It is known that "the integers under addition" form a group, that is (Z,+). I have always wondered how to actually proof that (Z,+) is a group? Definitions for a group from wikipedia: http://en.wikipedia.org/wiki/Group_(mathematics)#Basic_definitions I'm especially interested in two things: 1) Why does the associative law hold for (Z,+), that is a+(b+c) = (a+b)+c for a,b,c in Z. And moreover: 2) Why is closure fulfilled? That is, if a and b in Z, then a+b is also in Z.