part of the same equivalence class if they are ``essentially'' the same." One might say that Frege's defintion is circular because he would say that "42 is the equivalence relation of all sets of size 42". But he is not really doing that. Frege is defining the SET of natural numbers. Not one particular natural number. So too, I am defining the SET (actually category) of algorithms. Not one particular algorithm. All the best, Noson --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
