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Lambda the Ultimate Set ComprehensionFunctions are sometimes defined in terms of sets as the binary relation that relates each x to (f x), but this seems fundamentally wrong to me, because sets bear an immediate resemblance to lambda expressions.
Etc. So I think the proper way to do things is to equate sets and predicates and to define a set as a function that returns a Boolean. I thought I had come up with this but it turns out Church had thought the same thing (calling this function the characteristic function IIRC) and it is also called the indicator function. Given all this, can somebody tell me why mathematicians keep making a distinction between sets, predicates and their indicator functions (other than historcial reasons)? Why not simply equate sets, predicates and their characteristic functions? By xyzzy at 20060129 17:38  LtU Forum  previous forum topic  next forum topic  other blogs  25995 reads

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