I am looking for two infinite subsets of the natural numbers ( ), that any n natural numbers can be written in a unique way as a sum of an elemenet from each sets: n=a+b (where .

Any help would be appreciated!

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- Nov 3rd 2010, 12:41 PMdougUnique sum for all natural numbers
I am looking for two infinite subsets of the natural numbers ( ), that any n natural numbers can be written in a unique way as a sum of an elemenet from each sets: n=a+b (where .

Any help would be appreciated! - Nov 3rd 2010, 02:34 PMOpalg
You could for example take A to be the set of all natural numbers whose decimal expression has a 0 in all the even-numbered places (counting from the right), and B to be the set of all natural numbers whose decimal expression has a 0 in all the odd-numbered places.

So for example the number n = 31416265 can be written 1010205 + 30406060 (with the first of those numbers being in A and the second one being in B).