Posted by Benjamin Johnston on 2000-09-23
> What is the mathematical function that maps the set of all natural number > to the cartesian product of the set of all natural numbers. I know that it > exists, but I haven't been able to think of it on my own..... You'd just need a function that goes like this; 0 1 3 6 10 2 4 7 11 5 8 12 9 13 14 0->(0,0), 1->(1,0), 2->(0,1), 3->(2,0), 4->(1,1), 5->(0,2), 6->(3,0),.... To be more formal... that would be harder.... it looks like there's triangular numbers in there.... I'll take a go at it.... if G is the function that maps (x,y) to (sum from i=0 to (x+y) of i) + y then F : N -> N x N is the inverse of G. You could probably express F directly (instead of as the inverse of some other function), by using triangular numbers. I'll have to think about F a bit more, but I don't think it would be too hard if you use a "sigma". If you come up with a solution, post it. -Benjamin Johnston s355171@xxxxxxx.xx.xxx.xx (when I've said "sum from .... to .... of ....", I'm meaning a sigma notation kind of thing)
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