> Mathematically, dividing two integers yields a real not true. if you define 'divide' as inverse multiplication over the reals then that is closer to being tr

> Mathematically, dividing two integers yields a real not true. if you define 'divide' as inverse multiplication over the reals then that is closer to being true (zero is an integer, dividing an integer by zero doesn't yield a real). in that case every real can be expressed as n = a/b where a and b are integers and b != 0 then yes n is a real. But 'divide' could just as well be defined along the lines of divisibility in number theory (the study of integers) where every integer can be expressed as n = q*b + r, where n,q,b,r are all integers and r >= 0 > b. then you could say that n divide b = q, with r as remainder, and n mod b = r. These are my preferred definition of mod and integer division.