Iam working through Spivak calculus now. The book defines natural numbers as of form N=1,2,3,4.... Iam able to prove that every natural number is either odd or even. How can I extend to Z, integers? In one of the problems, Spivak says we can write any integer of the form 3n, 3n+1, 3n+2.( n is integer) He gives as hint to the problem.But am not convinced, In general how can we prove that if m is a natural number, n is an integer, then any integer can be expressed of the form km, km+1, km+2, km+3,.....,km+(k-1)?