MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

5 m; added 2 characters in body

Perform the usual addiction of natural numbers in decimal representation, but let's forget about carrying the extra digit in the next column. So e.g. 356+75=321 and 123+987=0 . Note: This is very particular, as it is linked to base 10; but makes the example very directconcrete and quick. The poster asked for an example, and in my view, for an example, simplicity is prior to generality.

Post Undeleted by Pietro Majer
4 deleted 160 characters in body

Perform the usual addiction of natural numbers in decimal representation, but let's forget about carrying the extra digit in the next column. So e.g. 356+75=321 and 123+987=0 You may use m-base expansion as well, of course (m=2 is the "nim sum" in the third answer). These group structures on N of course are just Note: This is very particularcases of the ones described above, as it linked to base 10; but maybe they appear more natural in that they take a bit into account the nature of makes the natural numbers (that isexample very direct. The poster asked for an example, and for an example simplicity is prior to be honest, please give me a +1).generality.

Post Deleted by Pietro Majer
3 added 1 characters in body
2 added 156 characters in body
1