After a night of reading lambda calculus things on the net i found out that lambda calculus is about math and turing complete,not about predecessors and fractions
there are two directions:to out and to in
to out,we can prove the turing completeness of this thing by making a [huge] turing machine using this stuff,accepting a list of instructions,passing lists,and returning the answer(loops?Y combinator!)
to in there is some thing called ski,skk and iota combinator
anyways telling students to do predessecor is a good method of teaching
this will be the [very] hard math problems ill do to avoid boredom in school two days after today
Oh yes, of course, sorry, I thought that was clear. Church numerals are just the best exercise I know in writing functions purely functionally, plus it's kind of amazing that you can invent arithmetic given nothing but lambda and call. It's the 21st Century equivalent of starting a fire by rubbing two sticks together.
We functional programming fans think it's a little unfair that everyone (including us) calls it "Turing completeness" when Church had a formalism for what functions are computable slightly before Turing got there; Church was Turing's thesis advisor when the latter got around to getting a PhD. :~)